Pilot symbol-assisted detection of CPM schemes operating in fast fading channels

We present in this paper a coherent detection technique for continuous phase modulation (CPM) operating in the Rayleigh Bat fading channel, The technique is based on the idea of inserting periodically data dependent pilot symbols that force the CPM signal to pass through known phase states, This transmission format enables the receiver to extract from the received signal the channel fading gains at regularly spaced instants, When coupled with proper channel estimation filters, very accurate channel state information (CSI) can be estimated at the receiver for fading compensation, Moreover, the accuracy of the CSI can be further refined by adopting a multiple-pass decoding approach, The paper discusses a) the pilot symbol encoding technique required to force a M-level CPM scheme with a modulation index of p/M, p an integer, to return periodically to a set of known phase states, b) the optimal channel estimation filters, c) a trellis-based preceding technique that can reduce the bit error rate in M-level CPM systems by close to 50%, and d) a multiple-pass channel estimator/demodulator. Analytical and simulation results are presented for minimum shift keying (MSK), Gaussian MSK, and four-level continuous phase frequency shift keying with a modulation index of 1/4, It is observed that our pilot symbol-assisted CPM schemes exhibit no irreducible error floor even at a channel fade rate of three percent the symbol rate, On the contrary, the implicit phase coding in CPM and the accurate CSI provided by the pilot symbols lead to a diversity effect in the bit error rate curves of these modulation schemes, Although only M-level CPM schemes with a rational modulation index of p/M are considered in this paper, we believe the idea of data dependent pilot symbols can be custom tailored to many other rational modulation indices of interest.