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Frequency domain equalization and multiuser detection techniques for DS-UWB systems Kaligineedi, Praveen 2006

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Frequency Domain Equalization and Mul t iuser Detection Techniques for D S - U W B Systems b y Praveen Kaligineedi B . T e c h , I n d i a n I n s t i t u t e o f T e c h n o l o g y , K a n p u r , 2 0 0 4 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M a s t e r o f A p p l i e d S c i e n c e i n T h e F a c u l t y o f G r a d u a t e S t u d i e s ( E l e c t r i c a l a n d C o m p u t e r E n g i n e e r i n g ) T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a A u g u s t 2 0 0 6 © P r a v e e n K a l i g i n e e d i , 2 0 0 6 Abstract Ultra wideband (UWB) is an emerging technique for high data rate transmissions over short distances. Direct sequence (DS)-UWB approach is one of the two com-peting high data rate U W B standards, along with multiband orthogonal frequency division multiplexing ( O F D M ) . One of the major challenges in a D S - U W B receiver design is the intersymbol interference (ISI). Several time domain equalization schemes to eliminate ISI have been proposed in the literature for D S - U W B systems. However, for long dispersive channels, these time domain equalization schemes require very high computational complexity in order to achieve desired bit error performance. Frequency domain equalization schemes which give better performance than time do-main equalization schemes for single carrier systems, over highly dispersive channels, are well known in the literature. In this thesis, performances of frequency domain minimum mean square error (MMSE) linear, decision feedback and iterative decision feedback equalizers are studied for uncoded single user B P S K and 4BOK D S - U W B systems. We compare bit error rate (BER) performance of various time domain and frequency domain equalization techniques and evaluate their computational complex-ity. We show that the frequency domain equalization techniques can offer better trade off between complexity and performance compared to the time domain equalization techniques for D S - U W B systems. We then consider frequency domain multiuser de-tection techniques for D S - U W B systems. We employ frequency domain successive interference cancelation and parallel interference cancelation schemes combined with frequency domain equalization schemes and study their average B E R performance. We derive low complexity frequency domain M M S E turbo equalization schemes for coded B P S K and 4BOK D S - U W B systems. Soft interference cancelation is used in the multiuser systems to remove multiple access interference (MAI) . The average B E R performance is obtained using simulations. The performance gain due to turbo equalization is shown to be significant, particularly, for D S - U W B systems with lower spreading gain. The improvement in the performance due to turbo detection is found to be very high for multiuser systems. ii T a b l e o f C o n t e n t s A b s t r a c t i i T a b l e o f C o n t e n t s i i i L i s t o f T a b l e s v L i s t o f F i g u r e s v i L i s t o f S y m b o l s v i i i L i s t o f A b b r e v i a t i o n s x i A c k n o w l e d g e m e n t x i i i 1 I n t r o d u c t i o n 1 1.1 D S - U W B vs M B - O F D M 2 1.2 Equalization for D S - U W B systems 3 1.3 S C - F D E 3 1.4 Turbo Equalization 4 1.5 Thesis Outline 5 2 F r e q u e n c y D o m a i n E q u a l i z a t i o n 6 2.1 Introduction 6 2.2 System model 6 2.2.1 Transmitter 6 2.2.2 Channel Model 8 2.2.3 Receiver 9 2.3 Linear M M S E equalization 9 2.4 Iterative M M S E D F E 10 2.5 Symbol based Equalizers 15 i i i 2.5.1 BPSK system 15 2.5.2 4B0K system 18 2.6 Computational Complexity 19 2.7 Simulation Results 20 3 M u l t i u s e r D e t e c t i o n 28 3.1 Introduction 28 3.2 System Model 28 3.3 Successive Interference Cancelation 29 3.4 Parallel Interference Cancelation 31 3.5 Single user 4BOK system 33 3.6 Simulation results 33 4 T u r b o E q u a l i z a t i o n 37 4.1 Introduction 37 4.2 Single User System 38 4.2.1 BPSK System 38 4.2.2 4BOK System 42 4.3 Multiuser System 44 4.3.1 Single user 4BOK system 48 4.4 Simulation Results 49 5 Conc lus ions 56 5.1 Future Work 57 B i b l i o g r a p h y 57 A D e r i v a t i o n of Frequency D o m a i n I tera t ive D e c i s i o n Feedback E q u a l -izer 62 B D e r i v a t i o n of Frequency d o m a i n M M S E T u r b o E q u a l i z e r 65 i v L i s t of Tables 2.1 Gray coding for 4 B O K D S - U W B system 18 2.2 Computational complexity of the receiver per output symbol for B P S K system 20 2.3 Complexity of equalizer design per block for B P S K system 20 2.4 Computational complexity of the receiver per output symbol for B P S K system with Na — 6 27 2.5 Complexity of equalizer design per block for B P S K system with Ns = 6 27 3.1 Ternary codes used for the 4 users 33 v L i s t o f F i g u r e s 1.1 Comparison of O F D M and S C - F D E system 4 2.1 Transmitter and channel for single user D S - U W B system 9 2.2 Frequency domain M M S E equalizer for a M B O K D S - U W B system . . 11 2.3 Decision device for a M B O K system . 12 2.4 Iterative frequency Domain M M S E D F E for a M B O K D S - U W B system 13 2.5 Symbol based frequency domain M M S E D F E for a B P S K D S - U W B system 17 2.6 B E R performance of various time domain and frequency domain equal-izers for a B P S K U W B system with spreading factor Ns — 6 22 2.7 B E R performance of various frequency domain equalizers for a B P S K D S - U W B system with spreading factor Ns = 12 23 2.8 B E R performance of frequency domain equalizers for a 4 B O K DS-U W B system with spreading factor Ns — 12 24 2.9 B E R performance of frequency domain equalizers for a 4 B O K DS-U W B system with spreading factor Ns = 6 25 2.10 B E R performance of F D IT D F E using chip inter leaver and F D IT D F E without using chip interleaver for a 4 B O K D S - U W B system with spreading factor Ns = 6 26 3.1 Transmitter and channel for a multiuser D S - U W B system 29 3.2 Successive interference cancelation 30 3.3 Parallel interference cancelation 32 3.4 B E R performance of receiver employing successive interference cance-lation for a 4-user B P S K D S - U W B system with spreading factor Ns = 12 34 3.5 B E R performance of receiver employing parallel interference cancela-tion for a 4-user B P S K D S - U W B system with spreading factor Ns — 12 35 v i 3.6 BER performance of receiver employing multiuser detection techniques for a single user 4BOK DS-UWB system with spreading factor Ns = 6 36 4.1 Transmitter and channel for single user coded DS-UWB system . . . 38 4.2 Receiver for single user coded DS-UWB system 39 4.3 Frequency domain SISO equalizer for single user coded MBOK DS-UWB system 39 4.4 System model for multiuser coded DS-UWB system 45 4.5 Receiver for multiuser coded DS-UWB system 46 4.6 BER performance of frequency domain turbo equalizers for a BPSK DS-UWB system with spreading factor Ns = 6 51 4.7 BER performance of frequency domain turbo equalizers for a BPSK DS-UWB system with spreading factor Ns = 12 52 4.8 BER performance of frequency domain turbo equalizers for a 4B0K DS-UWB system with spreading factor Ns = 6 53 4.9 BER performance of frequency domain turbo equalizers for a 4-user BPSK DS-UWB system with spreading factor Ns = 12 54 4.10 BER performance of frequency domain turbo equalizers for a 4BOK DS-UWB system with spreading factor -/Vs = 6, treating it as a 2-user BPSK DS-UWB system 55 vii L i s t o f S y m b o l s M' : constellation size M : number of symbols in a data block N S : spreading factor C : set of bi-orthogonal codes p(t) : transmitted pulse shape cL[-] : bi-orthogonal code transmitted during ith symbol period s'[] : block chip sequence obtained at the transmitter after spreading and chip interleaving Lp : length of prefix sm[-} : mth block chip sequence obtained at the transmitter after adding prefix x(t) : transmitted signal hp(t) : continuous time passband channel impulse response h(t) : continuous time baseband channel impulse response fc : carrier frequency ai : multipath gain 77 : multipath delay h[] : discrete time channel impulse response Ls : length of discrete channel impulse response h[-] z(t) : continuous time additive white Gaussian noise z[-] : discrete time additive white Gaussian noise Nq : power spectral density of additive Gaussian noise 1J2 : noise variance rm(t) : continuous time received signal corresponding to data block m rm[-] : discrete time received signal corresponding to data block m S(n) : discrete Fourier transform of s[k] Z(n) : discrete Fourier transform of z[k] H(n) : discrete Fourier transform of h[k] v i i i Y(n) : frequency domain output of the forward filter y[-] : inverse discrete Fourier transform of Y(n) YQ(n) : frequency domain output of the forward filter at the qth iteration yq[] : inverse discrete Fourier transform of Yq(n) E(-) : expected value operator J : metric to be minimized Wq(n) : feedforward filter at qth iteration Bq(n) : feedback filter at qth iteration Jq : metric to be minimized at qth iteration Sq(n) : D F T of the estimated chip sequence after qth iteration c r | : variance of the sequence S(n) v : decision feedback correction factor X : the log normal shadowing factor of the channel impulse h(t) Lc : total number of clusters in UWB channel model Nc : total number of rays in each cluster in UWB channel model L : number of symbols in the cyclic prefix for symbol based MMSE and MMSE-DFE d[-] : transmitted information bits Nfb : number of feedback filter taps in symbol FD-DFE b[-] : feedback filter taps in symbol FD-DFE Nr : number of rake fingers Nj : number of forward filter taps in rake MMSE and rake MMSE-DFE receivers Nj, : number of feedback filter taps in rake MMSE-DFE receiver P : total number of iterations for iterative D F E equalizer U : number of users du[-] : uth user data sequence Au : amplitude of user u at the receiver hu(t) : continuous time channel impulse response of user u hu[-] : discrete time channel impulse response of user u s'u[] : uth user block chip sequence obtained at the transmitter after spreading and chip interleaving su[-} : uth user block chip sequence obtained at the transmitter after adding prefix xu(t) : transmitted signal of user u Su(n) : discrete Fourier transform of su[k] ix c r | u : v a r i a n c e o f t h e s e q u e n c e Su(n) Hu(n) : d i s c r e t e F o u r i e r t r a n s f o r m o f hu[k\ Xu : t h e l o g n o r m a l s h a d o w i n g f a c t o r o f t h e c h a n n e l i m p u l s e hu{t) Wp'Q(n) : f e e d f o r w a r d filter a t qth e q u a l i z a t i o n i t e r a t i o n a n d pth P I C i t e r a t i o n Bp'q(n) : f e e d b a c k f i l t e r a t qth e q