Spread-spectrum Multiple-access Systems Research Articles

Moment-based performance evaluation of digital transmission systems

The average error probability Pe in many digital communications systems can be expressed as the statistical expectation of a known function f(·) of some random interference variable (or vector) X. This paper presents a unified theory to evaluate Pe based on moment error bounds or approximations, when the moments of X are available. The theory can also be extended to random variables with inaccurately known moments. The relevant numerical question of accuracy and roundoff errors due to averaging with the aid of high-precision rules is addressed. Examples of application to spread-spectrum multiple-access systems, optical fibre systems and microwave digital radio-relay links are presented to show the applicability of the proposed methods to different environments.

Performance of binary and quaternary direct-sequence spread-spectrum multiple-access systems with random signature sequences

The performance of synchronous and asynchronous, binary and quaternary (with and without offset) direct-sequence spread-spectrum multiple-access (DS/SSMA) communication systems using random signature sequences and arbitrary chip waveforms is investigated. The average probability of error at the output of the correlation receiver is evaluated using a characteristic-function approach for these systems. Numerical results are presented that illustrate performance comparisons between systems using random and deterministic signature sequences, synchronous and asynchronous systems, systems with rectangular or sinewave chip waveforms, and binary and quaternary systems with the same data rates and bandwidth. In all cases, the accuracy of the Gaussian approximation is also examined. >

Performance of direct-sequence spread-spectrum multiple-access systems in mobile radio

The performance of coherent directsequence spread-spectrum multiple-access (DS/SSMA) communications over different mobile radio channels is investigated. Analytical techniques and numerical methods were used for a channel having a number of resolvable, discrete Rayleigh fading paths, while simulations were employed for transmissions over urban mobile radio channels. We found that even a flat Rayleigh fading channel caused a severe degradation in system performance compared with the additive white Gaussian noise channel, and that the system was unusable even for a few users when a wideband urban mobile radio channel was used. By transmitting a sounding sequence of chip length Ns = 511 to allow the receiver to estimate the channel impulse response, spreading the symbol over N = 127 chips, and on deploying fifth-order combinative space diversity equipped with adaptive correlation diversity of Kβ = 1.0 (CD/ACD), we were able to obtain a residual probability of bit error PR of less than 10−3 for 10 users, in spite of the urban mobile radio channel having 19 resolvable fading paths. By increasing N to 511 and deploying fifth-order maximal-ratio-combining (MRC) space diversity, a PR of 4 × 10−5 for 20 users was achieved when the radio channel consisted of 10 resolvable independent Rayleigh fading paths.

New signature code sequence design techniques for CDMA systems

New design techniques are presented for carefully selecting subsets of signature code sequences with small crosscorrelation magnitudes for applications in code inversion keying (CIK) direct-sequence spread-spectrum multiple-access systems. Also, a new class of code sequences, which has been called the class of “structured code” sequences, with small crosscorrelation magnitudes is presented. The performance measure considered is the average probability of data-bit error at the output of a correlator receiver. The results presented are applicable to various applications of code-division multiple-access (CDMA) systems including optical fibre local area networks and indoor radio communications.

DS SSMA with some IC realizations

A direct-sequence spread-spectrum multiple-access (DS SSMA) system was examined, realized (hardware), and tested. Essentially, two transmitters were built: one had voice capability, whereas the other transmitted only binary data. Gold codes were used for the spreading sequence. The PN synchronization used a serial search technique for acquisition, and a tau-dither loop for tracking. A squaring loop and a differential encoding scheme (for carrier phase ambiguity) was used in the demodulation process, which was followed by conversion to a voice output when desired. The system was found to perform quite well under both single and multiple-access conditions. As a demonstration of the feasibility of implementing the system on chips, a few small blocks were put on ICs using CMOS technology. These performed as expected, and clearly demonstrated both the feasibility and attractiveness of a VLSI implementation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Combinations of an adaptive array antenna and a canceller of interference for direct-sequence spread-spectrum multiple-access system

