Symbol-by-symbol MAP demodulation of CPM and PSK signals on Rayleigh flat-fading channels

Abstract

Demodulation using the symbol-by-symbol maximum a posteriori probability (MAP) algorithm is presented. The algorithm is derived for the case of continuous phase modulation (CPM) signals transmitted over Rayleigh flat-fading channels, and a corresponding receiver structure is specified. It is shown that the MAP algorithm requires computing, for each trellis branch, the sum of the products of the weights of all paths through the trellis which pass through that branch, and that this generic computational problem can be solved efficiently by an approach that uses a forward and backward recursion through the trellis. Simulation results are presented which show both the hard and soft decision performance of the MAP receiver to be robust, even in the presence of fade rates of up to 30% of the symbol rate. The application of the receiver concept to phaseshift keying (PSK) signals is also discussed, and then evaluated via simulation. The concept of joint demodulation and decoding using iterative processing techniques is introduced. It is shown that the MAP receiver is well suited for iterative processing applications due to its use of a priori symbol probabilities and its production of optimal soft decisions. Simulation results for the reception of quaternary PSK (QPSK) show that the bit error rate (BER) performance of the iterative MAP receiver can approach that of a receiver operating with perfect knowledge of the fading process.

An algebraic receiver for full response CPM demodulation

“…Alternatively, a number of sub-optimum detectors have been proposed, but the required computational burden is still high [3], [4]. In terms of blind methods, [5] showed that the constant modulus criterion is not capable of equalizing a CPM signal.…”

“…In this case, considering the full-response modulation and using (4), the signals at the output of the receiver shown in figure 1 will be:…”

Equalization of Time-Varying Channels

“…In related work, Gertsman and Lodge [GL97] showed that the forward-backward algorithm, with per-branch linear prediction, can be used for near-MAP symbol detection under AR time-selective channels and CM alphabets. Independently, these ideas were generalized this approach to doubly selective channels and general signal alphabets by Hart and Pasupathy [HP00] and Davis, Collings, and Hoeher [DCH01].…”

Detection by multiple trellises

“…The FB algorithm in (14) operates on a trellis whose number of states is the number Ξ of states of the modulator-channel FSM times the number L of states of the channel parameter Markov chain. This can be interpreted as a "super-trellis" comprising L trellises, each with Ξ states.…”

“…In the case of phase-uncertain communications, parameter estimation may be embedded in the detection process, explicitly [5] or implicitly [6]- [9]. In [10]- [14], linear predictive receivers for fading channels are proposed, considering the Clarke model for fading channels [15], [16]: these receivers exploit the correlation characteristics of the fading process to predict its evolution. Another general approach consists of describing the evolution of the fading process through a suitable Markov chain [17]- [19], and then taking this model into account in the receiver design [20]- [24].…”