u a l i z a t i o n i t e r a t i o n a n d pttl P I C i t e r a t i o n dc[-] : u n i n t e r l e a v e d c o d e d c h a n n e l b i t s d°[-] : i n t e r l e a v e d c o d e d c h a n n e l b i t s L c ( - ) : l o g l i k e l i h o o d r a t i o g e n e r a t e d b y d e c o d e r Le(-) . : l o g l i k e l i h o o d r a t i o g e n e r a t e d b y e q u a l i z e r Y£(ri) : f r e q u e n c y d o m a i n o u t p u t o f t h e f o r w a r d f i l t e r f o r uth u s e r a n d qth i t e r a t i o n 2/2[•] : i n v e r s e d i s c r e t e F o u r i e r t r a n s f o r m o f Y£(n) ainter : v a r i a n c e o f t h e i n t e r f e r e n c e Eb : E n e r g y p e r u s e r s y m b o l x List of Abbreviations A W G N a d d i t i v e w h i t e G a u s s i a n n o i s e B E R b i t e r r o r r a t e B P S K b i n a r y p h a s e s h i f t k e y i n g C D M A c o d e d i v i s i o n m u l t i p l e a c c e s s D E I N T d e i n t e r l e a v e r D F E d e c i s i o n f e e d b a c k e q u a l i z a t i o n D F T d i s c r e t e F o u r i e r t r a n s f o r m D S d i r e c t s e q u e n c e F D f r e q u e n c y d o m a i n F D E f r e q u e n c y d o m a i n e q u a l i z a t i o n F E C f o r w a r d e r r o r c o r r e c t i o n F F T f a s t F o u r i e r t r a n s f o r m F H f r e q u e n c y h o p p i n g I D F T i n v e r s e d i s c r e t e F o u r i e r t r a n s f o r m I F F T i n v e r s e f a s t F o u r i e r t r a n s f o r m I N T i n t e r l e a v e r I R i m p u l s e r a d i o I S I i n t e r s y m b o l i n t e r f e r e n c e I T - D F E i t e r a t i v e d e c i s i o n f e e d b a c k e q u a l i z a t i o n L L R l o g l i k e l i h o o d r a t i o L O S l i n e - o f - s i g h t M A I m u l t i p l e a c c e s s i n t e r f e r e n c e M A P m a x i m u m a p o s t e r i o r i M B m u l t i - b a n d M B O K M - a r y b i o r t h o g o n a l k e y i n g M M S E m i n i m u m m e a n s q u a r e e r r o r N L O S n o n l i n e - o f - s i g h t O F D M o r t h o g o n a l f r e q u e n c y d i v i s i o n m u l t i p l e x i n x i PIC parallel interference cancelation PLL phase locked loop PN pseudorandom noise P/S parallel-to-serial conversion QPSK quaternary phase shift keying RF radio frequency SC single carrier SIC successive interference cancelation SISO soft input soft output SNR signal to noise ratio SOVE soft-output Viterbi equalizer S/P serial-to-parallel conversion UNII unlicensed national information infrastructure UWB ultra wideband WPAN wireless personal area networks x i i A c k n o w l e d g e m e n t F i r s t a n d f o r e m o s t , I w o u l d l i k e t o t h a n k m y s u p e r v i s o r , P r o f V i j a y K . B h a r g a v a , f o r h i s g u i d a n c e , e n c o u r a g e m e n t a n d s u p p o r t . I w o u l d l i k e t o t h a n k C h a n d i k a f o r c l a r i f y i n g a l l m y d o u b t s a n d c o n t r i b u t i n g v a l u a b l e i n s i g h t s t o m y t h e s i s w o r k . I w o u l d l i k e t o t h a n k t h e i n s t r u c t o r s o f m y g r a d u a t e c o u r s e s f o r h e l p i n g m e o b t a i n a g o o d u n d e r s t a n d i n g o f t h e b a s i c c o n c e p t s . F i n a l l y , I w o u l d l i k e t o t h a n k a l l m e m b e r s o f o u r l a b f o r t h e i r s u p p o r t a n d f o r p r o v i d i n g a s t i m u l a t i n g a n d f u n e n v i r o n m e n t i n w h i c h t o l e a r n a n d g r o w . x i i i Chapter 1 Introduction In recent years, rapid development has been observed in wireless personal area net-works (WPAN). WPAN connects devices within reach of an individual, using radio waves. Typical range of a WPAN is 1- 10m. WPAN is used to connect computer and its peripherals such as printer, keyboard, mouse, joystick etc, various personal digital assistants (PDAs) and portable computers without using cables. WPAN uses cheap low power devices. Working group 15 of IEEE L A N / M A N standards committee de-veloped various standards for WPAN. Task group 1 of this working group (802.15) deals with Bluetooth technology. Task group 3 and 4 deal respectively with high data rate and low data rate WPANs based on ultra wideband (UWB) technology. Bluetooth is a standard for short range, low power and low cost wireless commu-nication [2]. Bluetooth devices use unlicensed spectrum in 2.4 GHz band and have a range of lm to 100m. It achieves data rates up to 3 Mbps. Even though Bluetooth has been widely deployed and provides cheap short distance communication, there are still certain key challenges with Bluetooth which need to be addressed. Bluetooth suffers from interference from other devices operating in 2.4 GHz band [3]. This interference could severely limit the performance of Bluetooth devices as 2.4 GHz band is getting overcrowded very rapidly, partly due to Bluetooth devices themselves. Another major disadvantage of Bluetooth is that the data rates provided are not sufficient for high data rate multimedia applications. UWB achieves much higher data rates than Bluetooth at very low transmit power levels due to its large unlicensed bandwidth. UWB systems transmit signals with bandwidth greater than 500MHz or fractional bandwidth greater than 0.2 at all times [1]. The Federal Communications Commission (FCC) has allocated 7.5GHz of un-licensed spectrum in the 3.1GHz to 10.6GHz frequency band for the use of UWB devices [4]. UWB bandwidth is enough to effectively stream multiple simultaneous 1 high-quality video streams. Its low power consumption improves the battery life of the portable devices. Moreover, UWB technology requires less complex hardware as the transmission takes place in baseband eliminating the need for mixers, RF oscil-lators or PLLs which are necessary in narrowband systems. Thus, UWB technology is cost effective and UWB devices are more compact. Due to its low spectral density, unlicensed UWB radio emissions do not add up to cause harmful interference to other radio systems operating in dedicated bands. 1.1 D S - U W B vs M B - O F D M Presently, there are two competing UWB technologies used for high data rate wireless personal area networks (WPAN). One of them is the direct sequence (DS)-UWB [5] which is based on DS-code division multiple access (CDMA) technology and the other is multi-band orthogonal frequency division multiplexing (MB-OFDM) [6] which is based on OFDM technology. In DS-UWB system, the total available spectrum is divided into two sub-bands: a lower band (3.1-4.85 GHz) and a higher band (6.2-9.7 GHz). The use of UNII bands (5.15-5.35 GHz and 5.725-5.825 GHz) is intentionally avoided to prevent interference between UWB and the existing IEEE 802.11a devices. A DS-UWB signal consists of a train of very short pulses with duration in the order of fractions of nanoseconds. The information is carried in the amplitude and/or polarity of the pulses. Multiple access capability is achieved using DS-CDMA technique. A rake receiver can be used for a DS-UWB system to take advantage of the high multipath diversity of the indoor channel. DS-UWB can achieve data rates in excess of lGbps. DS-UWB devices are lower in cost compared to MB-OFDM devices. However, the short symbol duration of the DS-UWB signal leads to intersymbol interference (ISI), especially, at high data rates. So, an equalizer is necessary to compensate ISI for high data rate DS-UWB systems. In a MB-OFDM system, the total spectrum is divided into 5 band groups. Each band is further divided into subbands with bandwidth 528 MHz. A block of transmit data is scrambled, encoded, interleaved, and quaternary phase shift keying (QPSK) modulated to form a OFDM symbol. These OFDM symbols are transmitted over dif-ferent subbands determined by a pre-defined frequency hopping (FH) pattern. The use of OFDM makes the system robust to ISI, eliminating the need for a complex equalizer. OFDM can also exploit the frequency diversity inherent in multipath chan-nels, when combined with error control coding and interleaving. MB-OFDM can 2 achieve data rates up to 480 Mbps. However, MB-OFDM systems were found to be more sensitive to timing and frequency synchronization errors than DS-UWB systems [7]. 1 . 2 E q u a l i z a t i o n f o r D S - U W B s y s t e m s A typical UWB channel consists of a large number of realizable multipath compo-nents. Typically, in case of multipath channels, a rake receiver is used to yield di-versity gain from the multipaths, taking advantage of the good correlation properties of the spreading sequences. However for DS-UWB systems, at high data rates or correspondingly low spreading gains, the performance of the rake receiver is degraded due to presence of ISI. Hence, it becomes necessary to use an equalizer in the receiver to eliminate ISI. Various equalization schemes have been proposed in the literature for DS-UWB systems. In [8], [9] the performance of various linear and decision feedback time domain equalization schemes for DS-UWB systems were investigated. Application of widely linear processing to equalization was proposed in [9]. In [10], a suboptimal linear MMSE equalizer which exploits the sparse nature of the UWB channel to decrease the computational complexity was studied. However, the com-plexity of these equalization techniques could still be very high for severely dispersive UWB channels, in order to achieve a desired performance. A decision feedback equal-ization scheme based on energy detector was proposed in [11]. This scheme avoids estimation of the path amplitudes and delays and is less sensitive to synchronization errors. However, it leads to degradation in the bit error performance. 1 . 3 S C - F D E Frequency domain equalization (FDE) techniques were shown to offer performance similar to time domain equalization techniques at much lower complexity for single carrier (SC) systems over strong frequency selective channels [12]. SC systems with F D E are very similar in structure to a OFDM system. Fig 1.1 shows a SC system employing F D E and an OFDM system. However, SC systems with F D E exhibit certain advantages over an OFDM system. SC systems with F D E have lower peak to average power ratio. Thus, it has significantly lower RF front end costs compared to O F D M system. SC-FDE systems are more robust to phase noise and frequency offsets due to close frequency spacing of its subcarriers and therefore, have less stringent oscillator requirements compared to OFDM. 3 OFDM IFFT Cyclic Prefix addition Channel FFT Equalization — * \ Detect —*• - Transmitter - Receiver -SC-FDE Cyclic Prefix addition Channel FFT Equalization IFFT Detect Transmitter -•• - Receiver -Figure 1.1: Comparison of OFDM and SC-FDE system A frequency domain linear equalizer was first investigated for SC-FDE systems in [25]. SC-FDE as an alternative to multicarrier systems was studied in [24]. Fre-quency domain Decision feedback equalization in which the feedforward filter is ap-plied in frequency domain and feedback filter is applied in time domain was investi-gated in [12]. In [26], a decision feedback equalizer in which both feedforward and feedback filter operate in frequency domain was proposed. This was applied for DS-CDMA systems in [17]. Recently a frequency domain minimum mean square error (FD-MMSE) equalization scheme was proposed for DS-UWB and IR-UWB systems and was shown to have better performance compared to MMSE-Rake receiver [14], [15]. Time-division multiple-access (TDMA) scheme for the binary phase-shift key-ing (BPSK) SC-FDE DS-UWB systems was proposed in [16]. Frequency domain multiuser detection schemes have been investigated for DS-CDMA systems in [17]. 