The reduced-state Viterbi algorithm (VA), with feedback incorporated into the structure of path metric computations is presented for the differential detection of M-ary DPSK signals. The number of states in the trellis of the VA is reduced to M, and the phase reference used for differential detection is estimated recursively for each state in the trellis, along the surviving path ending in each state. The proposed differential detection is called reduced-state Viterbi differential detection (RSV DD). The most simple form of RSV DD, decision feedback DD (DF DD), is also derived. It allows only a single path to survive, so that a symbol-by-symbol decision is made. The BER performances possible with the proposed RSV DD and DF DD schemes are evaluated by means of computer simulations for 4DPSK transmission over AWGN and Rayleigh fading channels.
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