Bit Error Probability and Computational Complexity of Bi-directonal Fano Multiple Symbol Differential Detectors

We present in the paper a suboptimal multiple-symbol differential detector (MSDD) for differential PSK (DPSK) in Rayleigh flat fading channel that uses the Fano Algorithm as its decoding engine. In contrast to a conventional Fano decoder that only searches forward in time for the most promising transmitted pattern, our Fano decoder searches also in the reverse direction, thus providing a mechanism for error detection and correction. The resultant detector, termed a Bi-Fano MSDD, is capable of delivering excellent error performance at moderate implementation complexity over a wide range of signal-to-noise ration (SNR) and fading rates. As an example, for DQPSK modulation and a Doppler frequency of 3 percent the symbol rate, our Bi-Fano MSDD attains almost the same bit-error probability (BEP) performance as the sphere decoder (an efficient implementation of the optimal MSDD) and there is no noticeable irreducible error floor. The most interesting thing is that the computational complexity of the Bi-Fano MSDD is a very stable function of the SNR. In contrast, the sphere decoder has a complexity that grows exponentially as the SNR decreases. In conclusion, the Bi-Fano MSDD incorporates the desirable attributes of the sphere decoder and the DF-DD into one single embodiment. This is consistent with the observation that the Fano decoder is essentially an intelligent DF-DD that uses the accumulated path metric and a running threshold to guide its movement along the decoding tree