1.4 T u r b o E q u a l i z a t i o n Initially, turbo equalization was considered using full-state trellis based soft equalizers (e.g., the soft-output Viterbi equalizer (SOVE) in [20], the maximum a posteriori (MAP) algorithm based equalizer and its suboptimal variants in [21]). Unfortunately, full-state trellis based soft equalizers may be highly computationally-expensive for long channels and/or for large signal constellations. Later, MMSE-based iterative equalization schemes were proposed in e.g., [31]. In MMSE-based schemes, the MAP algorithm based equalizer (or a suboptimal trellis based soft equalizer) found in the original version of turbo equalization schemes is replaced with a combination of soft ISI cancelation and linear MMSE-based filtering. Because of low-complexity, MMSE-based turbo equalization is much more attractive to be employed in practical mobile 4 receivers compared to MAP-based turbo equalization. In [28], a turbo equalization scheme in which the equalizer operates in frequency domain was proposed for single carrier systems. This significantly reduces the computational complexity, especially, for highly dispersive channels. 1.5 T h e s i s O u t l i n e In this thesis, we adapt various frequency domain linear and non-linear equaliza-tion and multiuser detection schemes for MBOK DS-UWB systems and analyze their performance. We compare BER performances and corresponding complexities of var-ious time domain and frequency domain equalization schemes for single user uncoded BPSK DS-UWB systems and show that frequency domain equalization schemes can provide better trade off between performance and complexity compared to time do-main schemes. Frequency domain turbo equalization schemes for single user coded SC systems have been investigated in [28], [33] and [27]. In this thesis, we extend these results for BPSK and 4BOK DS-UWB for both single user and multiuser scenarios and investigate their performance. This thesis is organized as follows. In Chapter 2, we consider uncoded single user MBOK DS-UWB system. We present the frequency domain linear MMSE equalizer and iterative frequency domain decision feedback equalizers (FD-DFE) for MBOK DS-UWB systems. Then, we present symbol based frequency domain equalization schemes for BPSK and 4BOK DS-UWB systems. Computational complexities of various equalizers are evaluated and simulation results are presented. In Chapter 3, we consider frequency domain multiuser detection schemes, viz., parallel interference cancelation (PIC) and successive interference cancelation (SIC) for uncoded multiuser DS-UWB systems. In Chapter 4, we consider coded DS-UWB systems. We derive frequency domain turbo equalization schemes for BPSK and 4BOK DS-UWB systems and evaluate their BER performance. Conclusions are fi-nally drawn in Chapter 5. 5 Chapter 2 Frequency Domain Equalization 2.1 I n t r o d u c t i o n Frequency domain equalization techniques were shown to offer better trade off be-tween performance and complexity compared to time domain equalization techniques, for single carrier systems with severe channel dispersions [12]. In this chapter, we employ frequency domain equalization techniques for single user M B O K D S - U W B systems. We investigate both linear and non-linear frequency domain equalization techniques [17]. We also define chip based equalization schemes and symbol based equalization schemes for M B O K D S - U W B systems. The complexity of these equal-ization schemes is compared with that of time domain equalization schemes. 2.2 S y s t e m m o d e l 2.2.1 Transmitter We consider a single-user D S - U W B system employing M' -a ry Bi-Orthogonal Keying (M'-BOK) and short ternary codes. A M ' - B O K system maps log 2 M' bits into a bi-orthogonal ternary code of length Ns. The bi-orthogonal code is selected from an assigned code set C = { c i , c 2 , C w _ , — Ci, — c 2 , — C M : } where cx, c 2 , C M > / 2 are 2 2 . orthogonal to each other [5]. 6 The transmit signal of a M'-BOK DS-UWB system is given by oo N3-l = E Y,4r\j]p(t-iT8-jTc) i=—oo j=0 oo k=—oo (2.1) where {c^fj]}^!^-1 S C represents the ith transmitted data symbol and has unit energy. Ns denotes the spreading factor. Tc is the chip duration and Ts = Ns * Tc is the symbol duration. p(t) is the unit energy transmit pulse of time duration T c and s'[iNs + j]=4r[j]. In a system employing FDE, the data symbols are transmitted in blocks. In order to apply FDE, the convolution of the channel impulse response and data signal must be circular. This circularity can be achieved in two ways [13]. First method is to attach a cyclic prefix to the block of data i.e. for every MNS data samples we take last Lp data samples and attach them at the beginning. Thus transmit block m contains sm = [sm[0],sm[l],sm[2],...,sm[MNa + Lp-l]] = [s'[mMNs + MNs-Lp + l],s'[mMNs + MNs-Lp + 2], s'[mMNs + MNS - 1], s'[mMNs], s'[mMNs + 1], ...,s'[mMNs + MNS - 1]] The other method is to append a pseudo random sequence pn[i)fZo 1 to the data samples [12]. In this case the transmit block m is given by sm = [sm[0],sm[l],sm[2],...,sm[MNa + Lp-l]] = [s'[mMNs],s'[mMNs + 1], ...,s'[mMNs + MNS - 1], pn[0],pn[l],...,pn[Lp - 1]] (2.2) Moreover, a PN sequence is transmitted before transmission of first data block. For 7 M'-BOK, we transmit information regarding M l o g 2 M ' bits in each block. 2.2.2 Channel M o d e l UWB channel model proposed for IEEE 802.15.3a standard has been considered [22]. The IEEE 802.15.3a UWB channel model is a modification of the Saleh-Valenzuela [23] multipath channel model. The interarrival time of multipath components is exponentially distributed. Moreover, the multipath arrivals are grouped into two different categories: a cluster arrival and a ray arrival within a cluster. The amplitudes of the multipaths are lognormal distributed. The model also includes a lognormal shadowing term to account for total received multipath energy variation that results from blockage of the line-of-sight path. The passband physical multipath channel can be represented as JVc-l Lc - l = E E <i • ^ - T< - T w ) (2-3) fc=0 1=0 where Lc represents the total number of clusters, Nc represents the total number of rays in the cluster. TJ is the cluster arrival time and 77^ is the arrival time of the kth ray in Ith cluster. TJ and r^i are exponentially distributed. a'k l is multipath gain of kth ray in Ith cluster. The magnitude of a'k l is lognormal distributed. The amplitude of the multipath component is multiplied with +1 or -1 with equal probability to account for signal inversion. The total energy in the multipath components is normalized to one. Finally, X models the lognormal shadowing. Model parameters were designed to fit the measurement results. 4 different chan-nel models have been proposed for 4 different scenarios: CM1 channel model for line-of-sight (LOS) (0-4m) channel measurements, CM2 channel model for non LOS (NLOS) (0-4m) channel measurements, CM3 channel model for NLOS (4-10m) chan-nel measurements and CM4 channel model for extreme NLOS multipath channel. The above multipath channel model (2.3) can be expressed in simplified form as follows L - l M*) = Saj-<y(*-T,) (2-4) 1=0 L denotes the number of multipath components, a\ and 77 are, respectively, the path gain and the delay associated with the /th path. We assume that channel is quasi-static i.e the channel impulse response within a block is constant. 8 z(t) d[i] Symbol mapping and spreading Insertion of Prefix Pulse Shaping Channel h(t) r(t) Figure 2.1: Transmitter and channel for single user DS-UWB system The baseband equivalent of the passband channel model (2.4) is given by L-l h{t) = ^2aie-j2*f<T' -Sit-rt) (2.5) 1=0 where fc is the carrier frequency. 2.2.3 R e c e i v e r The received baseband signal corresponding to mth block is given by L-l MNs+Lp-l rm(t) = J2aie~j2*fcn 2 sm[k]V(t-kTc-T,) +z(t) (2.6) Z=0 fc=0 where z(t) is complex zero mean additive white gaussian noise with variance a2. After chip matched filtering and sampling at the chip rate, the discrete time received baseband signal is given by L3-l rm[k] = ] T h[l}sm[k-l] + z[k] k = 0,l,...,MNs +Lp-1 (2.7) (=0 where h[l] = p(t) <g> h(t) <8> p*(-t)\iTc and z[k] = p*(—t) <g> z(t)\krc- Since only one block is processed at a time, hereafter, we omit the block index m. Transmitter and channel for single user DS-UWB is shown in Fig 2.1. 2 . 3 L i n e a r M M S E e q u a l i z a t i o n For a DS-UWB system employing linear MMSE equalizer, a cyclic prefix of length Lp is attached at the transmitter. At receiver, the received samples corresponding to the cyclic prefix (k — 0,1, . . . , L P — 1) are removed and discrete fourier transform is applied to the rest to obtain 9 MNS~1 R(n)= e~^r[Lp + l]- n = 0 , 1 , M N a - 1 (2.8) (=0 Similarly, we obtain DFTs S(ri), Z{n) and H{n) of s[k], z[k] and h[k] respectively. Assuming that the length of the impulse response of the channel is less than L, the received signal can be expressed in frequency domain as follows R(n) = H(n)S(n) + Z(n) n = 0 , 1 , M N S - 1 (2.9) Fig 2.2 shows the structure of the receiver employing linear MMSE equalization. R(n) is multiplied with MMSE filter coefficients W(n) yielding Y(n) = W(n)R(n) n = 0 , 1 , M N S - 1 (2.10) The MMSE equalizer minimizes the metric MNS-\ J=TMTy E E[\Y{n)-S{n)?} (2.11) Assuming that {S{n)}^0a~x are independent and identically distributed, the filter coefficients minimizing the above metric (2.11) are given by The resultant output Y(n) is converted to time domain signal y[k] using inverse D F T (IDFT). The decision device, shown in Fig 2.3, then detects the symbol based on the time domain signal y[k}. The decision device forms the correlation of y[k] with ci, C 2 , C M 1 and decides in favor of the component with largest magnitude taking 2 into consideration the sign of the component. 