A multiple-bit differential-detection method has been proposed for the reception of radio signals modulated with offset quadrature phase-shift keying (offset QPSK or OQPSK). The method is also applicable to other spectrally efficient offset quadrature modulations.

The Asymptotic Upper Bound on the Average Bit-Error Probability for a receiver based on the proposed method has been computed as a function of the bit-energy/noise-energy ratio and the number (N) of bit periods in the observation time.

This method is based partly on the same principles as those of a multiple symbol differential-detection method for M-ary QPSK, which includes QPSK (that is, non-offset QPSK) as a special case. That method was introduced more than a decade ago by the author of the present method as a means of improving performance relative to a traditional (two-symbol observation) differential detection scheme. Instead of symbol-bysymbol detection, both that method and the present one are based on a concept of maximum-likelihood sequence estimation (MLSE). As applied to the modulations in question, MLSE involves consideration of (1) all possible binary data sequences that could have been received during an observation time of some number, N, of symbol periods and (2) selection of the sequence that yields the best match to the noise-corrupted signal received during that time. The performance of the prior method was shown to range from that of traditional differential detection for short observation times (small N) to that of ideal coherent detection (with differential encoding) for long observation times (large N).

The mathematical derivation of the present method began with the identification of an equivalent precoded continuous phase modulation (CPM) structure, first for OQPSK and then differentially encoded OQPSK. It was shown that the precoding needed to obtain the equivalence is such as to result in a ternary (0,-1,+1) CPM input alphabet that, during any given one-bit observation period, is equivalent to a binary alphabet. Next, some results of prior work by the same author on maximum- likelihood block detection of noncoherent CPM were utilized to derive a maximum-likelihood decision metric and an associated receiver structure for the precoded version that equivalently represents differentially encoded OQPSK.

The figure presents some results of computations of the bit-error performance of the present method. Because of its maximum-likelihood basis, this method is expected to be the most power-efficient method of differential detection of OQPSK. Furthermore, on the basis of the resemblance of this method to the prior multiple-symbol method of differential detection of nonoffset QPSK, the performance of a receiver based on this method is expected to improve with increasing N.

This work was done by Marvin Simon of Caltech for NASA’s Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free online at www.techbriefs.com/tsp under the Electronics/Computers category. NPO-30777

This Brief includes a Technical Support Package (TSP).
Multiple-Bit Differential Detection of OQPSK

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This article first appeared in the November, 2005 issue of NASA Tech Briefs Magazine.

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