In the realization of code-division multiple access based on a spread-spectrum communication system, i.e. spread-spectrum multiple access (SSMA), reduction of cochannel interference is an important problem. An adaptive array antenna system is proposed that includes a cancellor of cochannel interference, which can improve performance by a combination of temporal and spatial filtering. While the adaptive array suppresses interference sources with arrival angles different from those of the desired user, the adaptive digital filter-canceller rejects those whose arrival angles are the same as those of the desired user. The proposed system can achieve stable acquisition and low error rate of demodulated data even in a heavy-interference channel where a conventional array antenna system cannot achieve satisfactory acquisition.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The effect of clock and carrier frequency offsets on the performance of a direct-sequence spread-spectrum multiple-access system

It is widely known that the probability of symbol error in a direct-sequence spread-spectrum multiple-access network is dependent on the carrier and spreading code chip phases of the interfering terminals with respect to the signal of interest. As a result, for a given total interference power, the performance is worse for the case of one strong interferer when compared to the case of many weak interferers where the Gaussian assumption on the multiple-access interference holds. The author assumes a random-spreading code model and shows that if there is an offset on the carrier and spreading code frequencies of the interfering signals relative to the signal of interest, the above difference in performance between the cases of a set of balanced and a set of unbalanced interferers is drastically reduced. The result is that subject to such frequency offsets one may make the Gaussian assumption on the interference power regardless of whether it is composed of one strong interferer or many weak interferers of the same total power. In a network it may be desirable to actually force the offsets by putting a slight offset on the clock oscillators of the various transmitters. It is shown that to achieve a small variation of the noise variance, the spreading code and carrier offset frequencies should be greater than the symbol rate.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the error probability of coded frequency-hopped spread-spectrum multiple-access systems

A simple, exact calculation is presented of the probability distribution of the number of hits in a block of n symbols in a frequency-hopped, spread-spectrum, multiple-access communication system. While the sequence of hits is not Markovian, there is an underlying Markovian structure that allows the probability distribution of the number of hits to be calculated in a recursive fashion. Knowing the probability distribution of the number of hits makes it possible to calculate the probability of error for a system employing error correcting codes for several different types of receivers, including receivers with both errors and erasures. The numerical results show that both the approximation obtained by assuming the actual sequence of hits is Markovian and the approximation obtained by assuming the hits are independent are very good. When the number of frequency slots is not too small (less than five), calculations show that assuming the independence of hits gives an error probability accurate to within 1% of the actual error probability. Assuming the hits are Markovian gives error probabilities which are accurate to within 0.001%.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A comparison of trellis coded versus convolutionally coded spread-spectrum multiple-access systems

A system model is proposed that allows one to apply both trellis coding and PN spreading sequence to the data symbols to be transmitted. Rate n/n+1, trellis codes using 2/sup n+1/-point MPSK signal constellations are investigated when Gold sequences are used for PN spreading. Performance in an additive white Gaussian noise (AWGN) channel is investigated, with 5-20 users transmitting simultaneously. Using the criteria of equal complexity and throughput, the performance of the trellis codes in a SSMA (spread spectrum multiple access) environment is compared to that of medium-rate to low-rate convolutional codes through the use of a generalized transfer function bound. The average degradation due to the interuser interference is determined by the method of moments. The validity of approximating the interuser interference as a Gaussian random variable is also investigated. The numerical results illustrate that for a given complexity, chip rate and throughput, low-rate convolutional codes provide the best performance in an SSMA system. As lower-rate convolutional codes are used, there is an increase in the effective interuser interference due to the greater cross-correlation effects from using shorter PN sequences, or alternatively from the effects of partial cross-correlation. However, this increased degradation is more than overcome by the increased distance properties of the low-rate codes. >

On the error probability of coded frequency-hopped spread-spectrum multiple-access systems with more than one code symbol per dwell interval

