Inverting alternate symbols of the encoder output of a convolutionally coded system provides sufficient density of symbol transitions to guarantee adequate symbol synchronizer performance, a guarantee otherwise lacking. Although alternate symbol inversion may increase or decrease the average transition density, depending on the data source model, it produces a maximum number of contiguous symbols without transition for a particular class of convolutional codes, independent of the data source model. Further, this maximum is sufficiently small to guarantee acceptable symbol synchronizer performance for typical applications. Subsequent inversion of alternate detected symbols permits proper decoding.

The selection of a particular signal set design for a bandwidth-constrained multiple amplitude-and-phase-amplitude-and-phase-shift-keyed (MAPSK) communication system with a linear additive Gaussian noise channel is influenced by a number of factors, such as average and/or peak signal-to-noise ratio for a given error probability, dynamic range of signal amplitudes, simplicity of generation and detection, and number of bit errors per adjacent symbol error (Gray code properties). This paper compares two possible quadrature amplitudes-shift-keyed (QASK) signal sets when the number of bits per symbol is odd (for the even-bit case, the square array is the only viable QASK choice). The "symmetric" QASK version outperforms the "rectangular" QASK set at a very modest implmentation penalty.

A carrier regeneration loop which generates highly coherent quadrature reference signals for quadrature amplitude-shift keying (QASK) demodulation is presented. The loop employs the principle of decision feedback and has a structure analogous to a decision feedback loop for quadriphase signals suggested earlier in the literature. The error probabihty performance of QASK is computed in the presence of the noisy carrier reference signals provided by the above loop. It is demonstrated that when the ratio of data rate to loop bandwidth is 50 or greater, then for all practical purposes, ideal QASK error probability performance is achieved.

In this paper, we focus our attention on the decisionfeedback approach to carrier synchronization of offset quadrature phase-shift-keyed (QPSK) and more generally offset quadrature amplitude-shift-keyed (QASK) systems. In particular, we present two decision-feedback loops for tracking offset QPSK and offset QASK, which are modifications of comparable loops previously given in the literature for carrier synchronization of QPSK and QASK respectively. The performance gains obtained using such synchronization techniques are discussed. In particular, we show that the use of offset-quadrature communications rather than conventional quadrature communications permits a doubled loop bandwidth at fixed data rate, signal-to-noise ratio and probability of error. However, the more efficient phase-tracking loop (decision-feedback as opposed to phase-locked loop) used reduces substantially the total signal-to-noise ratio required.

Selection of a particular signal set array for a bandwidthConstrained multiple phase-and-amplitude-shift-keyed (MPASK) communication system for a linear additive Gaussian noise channel requires consideration of factors such as average and/or peak power versus symbol error probability, signal amplitude dynamic range, simplicity of generation and detection, and number of bit errors per symbol error (Gray code properties). A simple technique is presented for generating and optimally detecting the honeycomb (hexagonal.) signal set, i.e., the signal set that has the tightest sphere-packing properties. The symbol and bit error probability performance of this set is compared to other two-dimensional signal sets that have been investigated in the literature, and is shown to be slightly superior from an average power standpoint. The paper concludes with a comparison of all of these signal sets from the standpoint of the factors listed above.