2.4 I t e r a t i v e M M S E D F E In [17], an iterative FD MMSE-DFE was proposed for DS-CDMA which attains a better performance than linear FD equalizers. In iterative MMSE DFE, an FD-MMSE forward filter is applied during the first iteration. Hard symbol estimates are obtained from filter outputs through IFFT, chip deinterleaving, despreading and 10 13 « - E Q (A ion ce cis > cis CD CD O Q CO 5: t p. 5 P . o a: a: + CL 0. CO CO > 0_ mo o •4— CD o a: Figure 2.2: Frequency domain M M S E equalizer for a M B O K D S - U W B system 11 yM Symbol detection based on magnitude and sign Detected Symbol Figure 2.3: Decision device for a MBOK system threshold detection. These detected symbols are then spread, chip interleaved and converted into frequency domain to obtain an estimate of the frequency domain chip sequence S(n). This estimate is then fed back to obtain new symbol estimates based on MMSE criterion. This process is performed iteratively. Iterative MMSE-DFE equalization can achieve better performance than linear MMSE filter and MMSE-D F E at the cost of higher computational complexity. In a DS-UWB system employing iterative FD-DFE, a PN sequence of length Lp is appended to the data block. D F T of the entire block of length N = MNS + Lp is taken. It was shown in [17] that interleaving the chip sequence before addition of cyclic performance leads to an improvement in system performance. Therefore, a chip interleaver is used at the transmitter after spreading. Correspondingly, a chip deinterleaver is introduced- at the receiver. Structure of iterative FD-DFE is shown in Fig 2.4. The output after q = 1,2,Q iterations is given by [17] Y"(n) = W9(n)R(n) + Bq{n)Sq-\n) (2.13) where Wq(n) and Bq(n) is feedforward filter and feedback filters respectively for qth iteration. S^ - 1 is detected data at q — 1th iteration. The feedforward and feedback filter are chosen so as to minimize the following mean square error metric at qth iteration [17] JV-1 n=0 j q = Jp E E \Wq(n)R(n) + Bq(n)Sq-\n) - S(n)| 2 (2.14) Frequency domain chip sequence {S(n)}™ = ^ 1 is assumed to be independent and 12 2 Crq" C <~i CD to CD < CD CD Xi CD a o O o B £ 5" W<(0) x«-1(0) rfk] r[0] S/P DFT r[N-1] W'(N-1) X"-1(N-1) R(N-1) Y"(N-1) IDFT P/S and chip DEINTi Decision MBOK Device mapper /•[MNs-1] S/P and chip INT PN PFTl Bq(0) m i - X"(0) \S<{N-1 X"(N-1) Cd O o cn *-< <rt-CD 3 identically distributed with mean zero and variance cr|. Now, the average energy of \2\ - J L is chosen as 1), E(\S(n)\2) = NE(\s[k]\2) = jj-. Since mean of S(n) is zero, af = N_ chip sample for time domain signal s[k] is .E(|s[A;]|2) = ^- (as energy per symbol i  E(\S(n)\2) = jf-. We further impose the condition on feedback filter [17] J V - l £ £ ' ( n ) = 0 (2.15) n=0 so that the feedback filter does not remove the desired component. Minimizing the metric Jq under condition (2.15), yields the following feedforward filter at qth iteration (see Appendix A) [17] Wq(n) = G l H { n ) A / c T 2 + 6 t | ( 1 - H2)|tf(n)|2 Ns^ + {l-\p^)\H{n)\^ (2.16) where pg represents the correlation between the vectors Sq 1 and S. The feedback filter at qth iteration is given by [17] Bq(n) = -pq \H(n)Wq{n) - 7 9] (2.17) where A' In [17], following estimate for the correlation has been proposed N-l 7g = ^J2H(n)Wq(n) (2.18) n=0 ^ • - ^ E ^ W (2-19) where v < 1 is a correction factor to reduce decision feedback error propagation and Es = TH:o\S{n)\\ However, this estimate of pq is not accurate in case of UWB channels due to presence of spectral nulls. So we propose a new estimate of the correlation to overcome 14 t h i s p r o b l e m . I t i s a s f o l l o w s ±-\H(n)\> + o2 R(n)H(n)* . ( 2 . 2 0 ) w h e r e X r e p r e s e n t s t h e l o g n o r m a l s h a d o w i n g f a c t o r o f t h e c h a n n e l i m p u l s e h(t). T h e a b o v e e s t i m a t e o f pq i s f o u n d t o b e m o r e a c c u r a t e t h a n t h e e s t i m a t e i n ( 2 . 1 9 ) . w h e r e d[i] i s t h e t r a n s m i t t e d b i t a n d c[j] i s t h e s p r e a d i n g s e q u e n c e . T h u s , i n c a s e o f B P S K , k n o w l e d g e o f t h e s p r e a d i n g s e q u e n c e o f t h e u s e r c a n b e u s e d i n t h e e q u a l -i z e r . S y m b o l b a s e d e q u a l i z a t i o n s c h e m e s m a k e u s e o f t h e k n o w l e d g e o f t h e s p r e a d i n g s e q u e n c e t o m i n i m i z e t h e o p t i m i z a t i o n m e t r i c [18] . F o r s y m b o l b a s e d e q u a l i z a t i o n s c h e m e s , i n s t e a d o f a t t a c h i n g a c y c l i c p r e f i x o r P N s e q u e n c e o f l e n g t h Lp t o t h e c h i p s e q u e n c e , a p r e f i x o r P N s e q u e n c e o f l e n g t h L i s a t t a c h e d t o t h e B P S K s y m b o l s e q u e n c e a n d t h e n s p r e a d i n g i s p e r f o r m e d o v e r t h e r e s u l t a n t s y m b o l s e q u e n c e . M M S E E q u a l i z a t i o n I n c a s e o f s y m b o l b a s e d M M S E e q u a l i z e r , a c y c l i c p r e f i x o f l e n g t h L i s a t t a c h e d t o t h e s y m b o l s e q u e n c e , b e f o r e s p r e a d i n g , a t t h e t r a n s m i t t e r . T h e s a m p l e s c o r r e s p o n d i n g t o c y c l i c p r e f i x a r e r e m o v e d a t t h e r e c e i v e r a n d D F T i s t a k e n o f t h e b l o c k o f s i z e MNS. T h e s y m b o l b a s e d M M S E filter m i n i m i z e s t h e m e t r i c [18] 2 . 5 S y m b o l b a s e d E q u a l i z e r s 2.5.1 BPSK system F o r B P S K D S - U W B s y s t e m , t h e b i - o r t h o g o n a l c o d e c a n b e e x p r e s s e d a s CM = d\i}c[j] ( 2 . 2 1 ) M - l ( 2 . 2 2 ) w h e r e d[i] i s t h e filter o u t p u t . 15 The symbol based MMSE equalizer coefficients minimizing (2.22)are given by [18] W(n)= H { ^ * , 2 n = 0,l,...,MNa-l (2.23) u ^ Ns where Ns-1 \H{n)\2 = J2 \H(n + kM) mod MNsC(n + kM)modMNf (2.24) fc=0 The complexity to design the symbol based MMSE equalizer is higher compared to chip based MMSE equalizer presented in Section 2.3. However, the BER performance of symbol based MMSE equalization is better compared to BER performance of chip based MMSE equalization. M M S E - D F E The structure of the symbol based FD MMSE-DFE is shown in Fig 2.5. A PN symbol sequence is appended to the data symbol block. At the receiver, D F T is taken of the entire block of size N' = (M + L)NS. The feedforward filter is implemented in frequency domain and feedback filter is implemented in time domain. FD MMSE-D F E also minimizes the metric (2.22). The feedforward filter minimizing the metric (2.22) is given by [18] ffW = « [ . r N z a ^ i „ _ 0 i l N , _ , ( 2 . 2 5 ) a2 + \H(n)\2 where M' — M + L, {b[i}}fji represent the feedback filter taps and Ns-l \H(n)\2= \H(n + kM')modN,C(n + kM')modNI\2 (2.26) fc=0 and C{n) is the D F T of c\j]. Optimal feedback filter taps of length can be obtained by solving following set of equations. V b = - v (2.27) 16 D) c 1 o T3 co Q £ Q. CO t i Figure 2.5: Symbol based frequency domain M M S E D F E for a B P S K D S - U W B system 17 where M + L - l _j'2ir(!-fc)n ^ a 2 + |#(n) | 2 M+L-l _i2Ikn v(fc) = V — (2.29) for 1 < Z,/c > A /^b. Design of optimal MMSE-DFE equalizer involves solving a set of linear equations (2.27) and thus, has high complexity. Nevertheless, symbol based equalizers give better performance for BPSK systems because the assumption made by chip based equalizers that frequency domain se-quence is independent and identically distributed makes them suboptimal. , 2.5.2 4 B O K system In this section a single user 4BOK system using gray coding is considered. Let c\ and C2 be the two orthogonal spreading codes used for spreading. In Gray coding, the bits are mapped to spreading sequences as shown in Table 4.1. The transmitted Table 2.1: Gray coding for 4BOK DS-UWB system bits Spreading Sequence [-1 -1] C l [-1 1] c2 [1 1] - C l [1-1] - c 2 18 s i g n a l o f a b o v e 4 B O K s y s t e m c a n b e e x p r e s s e d a s oo N,-l = E J24r\J]p{t-iTa-jTc) i=—oo j=0 00 Ns-1 oo JVS-1 = E E {d[2i]ci [?] + d[2i + l}c2[j}}P(t - iTs - jTc) ( 2 . 3 0 ) i=—oo j'=0 oo = E { S iM + ^MM* - kTc) ( 2 . 3 1 ) fc = — 00 oo = J2 s'[k}p(t - kTc) k=—oo w h e r e cjj] = - S i l t o l z l , c 2 [ j ] = - i l t o l z l > s^/y, + j] = a n d §'2[iNs + j] d [ 2 i + l ] c 2 [ j ] . A t t h e r e c e i v e r , a f t e r m a t c h e d f i l t e r i n g a n d c h i p r a t e s a m p l i n g , w e h a v e L.-l Ls-l r[k}= h[l]s[k-l]+z[k] = ]T• h[l]{s1[k-l]+s2[k-l]}+z[k] k = 0 , 1 , M N S + Lp - 1 ( 2 . 3 2 ) w h e r e 5 j a n d s 2 a r e o b t a i n e d f r o m s'x a n d s'2 r e s p e c t i v e l y b y a d d i n g c o r r e s p o n d i n g c y c l i c p r e f i x e s . S o a s i n g l e u s e r 4 B 0 K s y s t e m c a n b e c o n s i d e r e d a s 2 - u s e r B P S K s y s t e m e m p l o y i n g o r t h o g o n a l s p r e a d i n g s e q u e n c e s . N o w , s y m b o l b a s e d e q u a l i z e r s c a n b e a p p l i e d a s s u m -i n g b i t s {d[2i]}™/02 t o b e b i t s o f u s e r 1 w i t h s p r e a d i n g s e q u e n c e c.\\j] a n d {d[2i+l]}^/02 t o b e b i t s o f u s e r 2 w i t h s p r e a d i n g s e q u e n c e c2[j]. W e a p p l y M M S E a n d M M S E - D F E f i l t e r s f o r e a c h u s e r , t r e a t i n g t h e o t h e r u s e r t o b e a n i n d e p e n d e n t w h i t e G a u s s i a n i n t e r f e r e n c e . 2 . 6 C o m p u t a t i o n a l C o m p l e x i t y C o m p u t a t i o n a l c o m p l e x i t i e s o f t h e v a r i o u s f r e q u e n c y a n d t i m e d o m a i n e q u a l i z e r s f o r B P S K D S - U W B s y s t e m s a r e s h o w n i n T a b l e 2 . 1 a n d 2 . 2 . T a b l e 2 . 1 p r e s e n t s t h e p r o c e s s i n g c o m p l e x i t y o f t h e e q u a l i z e r . T a b l e 2 . 2 , p r e s e n t s t h e o r d e r o f c o m p u t a t i o n a l c o m p l e x i t y o f e q u a l i z e r d e s i g n . 19 Table 2.2: Computational complexity of the receiver per output symbol for BPSK system Equalizer No. of complex multi. per detected symbol Rake NrNs Rake MMSE NrNs + Nf Rake D F E NrNs + Nf FD MMSE Nslog2MNs FD-IT-DFE C?£log 2 iV +{2Q - l)Na symbol FD-MMSE AUog 2 MNS symbol FD-DFE %log2N + Nfb Table 2.3: Complexity of equalizer design per block for BPSK system Equalizer Order of complexity Rake MMSE 0((Nf + LY) Rake D F E 0((Nf + Ly) FD MMSE 0(MNs) FD-IT-DFE 0(QN) symbol FD MMSE 0(MNs) symbol FD-DFE 0(N% + ^log2Nfb +%log2N) 2 . 