UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Gallager’s random coding exponent for differential space time modulation Srinivasan, Siddharth K.


In this thesis, we study differential space-time modulation with multiple transmit and receive antennas over a frequency non-selective block fading channel in the absence of channel state information (CSI) at both the transmitter and the receiver. We focus on the analysis of the random coding exponent proposed by Gallager for such spacetime channels employing differential modulation with finite signal sets, and consider multiple symbol differential detection (MSDD) with an observation window size N. The underlying principle of MSDD is to utilize an increased observation window of N > 2 consecutively received space-time samples to yield decision variables on N - 1 spacetime data symbols. We thus take into account the channel memory, and can improve power efficiency over conventional differential detection, which employs N = 2. We extend previous work for a similar setup, in that we consider channels where the fading coherence interval is different from the MSDD observation window N, and can be arbitrary with L independent fading realizations per coding frame. We analyze the effect of arbitrary fading coherence intervals on the random coding exponent, and therefore analyze the achievable performance of coded transmission over block fading channels with low to moderate code lengths, i.e. with decoding delay constraints. In this context we also analyze space-time transmission systems with spatial correlation between antennas. Such an analysis allows for a fair comparison of DSTM with MSDD where the window size may vary but the coded diversity remains fixed. We also devise upper and lower bounds and approximations for the random coding exponent, which allows us to not only bound the achievable performance of such space-time systems but also allows for efficient numerical evaluation of the random coding exponent by limiting the search space for the metric calculation. To this end, we make use of tree-search based sphere decoding algorithms for efficient decoding, and along with novel stopping criteria to control the accuracy of the approximation and correspondingly the computational complexity, we apply these sphere decoders for a reduction in complexity cost upto many orders of magnitude. The presented numerical results provide useful information on the performance of coded differential space-time transmission for short to moderate code lengths.

Item Media

Item Citations and Data


For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.