The multiple-access capability of an asynchronous, frequency-hopped spread-spectrum (FH-SS) communication system employing error correcting codes is reviewed. Many current FH-SS systems employ error correcting codes with more than one code symbol per dwell interval. A method of computing the codeword error probability induced in such spread-spectrum systems is presented. The codeword error probabilities induced in spread-spectrum systems utilizing more than one versus one code symbol per dwell interval are compared. It is concluded that FH-SS systems with one code symbol per dwell interval are more efficient in combating multiple-access interference than FH-SS systems with more than one code symbol per dwell interval. >

Performance evaluation of multiple access spread spectrum systems in the presence of interference

A simplified version of the Lee-Smith algorithm (W.C. Y. Lee and H.L. Smith, ibid., vol. VT-32, p.177-90, May 1983) is proposed for computing the probability of outage and the bit error rate (BER) due to autointerference in multiple-access spread-spectrum radio systems. The model assumes a pair of transmitting and receiving radios in a region where there are other radios operating in the same band. Each radio is characterized by its own spatial distribution, transmitting power, activity coefficient (denoting the percentage of time the radio is active), antenna height, and a set of carrier frequencies. The probability of outage with respect to the log-normal field-strength attenuation is derived assuming that the probability of having more than one interferer is very low. To allow maximal flexibility, the spatial, carrier frequency, and activity distributions are computer simulated for each radio. As an example of applying the method, the probability of error of an asynchronous frequency-hopping (FH) and a hybrid frequency-hopping/direct sequence (FH/DS) modulation schemes in environments with thousands of radios is reported.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Modulatable orthogonal sequences and their application to SSMA systems

A set of N-1 orthogonal sequences of period N/sup 2/ is proposed, where N is a natural number. Each orthogonal sequence proposed can be modulated by N complex numbers of absolute value 1, so the modulated sequence is also orthogonal. When N is an odd prime number, the absolute value of the cross-correlation function between any two of the N-1 orthogonal sequences is constant and satisfies the mathematical lower bound. This property of the cross-correlation function is not changed when each of the two orthogonal sequences is modulated by N complex numbers of absolute value 1. Two spread-spectrum multiple-access (SSMA) systems using these sequences are proposed. One system is an asynchronous SSMA system, using the proposed sequences unmodulated. The cochannel interference peak between any two channels in this system realizes the mathematical lower bound for an asynchronous SSMA system using a set of orthogonal sequences. The other system is a synchronous SSMA system without cochannel interference which uses the modulated form of the proposed sequences. >

Spread-Spectrum Multiple-Access Performance of Orthogonal Codes: Linear Receivers

This paper analyzes a direct-sequence, spread-spectrum, multiple-access (SSMA) communication system which assigns a set of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> orthogonal sequences to each user. With all direct sequence SSMA systems, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</tex> users share a channel by phase modulating their transmissions with signature sequences. However, the users of our system transmit <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">log_{2}M</tex> bits of information/sequence. This contrasts classical SSMA schemes which use a pair of antipodal sequences and transmit 1 bit/sequence. In this paper, we assume that the channel noise is a combination of additive white Gaussian noise (AWGN) and multiple-access interference. We employ the optimum (single-user) demodulator for orthogonal signals in Gaussian noise. The multiple-user performance of this receiver is analyzed. We obtain approximations for the multiuser probability of error by using a Gaussian approximation for the multiple-access interference. We also obtain an upper bound on the exact probability by using characteristic functions. Our SSMA system is Well suited for application at the lower radio frequencies. Therefore, a companion paper describes a realistic model for low-frequency radio noise, modifies the receiver to include a zero-memory nonlinearity, and studies the performance of the nonlinear receiver.

Spread-Spectrum Multiple Access Using Wideband Noncoherent MFSK

Two spread-spectrum multiple access systems which usewideband M-ary frequency shift keying (FSK) (MFSK) as theprimary modulation are presented. A bit error rate performanceanalysis is presented and system throughput is calculated for sample C band and Ku band satellite systems. Sample link analyses areincluded to illustrate power and adjacent satellite interferenceconsiderations in practical multiple access systems.

