Maximum-likelihood diversity combining is investigated for an FFH/MFSK spread spectrum system in partial-band noise (PBN). The structure of maximum-likelihood diversity reception in PBN plus white Gaussian noise is derived. It is shown that signal-to-noise ratio and the noise variance at each hop have to be known to implement this optimum diversity combiner. Several suboptimum diversity combining schemes are also considered. The performance of the optimum combining scheme is evaluated. It is shown that adaptive gain control diversity combining actually achieves the optimum performance when interference is not very weak.

A method is presented for the calculation of M-ary DPSK error probability in partial-band multitone jamming and white gaussian noise. Both unfaded and faded signals and jamming tones may be analyzed by the method. The fading considered is frequency-flat, time selective, Rician fading. The results have application in mobile, slow frequency-hopped, military, satellite systems. The method uses the Pawula-Rice-Roberts (1982) method for calculating the probability distribution function of the phase angle between two vectors when they are perturbed by noise. The worst case error probability in partial-band jamming with fading is efficiently computed using Houston's (1975) approach. A fundamental parameter, independent of the actual jammer power being used on the system, is identified. The effect of the ratio of the direct signal energy to the faded (indirect) signal energy is shown by example, as is the effect of fading bandwidth and Doppler shift. For practical values of the parameters, jammer fading was not found to be significant. Results for M=2, 4, and 8 are given.>

The problem of fine-time, or epoch, synchronization on the uplink of a frequency hopped FDMA satellite system is examined. All user signals are dehopped by the same device in the satellite receiver. For each transmitted signal the hop transition time must be adjusted so that when the signal arrives at the receiver, it is closely aligned with the transition time of the dehopper. To accomplish this fine-time synchronization, the system is probed by sending a known signal for a number of hop periods, L. For receivers which use a Fourier transform processor (FTP), such as may be realized by SAW devices, the early-late filter method provides a means for processing the probe response so that an estimate of the time error can be made. The resulting time error estimate is then sent via the downlink to the transmitter where it is used to adjust the user hop transition time accordingly. A unique method is introduced which uses estimates of three second order moments to give a low-biased, consistent estimate of the time error. The mean and standard deviation of the estimator are determined by an approximate analysis using the central limit theorem. Results from this analysis were found to agree closely with those from simulation for practical values of L. Performance results are given for several values of signal-to-noise ratio and a range of L. The performance of the estimator is also investigated when the probe is subject to degradations such as amplitude variations and fading. Results show that the method is extremely robust under these conditions.>

In this letter, we consider the error correlation in differential phase-shift keying (DPSK) demodulation in terms of its effects on the block and decoded error probabilities. The exact block and decoded error probabilities are derived and computed for additive white Gaussian noise (AWGN). Comparisons are made with the approximate block and decoded error probabilities based on a memoryless model which ignores the error correlation. The effectiveness of interleaving in improving the error performance is addressed under various conditions. Both binary and nonbinary DPSK are studied.>

The performance of M-ary differential phase shift keying (MDPSK) in both tone jamming and Gaussian noise is presented. Previous work has been extended by considering larger signal sets and skewed differential phases with unequal decision regions. The error performance when a frequency offset exists between the jamming tone and MDPSK carrier is also considered.>

Five methods for estimating the time error in a frequency-hopped spread-spectrum (FHSS) system are analyzed and compared. These methods are based upon estimation of the second-order moments of the envelope-detected, match-filtered, received signal. The performance of these estimators is determined as a function of the Gaussian noise level and of the number of samples L used to form the estimate. The estimator mean and standard deviation are approximated by means of the central limit theorem. Solutions compare favorably with simulation results. Results for signal-to-noise ratios of 0, 5, and 10 dB and with L between 1 and 512 show that these estimators are superior to previously known methods.>

An error-correction scheme for an M-ary symmetric channel (MSC) characterized by a large error probability p/sub e/ is considered. The value of p/sub e/ can be near, but smaller than, 1-1/M, for which the channel capacity is zero, such as may occur in a jamming environment. The coding scheme consists of an outer convolutional code and an inner repetition code of length m that is used for each convolutional code symbol. At the receiving end, the m inner code symbols are used to form a soft-decision metric, which is passed to a soft-decision decoder for the convolutional code. The effect of finite quantization and methods to generate binary metrics for M>2 are investigated. Monte Carlo simulation results are presented. For the binary symmetric channel (BSC), it is shown that the overall code rate is larger than 0.6R/sub 0/, where R/sub 0/ is the cutoff rate of the channel. New union bounds on the bit error probability for systems with a binary convolutional code on 4-ary and 8-ary orthogonal channels are presented. For a BSC and a large m, a method is presented for BER approximation based on the central limit theorem.>

The explicit form of the uncertainty principle for the 3-D signals of advanced television (ATV) is given, and the conditions for efficient use of spatiotemporal BW are discussed. Applications to extrapolation and to approximation in an interval by a bandlimited 3-D function are summarized. A theory for spatiotemporal interchange based on the analog between the inertia tensor of classical mechanics and a dispersion tensor for a 3-D image is described and a possible approach to spatio-temporal interchange is presented. Potential applications of previous results in image processing to location and resolution of objects and coding are discussed.>

A method is presented for determining the error probability of a receiver using differential detection in the presence of Gaussian noise and fast Rician fading. Equations for the covariances of the fading component are derived, which include the effect of IF filter distortion. It is shown that these equations may be readily evaluated numerically. A simple formula for the error probability is derived for systems using BPSK and a matched filter receiver. An example of the error probability is given using this receiver. Also given is an example of a system using MSK with a practical IF filter. Different spectral shapes and bandwidths for the fading process are investigated for this example and their effect on the error probability is determined.

A formula for the symbol error probability is derived which applies to differential detection ofM-ary phase-shift keying (MDPSK) in fast Rician fading and white Gaussiau noise. This formula is an extension of a result already known for MDPSK in Gaussian noise interference.

A formula for the probability of error in a digital system subjected to noise and intersymbol interference is derived. The transmitted symbols are encoded by forming the weighted sum of theMmost recent, independent, multilevel source digits. This linear coding operation in cludes, as a special case, the family of partial response codes.