Michael B. Pursley

Performance Evaluation for Phase-Coded Spread-Spectrum Multiple-Access Communication--Part I: System Analysis

An analysis of an asynchronous phase-coded spread-spectrum multiple-access communication system is presented. The results of this analysis reveal which code parameters have the greatest impact on communication performance and provide analytical tools for use in preliminary system design. Emphasis is placed on average performance rather than worst-case performance and on code parameters which can be computed easily.

Crosscorrelation properties of pseudorandom and related sequences

Binary maximal-length linear feedback shift register sequences (m-sequences) have been successfully employed in communications, navigation, and related systems over the past several years. For the early applications, m-sequences were used primarily because of their excellent periodic autocorrelation properties. For many of the recent systems applications, however, the crosscorrelation properties of such sequences are at least as important as the autocorrelation properties, and the system performance depends upon the aperiodic correlation in addition to the periodic correlation. This paper presents a survey of recent results and provides several new results on the periodic and aperiodic crosscorrelation functions for pairs of m-sequences and for pairs of related (but not maximal-length) binary shift register sequences. Also included are several recent results on correlation for complex-valued sequences as well as identities relating the crosscorrelation functions to autocorrelation functions. Examples of problems in spread-spectrum communications are employed to motivate the choice of correlation parameters that are considered in the paper.

Error Probabilities for Binary Direct-Sequence Spread-Spectrum Communications with Random Signature Sequences

Binary direct-sequence spread-spectrum multiple-access communications, an additive white Gaussian noise channel, and a coherent correlation receiver are considered. An expression for the output of the receiver is obtained for the case of random signature sequences, and the corresponding characteristic function is determined. The expression is used to study the density function of the multiple-access interference and to determine arbitrarily tight upper and lower bounds on the average probability of error. The bounds, which are obtained without making a Gaussian approximation, are compared to results obtained using a Gaussian approximation. The effects of transmitter power, the length of the signature sequences, and the number of interfering transmitters are illustrated. Each transmitter is assumed to have the same power, although the general approach can accommodate the case of transmitters with unequal powers.

The role of spread spectrum in packet radio networks

This paper is devoted to an examination of the key features of spread-spectrum signaling in packet radio networks. The multiple-access capability, capture, and anti-multipath capability of spread spectrum are the principal topics, and the basic features of spread spectrum that enable it to provide these capabilities are illustrated. The interaction between the spread-spectrum signaling and the network protocols is discussed. Methods for performance evaluation are reviewed, and analytical results on the multiple-access capability of spread spectrum are presented.

Error Probability for Direct-Sequence Spread-Spectrum Multiple-Access Communications--Part II: Approximations

Approximations are obtained for the average probability of error in an asynchronous direct-sequence spread-spectrum multiple-access communications system. Both binary and quaternary systems are considered, and the chip waveforms are allowed to be arbitrary time-limited waveforms with time duration equal to the inverse chip rate. The approximation is based on the integration of the characteristic function of the multiple-access interference. The amount of computation required to evaluate this approximation grows only linearly with the product of the number of simultaneous transmitters and the number of chips per bit. The accuracy of the approximation is extremely good in most cases, but it can be improved, if necessary, by an application of a series expansion. Numerical results are presented for specific chip waveforms and signature sequences.

Error Probabilities for Slow-Frequency-Hopped Spread-Spectrum Multiple-Access Communications Over Fading Channels

Bounds and approximations are obtained for the average probability of error in an asynchronous slow-frequency-hopped spread-spectrum multiple-access communications system with noncoherent binary frequency-shift-keyed (FSK) data transmission. Both nonselective fading and wide-sense-stationary uncorrelated-scattering fading are considered.

Performance Evaluation for Phase-Coded Spread-Spectrum Multiple-Access Communication--Part II: Code Sequence Analysis

An analysis of the code sequence parameters that are most important to the communication performance of an asynchronous phase-coded spread-spectrum multiple-access communication system is presented. Previously known bounds and computational techniques for such parameters are surveyed. Some new results on mean-square correlation are included.

Error Probability for Direct-Sequence Spread-Spectrum Multiple-Access Communications--Part I: Upper and Lower Bounds

Upper and lower bounds on the average probability of error are obtained for direct-sequence spread-spectrum multiple-access communications systems with additive white Gaussian noise channels. The bounds, which are developed from convexity properties of the error probability function, are valid for systems in which the maximum multiple-access interference does not exceed the desired signal and the signature sequence period is equal to the duration of the data pulse. The tightness of the bounds is examined for system with a small number of simultaneously active transmitters. This is accomplished by comparisons of the upper and lower bounds for several values of the system parameters. The bounds are also compared with an approximation based on the signal-to-noise ratio and with the Chernoff upper bound.

Spread-Spectrum Multiple-Access Communications

In a direct-sequence spread-spectrum multiple-access communications system several asynchronous signals simultaneously occupy the same channel. Each of the signals employs a signature sequence which is selected to have certain desirable correlation properties. For multiple-access communications the primary goal is to be able to separate the spread-spectrum signals at the receiver even though they occupy the same bandwidth at the same time. This problem is considered in the sections which follow for various forms of direct-sequence spread-spectrum modulation including binary phase-shift keying, quadriphase-shift keying, and minimum-shift keying. The emphasis is on the analysis of system performance rather than on the selection of signature sequences. Hence this material complements the recent paper of Sarwate and Pursley (1980) which examines in detail the problem of signature sequence selection.

Performance of Noncoherent Direct-Sequence Spread-Spectrum Communications Over Specular Multipath Fading Channels

The performance of coherent direct-sequence spread-spectrum communications over specular multipath fading channels is investigated. The average probability of error of the correlation receiver is derived for an arbitrary number of paths with deterministic or random gain coefficients. The gain coefficients, delays, and phase angles of any two distinct paths are modeled as mutually independent random variables. Numerical results for several values of the system and channel parameters are presented.