7 S i m u l a t i o n R e s u l t s We consider BPSK and 4BOK DS-UWB systems using ternary spreading sequences of length Ns = 12 and Ns = 6. We simulate the BER performance for CM4 channel model [22]. A root raised cosine function with roll off factor 0.3 is used as the pulse shape. We consider transmission in lower band (3.1-4.85 GHz). The chip rate is chosen to be 1313 MHz and the center frequency fc is 3939 MHz [5]. We assume complete channel information at the receiver. For BPSK systems, the following ternary spreading codes are used [5] iVs = 12 — • [0 — 1 — 1 — 1 1 1 1 — 111 — 11] Ns = 6 — • [1 0 0 0 0 0] 20 For 4BOK system, we use following ternary spreading codes [5] iVs = 12 — • [1 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 1 0 0 0 0 0] For frequency domain equalization, number of data symbols per block is M = 256 and length of prefix or appended PN sequence is Lp = 255. The decision feedback correction factor v is chosen to be 1. In case of symbol based FD-DFE for BPSK systems, we have chosen PN sequence length L = 31 for Ns = 12 and L = 63 for N„ = 6. The number of feedback filter taps is taken as Nfb = . For symbol based FD-MMSE we have chosen length of channel prefix as L = 22 for Ns = 12 and L — 44 for Ns = 6. The total number of iterations for FD iterative D F E is represented by Q. No = a2 is used to denote the power spectral density of the additive Gaussian noise. Eb is the average recieved energy per bit. We also simulate the time domain equalizers proposed in [9], we choose number of rake fingers Nr = 16. Nf and Nb represent the number of feedforward and feedback filter taps, respectively, of rake D F E receiver. Nf also represents number of MMSE filter taps in rake MMSE receiver. Performance of the chip level MLSE receiver is also shown. In Table 2.3 and 2.4, we present the numerical values of the computational com-plexities for various time and frequency domain equalizers for a BPSK DS-UWB system with Ns = 6. The parameters used in these tables for computing the numer-ical values correspond to the receivers whose BER performance is shown in Fig 2.6. We can see from Tables 2.3, 2.4 and Fig 2.6 that the frequency domain equalizers offer better performance than time domain equalization techniques at a much lower complexity especially at low signal-to-noise ratios (SNRs). Fig 2.7 and Fig 2.8 show the BER performance of the frequency domain equaliza-tion techniques for BPSK DS-UWB systems and 4BOK DS-UWB systems, respec-tively,- with spreading factor Ns = 12. Fig 2.9 shows the BER performance of the frequency domain equalization techniques for 4BOK DS-UWB systems with spread-ing factor Ns = 6. Fig 2.10, shows the performance gain due to chip interleaving before addition of the prefix for 4BOK system with Ns = 6. We see that the gain is substantial. Symbol based frequency domain equalizers were found to exhibit better perfor-21 . 1 1 \ [ [ 1 1 1 \ 1 • •. ^S-^  v • :::: f: T i-T:^ *:^  -:i^ :Li:::?:::::::::::::^  : "'" <.-•.•-• > />v^ .N. ."' '..-.-^ r -... ^v^. ... ..Ns^ Jl .\-, ^ N ^ - %o ;• > V , " v - s ^ > - . -- >s^-< \ "a s. . ... • \ • 'T>S:'",n. ... ... -V- Rake -A-. Rake MMSE, Nf = 30 . -a-. Rake MMSE DFE, N(=30, N6 = 15 ::: . . Rake MMSE DFE, N(=50, Nb = 25 y N y - A N ... —V— FD MMSE \N- v : \V \ ... FD IT DFE, Q = 2 • •: v & ... —a— FD iT DFE, Q = 3 - + - Symbol based FD MMSE - 9 - Symbol based FD DFE MLSE I 1 1 i i i i i N i 5 6 7 8 9 10 11 12 13 14 15 16 Figure 2.6: BER performance of various time domain and frequency domain equalizers for a BPSK UWB system with spreading factor Ns = 6 22 I I I. 5 6 7 8 9 10 11 12 13 14 15 16 Figure 2.7: BER performance of various frequency domain equalizers for a BPSK DS-UWB system with spreading factor N„ = 12 23 6 7 8 9 10 11 12 13 14 Figure 2.8: BER performance of frequency domain equalizers for a 4BOK DS-UWB system with spreading factor Ns = 12 24 ):::::::;:::: t:::::: :::::::::! :::::::::l::::::::::::::::::t 5 6 7 8 9 10 11 12 13 14 Figure 2.9: B E R performance of frequency domain equalizers for a 4 B O K D S - U W B system w i t h spreading factor N„ = 6 25 10" ••• - V - FD IT DFE, Q = 3, without chip —*— FD IT DFE, Q = 2, with chip — 6 - FD IT DFE, Q=3, with chip interieaver 'I I I i i i i i i 5 6 7 8 9 10 11 12 13 14 15 Figure 2.10: BER performance of FD IT D F E using chip interieaver and FD IT D F E without using chip interieaver for a 4 B O K DS-UWB system with spreading factor Ns = 6 26 T a b l e 2 . 4 : C o m p u t a t i o n a l c o m p l e x i t y o f t h e r e c e i v e r p e r o u t p u t s y m b o l f o r B P S K s y s t e m w i t h Ns = 6 E q u a l i z e r N o . o f c o m p l e x m u l t i . p e r d e t e c t e d s y m b o l . R a k e 9 6 R a k e M M S E 1 2 6 f o r Nf = 3 0 1 4 6 f o r Nf = 5 0 R a k e D F E 1 2 6 f o r Nf = 3 0 1 4 6 f o r Nf = 5 0 F D M M S E 6 3 . 5 1 F D - I T - D F E 1 6 9 . 2 f o r Q = 2 2 5 6 . 8 f o r Q = 3 s y m b o l F D - M M S E 6 3 . 5 1 s y m b o l F D - D F E 1 1 1 . 6 T a b l e 2 . 5 : C o m p l e x i t y o f e q u a l i z e r d e s i g n p e r b l o c k f o r B P S K s y s t e m w i t h Ns = 6 E q u a l i z e r O r d e r o f c o m p l e x i t y R a k e M M S E 2 5 0 0 f o r Nf = 3 0 4 9 0 0 f o r Nf = 5 0 R a k e D F E 2 5 0 0 f o r Nf = 3 0 4 9 0 0 f o r Nf = 5 0 F D M M S E 1 5 3 6 F D - I T - D F E 3 5 8 2 f o r Q = 2 5 3 7 3 f o r Q = 3 s y m b o l F D M M S E 1 5 3 6 s y m b o l F D - D F E 1 0 6 5 1 m a n c e t h a n c h i p b a s e d e q u a l i z e r s f o r B P S K D S - U W B s y s t e m s . H o w e v e r , s y m b o l b a s e d f r e q u e n c y d o m a i n e q u a l i z e r s d o n o t p e r f o r m w e l l f o r 4 B O K s y s t e m c o m p a r e d t o c h i p b a s e d e q u a l i z a t i o n s c h e m e s . 27 Chapter 3 Multiuser Detection 3 . 1 I n t r o d u c t i o n Performance of conventional rake receivers is severely degraded in the presence of multiple access interference (MAI). Multiuser detection schemes to eliminate MAI have been proposed for DS-UWB system in [19]. However, the complexity of these schemes can be quite high especially for long channels. In this chapter, we propose receiver structures for DS-UWB systems, in which multiuser detection and equal-ization are entirely performed in frequency domain, thus, significantly reducing the computational complexity. Performance of the frequency domain MMSE linear multiuser receiver for DS-CDMA systems was investigated in [29]. Iterative frequency domain multiuser de-tection techniques have been proposed for BPSK and 4BOK DS-CDMA systems in [17]. In this Chapter, successive interference cancelation (SIC) and parallel interfer-ence cancelation (PIC) techniques are used to eliminate MAI in DS-UWB systems. Receiver structures employed are similar to those employed in [17]. We also consider single user 4BOK system as a two-user BPSK system and apply multiuser detection schemes. 3 . 2 S y s t e m M o d e l A DS-UWB system with U users is considered. The multiuser system model is shown in Fig 3.1. du[i], i = 0 , 1 , M — 1 represents the uih user data sequence. s'u[k], k = 0,1,..., MNS — 1 is the chip sequence obtained after spreading. su[k],k = 0,1,N — 1 is obtained from s'u[k] by adding the pseudo random prefix of length Lp. Au is the 28 ^[[^Symbol mapping, spreading 1 and chip interleaving ^[^jSymbol mapping, spreading 1 and chip interleaving s'M s\[k} Insertion of Prefix Pulse Shaping Insertion of Prefix Pulse Shaping x,(t) Channel Channel Symbol mapping, spreading and chip interleaving s'v\k\ Insertion of 1 Prefix wl 1 — 1^ Pulse Shaping Channel Figure 3.1: Transmitter and channel for a multiuser DS-UWB system amplitude of the user' u at the receiver. Users are indexed in decreasing order of power. Uplink of a synchronous DS-UWB system is considered. At the receiver, after pulse matched filtering, chip rate sampling, and taking the DFT, for each transmitted block we have R{n) = J2AuHu{n)Su(n) + Z(n) n = 0 , 1 , N - 1 (3.1) u=l where Su(n) and Hu(n) are DFTs of su[k] and hu[k] respectively. 3.3 S u c c e s s i v e I n t e r f e r e n c e C a n c e l a t i o n The receiver structure employing SIC is shown in Fig 3.2. In SIC, interference can-celation is performed serially for each user. Users are detected in decreasing order of their power. Without loss of generality, here we assume that the users are indexed in decreasing order of their power. For the first user, the user bits of other users are unknown and are assumed to be independent and identically distributed. Equalizer structures from Section 2.4 are used to detect the user 1. After user 1 is detected, the interference caused due to user 1 on other users is removed, assuming that user 1 has been detected correctly. For second user, user bits u = 3 , U are as unknown are assumed to be independent and identically distributed. This process is iteratively done till all the U are detected. 29 r[k] S/P r[N-1] D F T R Equalize^ d \ U ] Equalizer «/ 2 [ i ] T -Equalizer «/ 3 [ i ] R u-\ u-\ R Equalizer d y [ i \ Figure 3.2: Successive interference cancelation 30 E i t h e r a f r e q u e n c y d o m a i n M M S E e q u a l i z e r o r i t e r a t i v e f r e q u e n c y d o m a i n d e c i s i o n f e e d b a c k e q u a l i z e r c a n b e e m p l o y e d t o d e t e c t e a c h u s e r . T h e f r e q u e n c y d o m a i n M M S E e q u a l i z e r f o r u s e r u i s g i v e n b y [17] Wu{n) = n = 0 , l , . . . , i V - l ( 3 . 2 ) tf.*2 + £ 2 = « ^ | f f « ' ( n ) l 2 F o r i t e r a t i v e d e c i s i o n f e e d b a c k e q u a l i z a t i o n , f e e d f o r w a r d f i l t e r f o r uth u s e r a n d qth i t e r a t i o n i s g i v e n b y W*{n) = Tl ( 3 . 3 ) ^ + ^ ( l - W ) | H u ( n ) | » + E S 5 = t t + i ^ | ^ ( n ) | a w h e r e ni v /i • R(n)Hu{n)* d g _ u ^ , . n=0 N. \Hu(n)\2 + a2 w h e r e Eu = E ^__n=Q \Su(n)\2^ = jj- a n d Xu r e p r e s e n t s t h e l o g n o r m a l s h a d o w i n g f a c t o r o f t h e c h a n n e l i m p u l s e hu(t). T h e f e e d b a c k f i l t e r a t qth i t e r a t i o n i s g i v e n b y B«(n) = -pl[Hu(n)W«(n)->fi] : ( 3 . 5 ) w h e r e T2 = i E ^ n » ) <3-6) n=0 3.4 P a r a l l e l I n t e r f e r e n c e C a n c e l a t i o n T h e r e c e i v e r s t r u c t u r e e m p l o y i n g p a r a l l e l i n t e r f e r e n c e c a n c e l a t i o n i s s h o w n i n F i g 3 . 3 . I n P I C , i n t e r f e r e n c e c a n c e l a t i o n i s p e r f o r m e d i n p a r a l l e l f o r a l l u s e r s . D u r i n g t h e f i r s t i t e r a t i o n , f o r e a c h u s e r , e q u a l i z e r s p r o p o s e d i n S e c t i o n 2 . 