In this paper we initially study degraded relay channels with finite-length intersymbol interference (ISI). For such channels, we show that the decode-and-forward strategy achieves the capacity, and prove a special structure for the capacity achieving distributions of the source and relay signals. We also prove that a general memoryless relay channel used with delayed feedback from the destination node to the relay node is an instance of a degraded relay channel with ISI, and observe that the delayed feedback from the destination node to the relay node does not decrease the capacity compared to instantaneous feedback. In all cases where the channel is used with delayed feedback from the destination node to the relay node the decode-and-forward scheme is optimal and the capacity is not decreased by delaying the feedback from the destination node. We extend these results to general (non-degraded) relay channels with ISI to obtain upper and lower bounds on their capacities.

The digital transmission of signals by transmitters and receivers that are time-invariant finite-state machines were investigated in general form. An average distortion criterion is used. Some general structure theorems are proved and some examples given that show improvement in performance as the memories of the transmitter and receiver are increased. Many conjectures and unsolved problems are mentioned, and areas for further study are indicated.

The capacity of a single-input single-output discrete memoryless channel is not increased by the use of a noiseless feedback link. It is shown, by example, that this is not the case for a multiple-access discrete memoryless channel. That is, it is shown that the capacity region for such a channel is enlarged if a noiseless feedback link is utilized.

The design of signals for digital communication over fast-fading Gaussian channels is considered; the emphasis is on nonorthogonal signaling schemes. A discrete channel model is used. Necessary and sufficient conditions on the transmitted signals are found that make the Bayes receiver independent of the channel parameters. By using a geometric interpretation of the resultant receiver a heuristic design criterion is developed. Then union bounds for particular nonorthogonal signaling schemes are evaluated. Nonorthogonal schemes based on modulation similar to differential-phase-shift-keyed (DPSK) modulation are found to use substantially less bandwidth than equivalent schemes based on generalized frequency-shift-keyed modulation.

The probability of error for binary permutation modulation with diversity on fading Gaussian channels is considered. Upper bounds on the probability of error are found in a simple manner. These bounds indicate that the probability of error decreases exponentially with increasing transmitter memory as long as the transmitter's rate is less than the ratio of average received signal power to noise power per unit bandwidth. This asymptotic behavior is true for any form of binary permutation modulation with the proper order of diversity. Furthermore, orthogonal signals are found to be the most efficient form of binary permutation modulation.

This paper considers the estimation of the location of a signal source; independent estimates of the signal arrival time at d different spatial locations are used to form the source location estimate. Since the maximum-likelihood estimate of the source location requires a search through at least a 3-dimensional space, easily computed estimates are considered. Their covariances are compared with the appropriate Cramér-Rao bounds.

The estimation of the scattering function of a random, zero-mean, homogeneous, time-variant, linear filter is considered. The sum of the random filter output and independent noise is the input to an estimator. The estimator structure is equivalent to a bank of linear filters followed by squared-envelope detectors; the envelope detector outputs are the input to a final linear filter. The estimator output is shown to be an unconstrained linear operation on the ambiguity function of the estimator input. Except for a bias term due to the additive noise, the mean of the estimator output is an unconstrained linear operation on the scattering function of the random filter. The integral variance of the output is found for a Gaussian channel. The mean and variance clearly indicate the tradeoff between resolution and variance reduction obtained by varying the estimator structure. For any well-behaved channel it is shown that an effectively unbiased estimate of the scattering function can be obtained if the input signal has both sufficient energy and enough time and frequency spread to resolve the random filter; the random filter is not required to be underspread. The variance of an estimate can be further reduced by increasing the time or frequency spread of the transmitted signal.

This paper considers the design of a detection system to optimally detect known signal fields--scalar functions of a vector argument--corrupted by an additive noise field. The detection system has as its inputsnsamples (in Space) of the signal-plus-noise field; each spatial sample is the output of a point detector. Optimal processing of the point-detector outputs, as well as the locations of the point detectors, is considered. For a fixed array and under assumptions that are often physically reasonable, the optimum detector is separable into a spatial combiner and a temporal processor. The probability of error of the optimum detector is a monotonic function of the array gain. Convenient expressions of the array gain are found for circular arrays; by using these expressions, optimal radii for circular arrays are found.

This paper considers the design of a detection system to optimally detect known spatially invariant signal fields corrupted by an additive, zero-mean, covariance-separable, and spatially isotropic noise field. The detection system has as its inputnsamples (in a plane) of the signal-plus-noise field; each spatial sample is the output of a point detector. In an earlier paper [1], optimal processing of the point detector outputs and the design of circular arrays were considered. This paper is concerned with the design of several other array configurations. Some of the results, which are related to singular detection problems, dramatically point out the need for proper modeling of covariance functions. These results also indicate that the use of derivatives in detection is extremely unreliable when there is any nonzero instrument noise.