UBC Theses and Dissertations
Optimal decoding of PSK and QAM signals in frequency nonselective fading channels Bouras, Dimitri
In this thesis, the maximum likelihood sequential decoder for the reception of coded digitally modulated signals with single or multiamplitude constellations transmitted over a multiplicative, frequency nonselective fading (Rayleigh or Rician) channel and corrupted by additive white Gaussian noise (AWGN), is derived. It is shown that its structure consists of a combination of envelope, multiple differential¹ and coherent detectors. The outputs of each of these detectors are jointly processed by means of an algorithm which is presented in a recursive form. The derivation of this new receiver is general enough to accommodate uncoded as well as trellis coded Phase Shift Keying (PSK) and Quadrature Amplitude Modulated (QAM) schemes. Differentially encoded signals, such as the π/4-shift DQPSK scheme which has been selected as the new transmission standard for the emerging all-digital North American and Japanese cellular system, can be also incorporated. Furthermore, there is no assumption made on the power spectral density (or equivalently on the autocorrelation function) of the fading process, although it is considered to be known to the receiver. In order to reduce the overall receiver implementation complexity, several reduced complexity, near optimal versions of the algorithm are presented. These reduced complexity receivers are based on the use of only few multiple differential detectors. Performance evaluation results for reduced complexity trellis coded π/4-shift DQPSK and π/4-shift 8-DQAM systems have demonstrated that the proposed receivers dramatically reduce the error floor occurring due to fading. For example, for the π/4-shift DQPSK scheme operated in a fast (B[formula omitted]T=0.l25) Rayleigh flat-fading channel at a Signal-to-Noise ratio (SNR) of about 25 dB, the new reduced complexity receiver structures result in a bit error rate (BER) reduction of more than three orders of magnitude as compared to a conventional Viterbi receiver. For a slower fading channel, these gains are even higher. What is even more interesting, though, is that this performance was achieved by employing only up to third order multiple differential detectors, thus maintaining reasonable levels of implementation complexity. By further increasing the order of the employed multiple differential detectors, the obtained BER performance improvements were found to be minimal. To verify experimentally the effectiveness of the proposed receivers and to gain additional insight into some of the real-life implementation problems involved, we designed and realized in hardware a prototype π/4-shift DQPSK modem. Although its transmitter was designed with off the shelf digital TTL chips, linear analog devices and RF modules, its receiver was implemented by means of a TMS320C30 Digital Signal Processor. Employing this "flexible" receiver, the proposed algorithms could be evaluated very efficiently. The various experimental BER results obtained were in excellent agreement with the equivalent results obtained by means of computer simulation. Motivated by these very encouraging experimental performance results, it is believed that LSI/VLSI implementation of such a π/4-shift DQPSK modem would be a very worthwhile task. ¹ As it will be explained later on, a k[formula omitted] order multiple differential detector is a differential detector employing a k[formula omitted] symbol delay element.
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