4 i s u s e d t o d e t e c t t h e u s e r s y m b o l s t r e a t i n g t h a t s i g n a l s o f a l l o t h e r u s e r s a s u n k n o w n . T h e n t h e e s t i m a t e s o f t h e s y m b o l s s o o b t a i n e d a r e u s e d t o c a n c e l t h e i n t e r f e r e n c e o f o t h e r u s e r s o n e a c h u s e r . D u r i n g 2 n d i t e r a t i o n , e q u a l i z e r s d e t e c t e a c h u s e r a s s u m i n g t h e r e s i d u a l i n t e r f e r e n c e f r o m o t h e r u s e r s a s G a u s s i a n . T h i s p r o c e s s i s c a r r i e d i t e r a t i v e l y . L e t P b e t h e n u m b e r o f i t e r a t i o n s u s e d f o r i n t e r f e r e n c e c a n c e l a t i o n . M M S E e q u a l -31 r[k] S/P r[0] r[N-1] D F H R -I Equalize^ Equalizer ~*"U7 Equalizer Figure 3.3: Parallel interference cancelation izer for user u at pth iteration is given by [17] Hu(n)* where ^ 2 + E„'=i(i-l^l2)^I^HI2 a2Ns. ^ R{n)Hu{n)* n = 0,l,...,N -1 (3.7) TP V 42 5rX (n)* « ^ ^ f | ^ ( n ) | 2 + a 2 (3.8) where 5 £ - 1 ( n ) is the F F T of the chip sequence corresponding to estimates of uth user bits after p — 1th PIC iteration. For iterative decision feedback equalization, the feedforward filter at qth iteration is given by [17] Nsa2 + AK1- K T ) \Hu(n)\2 + E v * . K> (1 - l&l2) (3.9) where ^ = v fi | W g u ( n ) * AS = ttQ S T 1 , ' - 1 ( n ) ' (3-10) (3.11) where £ u = ^ |5 t t(n)|2 = ^. Sfr^-^n) is the F F T of the chip sequence 32 corresponding to estimates of uth user bits after q — Ith equalizer iteration and p — 1th PIC iteration. The feedback filter at qth iteration is given by [17] Bpu'q{n) = -pi [Hu{n)W™(n) - (3.12) where N-l 3.5 S i n g l e u s e r 4 B O K s y s t e m As shown in Section 2.5.2, single user 4BOK system can be treated as a 2 user BPSK system. So, above multiuser detection schemes (PIC and SIC) can be applied for a single user BPSK system. We apply these schemes for single user 4B0K system and compare their performance with equalization schemes proposed in chapter 2. 3.6 S i m u l a t i o n r e s u l t s We consider 4-user BPSK DS-UWB systems using ternary spreading sequences of length Ns = 12. All users are assumed to have equal transmit power. We simulate the average BER performance for CM4 channel model [22]. We consider transmission in lower band (3.1-4.85 GHz). We assume complete channel information at the receiver. The ternary spreading codes of the 4 users are given by Table 3.1: Ternary codes used for the 4 users [0 -1 -1 -1 1 1 1 -1 1 1 -1 1) [-1 1 -1 -1 1 -1 -1 -1 1 1 1 0] 1 [0 -1 1 -1 -1 1 -1 -1 -1 1 1 1] i [-1 -1 -1 1 1 1 -1 1 1 -1 1 0] The decision feedback correction factor u is chosen to be 0.8. Fig 3.4 shows the average BER performance of receiver using SIC for number of equalization iterations, Q = 1,2,3. Fig 3.5 shows the average BER performance of receiver using PIC for number of PIC iterations P = 1,2,3 and number of equalization iterations Q = 1,2. It can be seen from the simulation results that significant improvement in the performance is achieved during first two PIC and first two equalization iterations. 33 Figure 3.4: BER performance of receiver employing successive interference cancelation for a 4-user BPSK DS-UWB system with spreading factor Ns = 12 The improvement in performance with further equalization or interference cancelation iterations is not so significant. For single user 4 B O K case, performance improvement is observed over the symbol based 4 B O K system but it is not as good as the chip based equalizers. 34 1 5 10 15 20 25 <°'°810<W F i g u r e 3.5: B E R p e r f o r m a n c e o f r e c e i v e r e m p l o y i n g p a r a l l e l i n t e r f e r e n c e c a n c e l a t i o n f o r a 4 - u s e r B P S K D S - U W B s y s t e m w i t h s p r e a d i n g f a c t o r iV s = 12 35 i r | —B— FD IT DFE, Q=2 | : : : : : : : : •I i i i i i i i i i 5 6 7 8 9 10 11 12 13 14 15 Figure 3.6: BER performance of receiver employing multiuser detection techniques for a single user 4 B O K DS-UWB system with spreading factor Ns = 6 36 Chapter 4 Turbo Equalization 4.1 I n t r o d u c t i o n In this chapter, we consider a DS-UWB system with a forward error correction(FEC) scheme. Usually for the coded systems, decoding and equalization are carried out separately at the receiver. An equalizer is used to compensate for channel effects and make estimate of channel transmitted symbols. From these symbol estimates, a de-mapper is used to obtain estimates of interleaved coded bits. Then a de-interleaver and a decoder are used to obtain the information bits. However, the above process of making hard decisions by the equalizer destroys the information regarding how likely each code bit might have been. There are many decoders which exploit this "soft" information to give a better performance. In turn, the decoder can generate its own soft information and this soft information can be exploited at the equalizer to improve channel symbol estimates. This process can be carried on iteratively. When processing soft information regarding a given bit, it is assumed that the soft information about each bit is independent. This assumption enables use of simple and fast algorithms for equalizer and decoder. However, this assumption can only be valid if the soft information of a given bit is generated based on soft information of bits other than the given bit. This information is called the "extrinsic information". The process of passing extrinsic information recursively between equalizer and decoder is essential for turbo decoding [30]. The extrinsic information is expressed by log likelihood ratios(LLRs). The equalizer used could either be trellis based, linear or decision feedback. How-ever, trellis based equalizers generally have very high complexity. So linear or decision 37 d[i Channel. Encoder Symbol Interieaver Symbol mapping, spreading and chip interleaving Insertion of il*L Pulse Shaping Channel h(t) — • Prefix r(t) Figure 4.1: Transmitter and channel for single user coded DS-UWB system feedback equalizers are used. Turbo equalization schemes with MMSE equalization in time domain have been studied in [31]. In [28], a turbo equalization scheme in which MMSE equalization is carried in frequency domain was proposed for BPSK SC systems. In this chapter, we propose low complexity frequency domain MMSE turbo equal-ization schemes for single user BPSK and 4BOK DS-UWB systems based on the frequency domain turbo equalization scheme proposed for single carrier BPSK sys-tems in [32]. We later consider multiuser DS-UWB system. We combine the single user frequency domain turbo equalization schemes with soft interference cancelation [34] to obtain multiuser frequency domain turbo detectors. The multiuser turbo de-tector is then applied over single user 4BOK system by considering it as a two-user BPSK system. Maximum a posteriori (MAP) decoder is used in all the schemes. Cyclic prefix is used for all the systems presented in this chapter. 4 . 2 S i n g l e U s e r S y s t e m The transmitter structure for a single user DS-UWB system is shown in Fig 4.1. The receiver structure is shown in Fig 4.2. 4.2.1 BPSK System First, a single user BPSK DS-UWB system is considered. Let Lc(dc) = [Lc{dc[0]),Lc(dc[l}),Lc(dc[2}),...,Lc{dc[M - 1])] represent the log likelihood ratios of the symbols obtained from the decoder and interieaver. The log likelihood ratio is defined as Lc{dc) = log V{dc = 1) p{dc = -1) (4.1) The structure of the frequency domain SISO equalizer is shown in Fig 4.3. Soft 38 Lc(dCU}) r[k] SISO Equalizer Symbol Interieaver Lc(dc[i\) LAdc[i\) Symbol Deinterleaver SISO channel decoder j Le(dc[i\) Figure 4.2: Receiver for single user coded DS-UWB system Calculation ofW(n),u and s(n) W(0) R J O L ^ W(MN-1) R(MNS-1) X(0) X(MN-1) ® *® X(n) = (p-W(n)H(n))5(«) Y(0) Y(Mr)s-1) IDFT P/S and chip DEINT Despreading Calculation ofLLRs Figure 4.3: Frequency domain SISO equalizer for single user coded MBOK DS-UWB system 39 bit estimates dc[i] are first obtained using the a priori information from the channel decoder. dc[i\ = tanh(0.5Lc(dc[z])) (4.2) After spreading and addition of prefix, soft chip sequence estimate s[k] is obtained. The F F T of s[k] is represented by S(n). Frequency domain chip sequence {S(n)}'!^INs' is assumed to be independent and identically distributed with mean zero and vari-ance c t | . This assumption makes the turbo equalization schemes proposed in this chapter suboptimal. However, this greatly reduces the computational complexity of the equalizer. Now, the average energy of chip sample for time domain signal s[k] is £( | s [ fc ] | 2 ) = ±. (as energy per symbol is chosen as 1), E(\S(n)\2) = MNsE(\s[k]\2) = M. Since mean of S(n) is zero, a2s = E(\S(n)\2) = M. Using statistical estimation theory, it has been shown in [32] that S(n) can be mod-eled as a zero mean and uncorrelated sequence with variance c r | « Yln=o~l l ^ ( n ) | 2 S(n) and cr| are required for the frequency domain soft MMSE equalization. A MMSE SISO equalizer minimizes the metric J = E[\y[k}-s[k]\2' MNs-l MNs-1 (4.3) subject to constraint MNs-l B(n) = 0 (4.4) To minimize J , its sufficient to minimize J(n) = E [\W{n)R(n) + B(n)S{n) - S{n)\2' (4.5) for all n = 0,1,..., MNS - 1. The cost function to be minimized for each n, is given by Jp(n) = E [\W(n)R(n) + B{n)S{n) - S{n)\2] + (3 MNs-l £ B(n) (4.6) 71=0 40 where (3 is the Lagrange multiplier to account for the constraint. Minimizing the above cost function, we arrive at following equalization algorithm (see Appendix B): S = FFT(s) (4.7) 1 MNs-\ W £ |5(n)|2 (4.8) s n=0 W { U ) MNsa* + (al-al)\H{nW ( 4 ' 9 ) 1 MNa-l — W(n)H{n) (4.10) " n=0 1 + a§/x W(n) = \W(n) (4.12) H = A/2 (4.13) F(n) = VK(n)/?(n) + {y. - W(n)#(n))S(n) (4.14) Output after soft MMSE filtering can be assumed to be an output of an equivalent AWGN channel with input s[k] [34]. y[k] = ns[k] + z[k] + z[k] (4.15) It can be shown that for MMSE filtering (see Appendix B) E(\y[k]-s[k}\2) = ^ 4 ( 1 - p ) (4.16) 41 Variance of z[k],al can be found from above as follows = E(\y[k] -#]|2) = E(\(p-l)s[k} + z[k}\2) ., o\ = ^/x( l -Ax) (4.17) LLRs generated by the equalizer are given by p({y[k}}t^)Ns\dc\i] = 1) Le(dc[i\) = log , r I l l l i = i J V , _ 1 ^ ' ( y [ ( i - l ) ^ + j]-Axc[;])2 , (y[(i-l)Ns + j}+pc[j}f j = 0 2^/x(l-/x) 2 ^ ( 1 - M ) 2 ^ E H » [ ( i - i ) J y . + Jlcb1 1- / / where = £ y[(i - l)Ns + j]c[j] (4.18) 2iV>[i1 N ' ~ l 1-/* It should be noted that a single MMSE frequency domain filter is used for all bits in a transmitted block unlike time domain turbo equalization in which different filter coefficients are used for each bit. Although this degrades the performance of the turbo equalizer, it significantly reduces the computational complexity. 