Coding for the Rayleigh fading channel
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
The problem of effective coding for the Rayleigh fading channel is addressed. A signal transmitted over the Rayleigh fading channel experiences quasi-periodic deep fades in the signal amplitude, and random phase shifts. The fades in signal amplitude are the cause of error events and limit the bit error rate of an uncoded system to about 10-4 at a signal-to-noise ratio of 30 dB. For applications where a lower error rate is desired, more sophisticated methods of transmission and detection are required. We present an extensive generalised analysis of the probability of error of maximum likelihood sequence estimation techniques for the Rayleigh fading channel This analysis provides the criteria for good code design for the Rayleigh fading channel and we extend the recently developed area of geometrically uniform (GU) codes for the AWGN channel, to the Rayleigh fading channel, and present the results of searches for good GU trellis codes. The concept of geometric uniformity is extended to set of points to form geometrically uniform partitions of signal sets. The GU partitions readily allow powerful multi-level codes to be defined with good distance properties. Multi-level codes have the advantage of outperforming trellis codes in terms of decoding complexity at the cost of greater decoding delay. Good multi-level codes over GU partitions are presented and compared with similarly performing trellis codes. Finally a system is presented which combines the techniques of multiple symbol differential detection (MSDD) with multi-level coding to obtain a good probability of error performance without assuming coherent detection, or ideal channel state information.