Linear receivers for correlatively coded MSK

Using an in-phase-quadrature (I-Q) receiver with a proper choice of carrier-phase offset, it is possible to demodulate many spectrally efficient modified MSK schemes. A study of correlatively coded MSK schemes with I-Q receivers is carried out, and it is shown that duobinary MSK and (1 + 2D + D sq)/4 MSK are good performance-bandwidth trade-offs among first-degree and second-degree correlative coding polynomials. The optimal design of the receivers is subject to the constraint of a finite-duration impulse response, especially for asymptotic cases of vanishingly small SNR and aribitrarily large SNR. A filter design which is based on a constraint of zero-intersymbol interference for PAM-based approximations of the signals is considered. The optimized linear I-Q receivers are given for (1 + D)/2 MSK and (1 + 2D + D sq)/4 MSK. The receivers are found to be only 0.28 and 1.24 dB poorer than the optimal (Viterbi) receivers at high SNR. Thus, for a generalized MSK signal, the simple linear receiver can result in a performance comparable to that of the more complicated Viterbi receiver.