Modulation and Coding for Noncoherent Communications

Abstract

Abstract. Until recently, the theory of noncoherent communications was premised on the use of orthogonal multi-pulse modulation such as frequency shift keying. The main drawback of this modulation scheme has been its poor spectral efficiency (rate/bandwidth). This paper considers instead the more general non-orthogonal multi-pulse modulation (NMM) technique. Optimal and suboptimal noncoherent detection strategies for NMM are reviewed and their asymptotic (high SNR) performances are characterized for the additive Gaussian as well as the Rayleigh fading channels. The resulting non-Euclidean distance measures are then used to design NMM signal sets that yield significantly higher bandwidth efficiencies than their orthogonal counterparts. NMM in conjunction with convolutional coding is also studied as a way to improve energy efficiency. Several optimal convolutional codes are examined together with our signal designs. An introduction to equalization on the noncoherent channel is also presented and illustrated by example. This paper thus contains several new results and attempts at the same time to give a tutorial exposition of the subject of noncoherent communications.

Signal design and convolutional coding for noncoherent space-time communication on the block-Rayleigh-fading channel

“…Luckily, however, for high SNRs, the Chernoff bound displays the same dependence on the two signals as the asymptotically tight expressions found in [5], [11], so that at least asymptotically, signals are designed by minimizing a lower bound on the SER. However, in [13] and [14] the Chernoff bound on the pairwise error probability is further loosened by upper-bounding it [13, eq.…”

“…We find that (11) The strategy is to minimize the second term in (11) under the constraint that the additional signal have unit energy . We initialized each optimization step with a random "unitary" signal.…”

“…As a signal design criterion we choose to minimize the asymptotic union bound (AUB) on the symbol error rate (SER), derived for the single-antenna channel in [11] and for the general space-time channel in [5]. This criterion depends on all of the pairwise error probabilities, which in turn admit asymptotically tight expressions for channel models in which even correlated fading (across antennas) may be present.…”

Joint data detection and estimation of time‐varying multipath rayleigh fading channels in asynchronous DS‐CDMA systems with long spreading sequences

“…The employed modulation scheme is a special case of the orthogonal multi-pulse modulation introduced in [13] and is implemented with the Walsh (Hadamard) code. The system resembles the uplink of an IS-95 system in that the narrow-band bit stream is spread by one of M possible Walsh codewords, which are not used for user separation, but for M -level modulation.…”

Code design for the low SNR noncoherent MIMO block Rayleigh fading channel

“…This is because maximizing B intra does not depend on either r k or π k as they occur as constant multiplicative factors in the expression. The problem of finding the best constellation within each sphere is studied for instance in [11][12][13], and so we may use these constellations and their minimum distances for this stage of the optimization. This procedure may be adopted for each iteration corresponding to a set of {l k } K k=1 with the minimum distance, {r k } K k=1…”