Efficient Digital Communication over the Time Continuous Rayleigh Fading Channel
Frequency flat, fast Rayleigh fading may be considered the most critical disturbance in a wireless communication system. In its most general form, it is modeled as a multiplicative time continuous random (zero mean complex Gaussian) distortion of the transmitted signal. In order to achieve an efficient communication here, each part of the communication link must be carefully designed based on the properties of the time continuous channel. Such an approach is distinct from most previous works, which have used strategies developed for the additive white Gaussian noise channel (AWGN) as starting points.
Crucial in this development is how to deal with the deep fades and the rapid fluctuations of the received signal power. To reduce the influence of the deep fades on the error probability, diversity techniques must be used. Coded interleaved modulation can be regarded one such strategy, where the diversity effect arises as a result of nearby encoder output symbols being subjected to statistically independent fading. Central in achieving this independence is the interleaver, which spreads the symbols in time. A higher diversity order is obtained if the encoder output bits, instead of symbols, are interleaved. By also using codes of lower rates, the diversity is increased even further. To avoid bandwidth expansion here, the channel symbol constellation must be expanded accordingly. The resulting system is referred to as bit-interleaved channel symbol expansion diversity (CSED) and is the best low-complexity coded modulation scheme presented so far for the Rayleigh fading channel.
On the fast fading channel, coding is only part of the solution, however. Here, matched filter detectors originally developed for AWGN are unable to efficiently handle the rapid (compared with the signaling rate) fluctuations of the received signal power. More sophisticated solutions are needed. It is essential to make the transition from the time continuous received signal to a discrete representation in the receiver, without losing too much accuracy. Both an adequate number of discrete observables and a sufficiently long observation interval are required. When this is fulfilled, error probability curves with steeper slopes and considerably lower error floors than those of matched filter based receivers are obtained. The steeper slopes are results of the implicit diversity of the random message component in the received signal, which is captured when multiple discrete observables (per symbol interval) are used. This effect is more pronounced the faster the fading is, therefore uncoded signaling has a potentially better performance at fast fading than in slow fading.
Use of observation intervals larger than the symbol interval in the receiver, immediately leads to detectors based on sequence detection. The MAP (maximum aposteriori) sequence detector becomes prohibitively complex, consequently simpler suboptimal detectors are required. A near optimal detector needs to maintain only a small fixed number of candidate symbol sequences as the length of the received message increases. This is in contrast to the MAP sequence detector, where the number of sequences grows exponentially in the length of the message. By minor modifications, the suboptimal detector can also produce the bitwise soft outputs needed in the decoder part of a bit-interleaved CSED system.