4.2.2 4BOK System LLRs of the bits generated by the decoder are given by Lc{dc) = [Lc(dc[0]),Lc(dc[l]),Lc(dc[2]),...,Lc(dc[2M- 1])]. The structure of the frequency domain SISO equalizer is shown in Fig 4.3. Soft bit estimates dc[i] are first obtained using the a priori information from the channel decoder. d,[i] = tanh(0.5Lc(dc[i])) (4.19) After spreading and addition of prefix, soft chip sequence estimate s[k] is obtained. Frequency domain chip sequence {S(n)}7^Z0MNs~1 is assumed to be independent and 42 identically distributed with mean zero and variance erf = M. Now the LLRs of the bits dc[i] are obtained in a way very similar to that of BPSK. First equalization is performed using equation (4.7-4.14) to obtain Y(n). Inverse F F T is performed over Y(n) to obtain y[k]. Output after soft MMSE filtering can be assumed to be an output of an equivalent AWGN channel with input s[k\. y[k] — fj,s[k] + z[k] = n{§i[k] + §2[k]} + z[k] = Lid 21— J Cl + pdc 2 W + 1 c2 I—J + z[k] (4.20) As shown in Section 2.5.2, 4BOK user can be seen as a 2-user BPSK system. Therefore, at the receiver, after matched filtering and chip rate sampling, we have L,-l Ls-1 r[k] = £ h[l]s[k-l]+z[k] = £ h[l]{si[k-l]+h[k-l]}+z[k] k — 0,1,MNS + Lp 1=0 1=0 (4.21) where §i and s2 are obtained from s[ and s2 respectively by adding corresponding cyclic prefixes. For calculating the LLRs of dc[2i], s2[k] is assumed to be zero mean Gaussian distributed and independent of §i[k]. Similar to the case of BPSK, variance of the interference z[k] + ps2[k], tT?nter can be obtained as follows i - ( l - M ) = E(\y[k]-s[k]V) = E(|(Ai-l)Si[fc] + #]+)US 2 [A;] | 2 ) = (1 ~V)2^jy + Winter =>°Ler = ^ r ( l - / ^ 2 ) (4-22) 43 Le(dc[2i}) = log U 1 J / f c=(1-1)^1 N y p({y[fc]>M^. |6[*] = - i ) = ^ (y[(i-l)N. + j ] ( y [ ( i - 1 ) ^ + 3] + ^])' 2 ^ ( 1 - ^ ) 2 ^ ( 1 - ^ ) \ - n 2 4Nfd°f] where d^[2i] = Y] y[(i - lJ/V". + j)cx\j) (4.23) j=0 Similarly, LLRs of dc[2i + 1] can be obtained as ANs^[2i + 1] w h e r e d f ^ y [ { i _ l ) N s + m j ] (4.24) 4.3 M u l t i u s e r S y s t e m In this section, U user DS-UWB system is considered. Soft interference cancelation [34] is used to mitigate MAI and soft MMSE filter is used to tackle ISI. The transmitter and receiver structure for multiuser DS-UWB systems are shown in Fig 4.4 and Fig 4.5, respectively. First, soft estimates of bits of all users are obtained based on a priori information from the U decoders. dcu\i] = t anh(0 .5L e «[z ] ) ) (4.25) After spreading and prefix addition for each user u, soft chip sequence estimate su[k] are obtained. Soft interference cancelation is then performed to eliminate the inter-ference of all other users over the signal of a given user to obtain Kin) = R(n) - ]T Au,Hu,{n)Su,(n) (4.26) 44 '.Ml Channel Encoder d\\i\\ Symbol Interleaver 4i {Symbol mapping, spreading and chip interleaving Insertion of Prefix -^-W Pulse Shaping Channel A,ht(t) 4'L Channel r Encoder Symbol Interleaver ^ t|Symbol mapping, spreading 1 and chip interleaving Insertion of Prefix Sl\k •Pulse Shaping 4 \ Channel <U«. Channel Encoder Symbol Interleaver. (^Symbol mapping, spreading IfjW Insertion of and chip interleaving Prefix Pulse Shaping *»('] Channel rfk] SISO Multiuser Detector Symbol Deinterleaver L.(d\[iD. SISO channel decoder Symbol Interleaver Symbol Deinterleaver L.(d\[i\) SISO channel decoder Symbol Interleaver LM\[i\) Symbol Deinterieave^ SISO channel decoder Symbol Interleave^ w h e r e Su d e n o t e s F F T o f su. S i m i l a r t o t h e s i n g l e u s e r c a s e , Su(n) i s a s s u m e d t o b e i n d e p e n d e n t a n d i d e n t i c a l l y d i s t r i b u t e d w i t h z e r o m e a n a n d v a r i a n c e c r | u = M. F o l l o w i n g e q u a l i z a t i o n a l g o r i t h m i s u s e d f o r e a c h u s e r 1 MNS-1 M W r E (4-27) n=0 W (n) = KHM* j MNs-1 ^ = M A T E Wu(n)AuHu(n) ( 4 . 2 9 ) 3 n=0 K = °\ , ( 4 . 3 0 ) 1 + olsjiu Wu(n) = \uWu{n) ( 4 . 3 1 ) • / / „ • = A u / i u ( 4 . 3 2 ) V u ( n ) - V ^ ( n ) i ? u ( n ) + (/z - V K u ( n ) A U J f 7 u ( n ) ) 5 u ( n ) ( 4 . 3 3 ) F o r B P S K s y s t e m , t h e s p r e a d i n g s e q u e n c e o f u s e r u i s d e n o t e d b y { c [ j ; u ] } ^ 1 . T h e L L R s f o r B P S K s y s t e m a r e g i v e n b y Le(dcu[i}) = 1 —— J- fJ-u = 2 A ^ [ i ] w h e r e im=Y^yu[{i_1)Ns + j]c[j.u] ( 4 . 3 4 ) F o r 4 B O K s y s t e m , t h e o r t h o g o n a l s p r e a d i n g s e q u e n c e s o f u s e r u i s d e n o t e d b y 47 {ci[j;v]}"=ol and {c2[j;u}}?^1. The L L R s for 4 B 0 K system are given by 4 i V X Ef=o 1 V[(i - W + jjcib'; it] Le(dc[2i}) = 4 A / . s / i _ " d C J 2 ' ] w h e r e #[2i] = £ - 1)NS + 3%]j-u] (4.35) Le{a \zi + i j j — -1 - K = 4N'^[2l + 1 ] where + 1] = £ yu[(z - 1)N. + j}~c2[j;u) (4.36) W i t h ~CX[J-U\ = -C'fr»l+<*[J>I A N D = - Q M + C ^ U ] 4.3.1 Single user 4 B O K system As shown in Section 2.5.2, a single user 4 B O K system is equivalent a two-user B P S K system. So, multiuser B P S K turbo equalization algorithm can be used for detection of information bits. First, soft estimates of the bits are obtained. d°[i] = tanh(0.5L e((f [i])) (4.37) Spreading estimated user bits dc[2i] with the spreading sequence c\ and adding corresponding cyclic prefix, chip sequence S\[k] is obtained. Similarly, from estimated user bits d°[2i + 1], chip sequence s2[k] is obtained. For user bits d c[2i], soft interference cancelation is performed to remove the inter-ference from bits dc[2i + 1] Ri(n) = R(n) - H(n)S2(n) (4.38) Similarly, for user bits dc[2i + 1], we have R2(n) = R(n) - H{n)Si(n) (4.39) S\ and S2 represent F F T s of Si and s2 respectively. Si[k] and S2[k] are assumed to be independent and identically distributed with zero mean and variance tr| = cr| = E(\S2(n)\2) = MNsE(\s2[k}\2) = MN3^ = 48 M/2 For u = 1,2 1 MNS-1 °k = MW E i s » l 2 (4-40) s n=0 W (n) = Hu{n)* ( 4 41« MNs-1 — ]T Wu(n)Hu(n) (4.42) Pu MX. a n=0 K = 5 2" , (4.43) 1 + a | u / t u Wu(n) = XuWu(n) (4.44) A*u = Kfiu (4.45) i ; (n) = Wu{n)Ru(n) + {p - Wu(n)Hu(n))Su{n) (4.46) L L R s are given by Le{dc[2i}) 1 - Hi ANsdc[2i] N s _ 1 where dc[2i] = ]T Vl[{i - 1)N„ + j]ci[j] (4.47) 1 " ^ L e (d c [2i + 1]) = 4^Ego ^ [ ( ^ - i ) ^ + j]c2b1 1 - £*2 ' = ANf[2i + 1 1 where d?\2i + 1} = T - 1)JV. + j]c2[j] (4.48) This method has higher complexity since two forward equalization filters need to be evaluated for each block. 4 .4 S i m u l a t i o n R e s u l t s A half-rate convolutional code with constraint length K = 6 and generating polynomial (65,57) (notation in octal) is used [5]. The simulation parameters for single user 49 as well as multiuser BPSK and 4B0K systems are same as those used in previous chapters. Transmission in lower band (3.1-4.85 GHz) over CM4 channel is considered. Fig 4.6 and Fig 4.7 show the BER performance of turbo equalizers for coded BPSK DS-UWB systems with spreading factor Na — 6 and Ns = 12 respectively. The performance of turbo equalizer with perfect a priori information is also shown. Fig 4.8 shows the performance of turbo equalizers for coded 4BOK DS-UWB systems with spreading factorA^ = 6. Fig 4.9 shows the average BER performance of turbo equalizers for 4-user BPSK DS-UWB system with spreading factor Ns = 12. The performance gain of second turbo iteration over the first iteration is more sig-nificant compared to the performance gain of third iteration over the second iteration. The improvement in performance with each turbo iteration is higher for systems with spreading factor 6 than system with spreading factor 12. This is expected since the systems with lower spreading factor suffer from more severe ISI and hence exhibits much better performance after soft ISI cancelation. Performance gain is very high especially for multiuser systems. Also from Fig 4.10, we can see that turbo equalization scheme proposed in Section 4.3.1 for single user 4BOK system gives better performance than the scheme proposed in Section 4.2.2 at the expense of higher complexity. 50 Figure 4.6: B E R performance of frequency domain tu rbo equalizers for a B P S K D S -U W B system w i t h spreading factor Ns = 6 51 Figure 4.7: BER performance of frequency domain turbo equalizers for a BPSK DS-UWB system with spreading factor N3 = 12 5 2 5 6 7 8 9 10 11 12 13 ,0I°9,0<W Figure 4.8: B E R performance of frequency domain turbo equalizers for a 4BOK D S -U W B system w i t h spreading factor Ns = 6 53 Multiuser Turbo Equalizer, Perfect a priorij 5 6 7 8 9 10 11 12 13 10l°9,o<W Figure 4.9: BER performance of frequency domain turbo equalizers for a 4-user BPSK DS-UWB system with spreading factor N„ = 12 54 Two user BPSK Turbo Equalizer, Perfect a priori 5 6 7 8 9 10 11 12 13 Figure 4.10: B E R performance of frequency domain turbo equalizers for a 4 B O K D S -U W B system w i t h spreading factor' Ns = 6, t reat ing it as a 2-user B P S K D S - U W B system 55 Chapter 5 Conclusions In this thesis, we considered frequency domain equalization for MBOK DS-UWB sys-tems. The BER performances of various frequency domain equalization techniques were compared with that of time domain equalization techniques for single user sys-tems. Symbol based frequency domain equalizers were first defined for BPSK DS-UWB systems. Later, it was shown that a single user 4 B O K system can be seen as two-user BPSK system employing orthogonal codes. We then defined symbol based equalizers for a 4 B O K system. We further analyzed the computational complexities of these equalization techniques for single user BPSK DS-UWB systems. Through simulations, it was shown that the frequency domain equalization techniques can offer better trade off between performance and complexity than time domain equalization techniques. The performance gain is more prominent for high data rate DS-UWB systems employing short spreading sequences over severely dispersive channels such as C M 4 . We then considered multiuser DS-UWB systems. Iterative frequency domain mul-tiuser detectors viz. SIC and PIC, were derived and their average BER performance was simulated. We then expressed a single user 4 B O K system as a two user BPSK system and applied these multiuser receivers to detect transmitted bits. The perfor-mance of multiuser detectors was found to almost saturate after two decision feedback iterations. The performance of multiuser detection schemes for single user 4 B O K sys-tem was found to be better compared to symbol based equalizers in chapter 2 but not as good as chip based equalizer. We later considered coded DS-UWB systems. We proposed low complexity fre-quency domain turbo equalizers for single user BPSK and 4 B O K DS-UWB systems and their performance was evaluated through simulations. We then considered coded multiuser DS-UWB system. Combining the single user frequency domain turbo equal-56 ization with soft interference cancelation, we derived a frequency domain multiuser turbo detector. We used this multiuser turbo detection technique to detect single user coded 4BOK system by considering it as a two-user BPSK system. The performance improvement with use of turbo equalization techniques was found to be significant. Especially, in the case of multiuser systems, the performance gain was found to be very high. An improvement in performance was observed when multiuser turbo detector was used for single user 4BOK system, by considering it as a two-user BPSK system, compared to single user turbo equalizer. 5.1 Future Work There are many interesting problems which can be pursued for future work. • One of the main challenges for a UWB system is to mitigate the interference from narrowband systems [35]. Narrowband interference rejection techniques which operate in frequency domain have been studied in the literature for DS-CDMA systems [36]. These interference rejection schemes can be combined with the equalization and multiuser techniques presented in this thesis to improve the performance of DS-UWB systems by operating entirely in frequency domain. • Recently, multi-input multi-output (MIMO) UWB systems are being considered to further increase the data rate of UWB systems. Frequency domain equaliza-tion for space-time block coded systems was studied in [37]. These equalization techniques can be applied for MIMO DS-UWB systems. 