Polar quantizing for coded PSK transmission

The issue of demodulator quantization prior to decoding in error control systems employing M-ary phase-shift keying (PSK) as a modulation technique is considered. The use of angle-only, or polar, quantization with J⩾M levels, which is an easily implemented alternative to rectangular quantization, is described. The R₀ parameter is presented as an effective indicator of coding potential for quantized M-ary PSK channels, and different designs in the R₀ context are discussed. The principal results are that for J=2M, a polar quantizer satisfies the necessary condition for optimality, and it is conjectured that the design is in fact optimal. The corresponding performance closes about half the gap (in decibels) between the hard-decision demodulator and the unquantized demodulator. Angle-only quantization, in the limit of fine precision, costs only a fraction of a decibel in performance for typically operated coded 8-PSK and 16-PSK. Numerical results for quantizers with J=2M and J =4M are presented, and the case of an added erasure zone is considered