Improvement of multiple access capability in m‐ary‐FSK/direct‐sequence SSMA

AbstractIn the conventional SSMA (Spread Spectrum Multiple Access) system, the number of co‐channel users is unexpectedly small and the increase in the number of co‐channel users is one of the subjects of SSMA. Introduction of error correcting codes, improvement on primary modulation, etc., have previously been proposed. Especially in direct‐sequence SSMA, primary modulation using modified M‐ary FSK has been reported to provide a remarkable improvement. A primary modulation scheme using modified M‐ary FSK, named “unpacked MFSK/DS,” is presented here for improving the multiple access capability on direct‐sequence SSMA by flattening the power spectrum of transmitted SS signals. It is shown that the number of co‐channel users in SSMA can be increased to twice as many as that of the conventional MFSK/DS systems only by modifying the frequency allocation of MFSK symbols and without modifying the conventional MFSK transmitter/receiver configuration.

A Frequency-Hopping SSMA System for Speech Communication

A frequency-bopping spread-spectrum multiple-access (FH-SSMA) system suitable for speech communication over a TV channel has been described. Design of addresses for the FH-SSMA has been considered. Following an algorithm suggested by Cooper and Nettleton, addresses for 12 subscribers of the system have been obtained. It is shown that a larger number of addresses would be possible provided a larger channel bandwidth is available. A practical situation where more than two subscribers start their communication at random time intervals has been studied. System performance in terms of the probabilities of error and false detection is reported.

Cross‐correlation functions for quadratic‐phase sequences with different periods

AbstractThe author has previously proposed new polyphase periodic sequences with autocorrelation sidelobe 0 and minimum cross‐correlation peak value. the periods of the sequences are odd prime N; the number of sequences is N ‐ 1. the sidelobe of the autocorrelation function is 0 and the absolute value peak of the cross‐correlation function for arbitrary two sequences of the same period satisfies the mathematical lower bound 1/√. This paper shows that the crosscorrelation function for these sequences with different periods is 1/√ at every term, where N1 and N2 are the periods of these sequences (Ni is the odd prime, N1 ≠ N2). Thus these sequences of various periods are useful for spread spectrum multiple access system because the number of channels can be increased remarkably by assigning sequences with different periods to the same frequency band.

Cancellation techniques of co‐channel interference in asynchronous spread spectrum multiple access systems

AbstractA spread spectrum multiple access (SSMA) communication scheme employing asynchronous code‐multiplexing technique has been used in both mobile and satellite communication systems. One shortcoming of the SSMA system is the co‐channel interference due to the correlations among the pseudo noise (PN) sequences being used by multiple channels. Such co‐channel interference in the reception limits the number of channels that can share one common frequency band. Furthermore, there is a distant‐dependent problem of different received‐powers from different transmitters.This paper describes a technique for cancelling the co‐channel interference in asynchronous SSMA systems. This technique does not treat the co‐channel interference as thermal noise. It considers the co‐channel interference as components that can be recreated at each receiver. If the correlations among the PN sequences of all the active channels become known, the co‐channel interference can be cancelled using the linear algebraic approach. As a result, a larger number of channels can share the same frequency band more efficiently. Further, if initial synchronization can be implemented then the distant‐dependent problem can be alleviated.

Spread spectrum communication with white gaussian noise

AbstractOne of the basic problems in the Spread Spectrum Multiple Access (SSMA) system is interchannel interference noise. Noise is an important determinant of the possible number of system characteristics of the SSMA system using White Gaussian Noise (WGN) for the spreading signal. The ratio of signal to interchannel interference noise (S/Ni) obtained herein can be the theoretical upper bound for direct sequence SSMA systems.This paper also proposes a new SSMA system in which the delayed WGN and the spread information signal are transmitted together. The system has no synchronizing problem between spreading and despreading signals. Therefore, receiver structure can be very simple.

Performance of FH-MFSK serial search synchroniser for mobile radio

A scheme for coarse acquisition of an FH-MFSK spread-spectrum multiple-access system is proposed. Performance curves showing the behaviour of the scheme in terms of false alarm and miss rates are given for a simplified mobile radio transmission model (white Gaussian noise and Rayleigh distributed fading). An optimisation procedure to minimise the acquisition mean time is outlined.