57 Bibliography [1] L. Yang and G. B. Giannakis,"Ultra-wideband communications : an idea whose time has come," IEEE Signal Process. Mag , vol. 21, issue 6, pp.26-54, Nov 2004. [2] J. Haartsen, M. Naghshineh, J. Inouye, 0. J. Joeressen, and W. Allen,"Bluetooth: vision, goals, and architecture," Mobile Computing and Communications Review , vol. 2, pp. 38-45, Oct. 1998. [3] C.R. Buffler and P.O. Risman, "Compatibility Issues between Bluetooth and High Power Systems in the ISM Band," Microwave Journal, pp. 126131, July 2000. [4] FCC Document 00-163: Revision of Part 15 of the Commission's Rules Regarding Ulra-Wideband Transmission Systems, E T Docket No 98-153, April 22, 2002. [5] "DS-UWB physical layer submission to 802.15 Task Group 3a," IEEE P802.15-04/0137r3, July 2004. [6] "Multi-band OFDM Physical Layer Proposal for IEEE 802.15 Task Group 3a," available on line www.multibandofdm.org. [7] S. Oh-Soon, S. S. Ghazzemzadeh, L. J. Greenstein and V. Tarokh, "Perfor-mance evaluation of MB-OFDM and DS-UWB systems for wireless personal area networks," in Proceedings of IEEE International Conference on Ultra-Wideband (ICU), Zurich, pp. 214-219, September 2005. [8] K. Takizawa and R. Kohno, "Low-complexity rake reception and equalization for MBOK DS-UWB systems," Global Telecommunications Conference, 2004-GLOBECOM '04. IEEE, vol.2, pp.1249 - 1253, 29 Nov.-3 Dec. 2004. [9] A. Parihar, L. Lampe, R. Schober and C. Leung, "Analysis of equalization for DS-UWB systems," in Proceedings of IEEE International Conference on Ultra-Wideband (ICU), Zurich, pp.170-175, September 2005. 58 [10] Z. Lin, B. Premkumar and A.S. Madhukumar, "Tap selection based MMSE equal-ization for high data rate UWB communication systems," IEEE International Symposium on Circuits and Systems, 2005. ISCAS 2005, vol. 6, pp. 5421-5424, May 2005. [11] M. E. Sahin and H. Arslan,"Inter-symbol interference in high data rate UWB communications using energy detector receivers ," in Proceedings of IEEE In-ternational Conference on Ultra-Wideband (ICU), Zurich, pp.176-179, September 2005. [12] D. Falconer, S. L. Ariyavisitakul, A. B. Seeyar and b. Eidson, "Frequency domain equalization for single-carrier broadband wireless systems," IEEE Commun. Mag., vol 40, pp.58-66, Apr 2002. [13] N. Benvenuto and S. Tomasin, "On the comparison between OFDM and single carrier modulation with D F E using a frequency-domain feedforward filter," IEEE Trans, on Commun., vol 50, no. 6, pp. 947-955, June 2002 [14] Y. Ishiyama and T. Ohtsuki, "Performance evaluation of UWB-IR and DS-UWB with MMSE-frequency domain equalization," Global Telecommunications Confer-ence, 2004. GLOBECOM '04. IEEE, vol 5, pp.3093-3097, 29 Nov.-3 Dec. 2004. [15] H. Sato and T. Ohtsuki, "Performance evaluation of frequency domain equal-ization and channel estimation for direct sequence - ultra wideband (DS-UWB) system," IEE Proceedings on Communications , vol 135, issue 1, pp.93-98, 2 Feb. 2006. [16] Y. Wang and X. Dong, "A time-division multiple-access SC-FDE system with IBI suppression for UWB communications," IEEE Journal on Selected Areas in Communications, vol. 24, issue 4, pp. 920-926, Apr. 2006. [17] S. Tomasin and N. Benvenuto,"Frequency-domain interference cancellation and nonlinear equalization for CDMA systems," IEEE Trans. Wireless Commun., vol 4, pp.2329-2339, Sept 2005. ' [18] D. Falconer and S. L. Ariyavisitakul, "Broadband wireless using single carrier and frequency domain equalization," in The 5th International Symposium on Wireless Personal Multimedia Communications, 2002. , vol 1, pp.27-36, Oct 2002. 59 [19] Q. Li and L. A. Rusch, "Multiuser detection for DS-CDMA UWB in the homw environment," IEEE Journal on Selected Areas in Communications, vol. 20, no. 9, pp. 1701-1711, Dec. 2002. [20] C. Douillard, M. Jezequel, C. Berrou, A. Picart, P. Didier, and A. Glavieux, "Iterative correction of intersymbol interference: Turbo equalization," European Trans. Telecomm., vol. 6, pp. 507-511, Sept-Oct 1995. [21] G. Bauch, H. Khorram, and J. Hagenauer, "Iterative equalization and decod-ing in mobile communications systems," in The Second European Personal Mo-bile Communications Conference (2.EPMCC'Sr) together with 3. ITG-Fachtagung "Mobile Kommunikation", pp. 307-312, V D E / I T G , September/October 1997. [22] A.F.Molisch, J.R. Foerster and M. Pendergrass, "Channel models for ultrawide-band personal area networks ," in IEEE Wireless Commun., vol.10, no.6, pp.14 -21, Dec. 2003. [23] A. Saleh and R. Valenzuela, "A Statistical Model for Indoor Multipath Propa-gation," IEEE Journal on Selected Areas in Communications, vol. SAC-5, no. 2, pp. 128-137, Feb. 1987. [24] H. Sari, G. Karam and I. Jeanclaude, "Frequency domain equalization of mobile radio and terrestrial broadcast channels," Global Telecommunications Conference, 1994. GLOBECOM '94. IEEE, vol 5, pp. 1-5, Nov.-Dec. 1994. [25] T. Walzman and M. Schwartz, "Automatic equalization using the discrete Fourier domain," IEEE Trans. Inform. Theory, vol. 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Signal Processing, vol. 50, no. 3, pp.673-683, March 2002. [32] C. Laot, R. L. Bidan and D. Leroux, "Low-complexity MMSE turbo equalization: a possible solution for EDGE," IEEE Trans. Wireless Commun., vol. 4, no. 3, pp. 965-974, May 2005. [33] B. Ng, D. Falconer, K. Kansanen and N. Veselinovic, "Frequency domain it-erative methods for detection and estimation," EURASIP 14th 1ST Mobile and Wireless Communications Summit, Dresden, 19-23 June 2005. [34] X. Wang and H. V. Poor, "Iterative (turbo) soft interference cancellation and decoding for coded CDMA," IEEE Trans. Commun., vol. 47, no. 7, pp.1046-1061, July 1999. [35] L. Zhao and A. M. Haimovich, "Performance of ultra-wideband communications in the prescence of interference," IEEE Journal on Selected Areas in Communi-cations, vol. 20, no. 9, pp.1684-1691, Dec 2002. [36] J. A. Young and J. S. Lehnert, "Analysis of DFT-based frequency excision algo-rithms for direct-sequence spread-spectrum communications," IEEE Trans. Com-mun., vol. 46, no. 8, pp.1076-1087, Aug 1998. [37] N. Al-Dhahir, "Single-carrier frequency-domain equalization for space-time block-coded transmissions over frequency-selective fading channels ," IEEE Commun. Letters, vol 5, issue 7, pp.304-306, July 2001. 61 Appendix A Derivation of Frequency Domain Iterative Decision Feedback Equalizer We assume that the frequency domain sequence S(n) is independent and identically distributed with zero mean and variance cr|. The problem is to minimize [26] Jq = E [\y[k] - s[k]\*} N-l = ^ E M i n * ) - s ( » ) i 2 ] n=0 N-l N2 n=0 \Wq{n)R(n) + Bq(n)Sq-1(n) - S(n) (A.l) subject to constraint N-l E = o n=0 To minimize Jq, its sufficient to minimize Jq{n) = E \Wq{n)R{n) + Bq(n)Sq-\n) - S(n) (A.2) (A.3) for all n = 0,1 , . . . ,N- 1. 62 T h e c o s t f u n c t i o n t o b e m i n i m i z e d f o r e a c h n, i s g i v e n b y N-l J | ( n ) = E \Wq{n)R{n) + Bq(n)Sq-\n) - S{n)\2 +0[jjYl J ( A ' 4 ) 71=0 w h e r e (3 i s t h e L a g r a n g e m u l t i p l i e r t o a c c o u n t f o r t h e c o n s t r a i n t . T h e c o r r e l a t i o n b e t w e e n s e q u e n c e s S(n) a n d S ' 9 - 1 ^ ) i s a s s u m e d t o b e E S(n)Sq-\n')* = pq5(n - ri) (A.5) T h i s a s s u m p t i o n h o l d s t r u e i n m o s t o f t h e c a s e s . N o w , N - l Jqp(n) = E \Wq{n)R(n) + Bq(n)Sq-\n) - S{n)\2 + /3 ( — £ Bq(n) 71=0 E \(Wq{n)H(n) - l)S{n) + Bq{n)Sq-\n) + Wq(n)Z(n) N-l 71=0 = E \{Wq{n)H{n) - l)S(n) + Bq(n)Sq~l{n)\2 + No2\Wq(n)\2 o2s\Wq(n)H(n) - 1 | 2 + (Wq{n)H(n) - l)Bq{n)*o2spq + (Wq(n)H(n) - l)*Bq(n)o2pq* + <J2s\Bq[n)\2 + No2\Wq(n)\2 n=0 (A.6) D i f f e r e n t i a t i n g J g ( n ) w . r . t S 9 ( n ) a n d e q u a t i n g t h e d e r i v a t i v e t o z e r o , w e o b t a i n Bq(n) = -(Wq(n)H(n) - \)pq o2sN (A.7) U s i n g t h e c o n s t r a i n t Yln=o Bq(n) = 0, w e g e t 63 N - l P = - 4 ^ £ ( W " ( n ) f f ( n ) - l ) n=0 = -a2pqN(7q - 1) (A.8) where f ^ E S ^ W W Substituting (A.8) in (A.7), we obtain B 9 ( n ) - -pq{Wq(n)H{n) - 7 9 ) (A.9) Now, differentiating «/J(n) w.r.t i y 9 ( n ) and equating the derivative to zero, we obtain qfff(n)*(l + |p 9 |V) No2 + a2s{l-\pq\2)\H(n)\2 We can neglect the factor 1 + \pq\2j9, as it is independent of n. Therefore, ^ W = ^ + 4 ( l - W ' ) | g ( n ) P ( A - U ) 64 Appendix B Derivation of Frequency domain M M S E Turbo Equalizer T h e c o s t f u n c t i o n t o b e m i n i m i z e d f o r e a c h n, i s g i v e n b y [32] Mn) = E[\W(n)R(n) + B(n)S(n)-S(n)\2]+P — ]T *(«•)) 03-1) 3 n=0 w h e r e (3 i s t h e L a g r a n g e m u l t i p l i e r . N o w , / M J V S - I \ J0{n) = E[\W(n)R(n) + B(n)S(n)-S(n)\2]+(3 — £ B(n) \ s n=0 / = £ [|(W(ra)#(n) - l )S(n) + 5(n)5(n) + W{n)Z(n)\2) = E [|(W(n)#(n) - l )S(n) + £ ( n ) S ( n ) | 2 ] + M i V > 2 | W ( n ) | 2 / 1 MN,-1 \ - <7||W(ra)#(n) - 1|2 + cr§[\B(n)\2 + (W(n)H(n) - l)B(n)* / MNs-l \ HW(nyH(ny-l)B(n)} + MNsa2\W(n)\2 + 0[— £ B(n)\ \ 3 n=0 / ( B . 2 ) 65 D i f f e r e n t i a t i n g Jp{n) w . r . t B(n) a n d e q u a t i n g t h e d e r i v a t i v e t o z e r o , w e o b t a i n B(n) = -(W(n)H(n) - 1) - ^j^P (B.3) U s i n g t h e c o n s t r a i n t Yln^o'1 = 0, w e g e t M J V . - l 0 = -4 E (W(n)H(n) - 1) n=0 = - a f M i V s ( / i - l ) . ( B . 4 ) w h e r e //= ^ ES _ 1 W ( n ) t f ( n ) S u b s t i t u t i n g ( B . 4 ) i n ( B . 3 ) , w e o b t a i n £ ( n ) = // - i y ( n ) # ( n ) •" ( B . 5 ) N o w , d i f f e r e n t i a t i n g Jp{n) w . r . t - W ( n ) a n d e q u a t i n g t h e d e r i v a t i v e t o z e r o , w e o b t a i n W { U ) ~ (al-o*s)\H(n)\* + MN.** ( R 6 ) W e d e f i n e W(N) = T-2 2 M 5 / " N I 9 7^77-^  (B-7) ( ° s — a l ) l - ^ ( n ) l + MNsa2 1 M J V . - l — £ W(n)£T(n) (B.8) A* MN, T h e n , e q u a t i o n ( B . 6 ) i s e q u i v a l e n t t o W ( n ) - \W(n) (B .9) w h e r e A = a | - a | / i (B .10) T h e r e f o r e , \i = A / 2 ( B . l l ) 66 U s i n g ( B . 1 0 ) a n d ( B . l l ) , w e o b t a i n a A = n ( B . 1 2 ) S u b s t i t u t i n g ( B . 5 ) , ( B . 9 ) i n ( 4 . 5 ) , w e o b t a i n J ( n ) = (*l-elwtw + MN,o> tA + ~ ^ + ^ " + °* < B 1 3 ) U s i n g ( B . 9 ) - ( B . 1 2 ) a n d ( 4 . 3 ) , w e o b t a i n ( M ^ j 2 Y.] E[\W(n)R(n) + B(n)S(n)-S(n)\2} n=0 MNs-l M i V s 1 M A T , (tf| - 2<r|/x + /i<r|) 1 o - l ( l - / x ) ( B . 1 4 ) MAT, T h u s , f o r M M S E f i l t e r i n g E(\y[k] - #]|2) = •jj^oiO- - ( B . 1 5 ) 67 

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