On nonlinear direct-sequence detectors in arbitrary power-limitedinterference

Communication over a waveform channel corrupted by additive white Gaussian noise and by an unknown and arbitrary interference of bounded power is considered. For this channel, an upper bound is presented for the worst-case error probability of a communication system comprising a direct-sequence spread spectrum modulator and a nonlinear correlation receiver. It is shown that this bound is exponentially tight as the number of chips used in the modulator becomes large. This bound is evaluated for several detector nonlinearities. Numerical examples and comparisons to the performance of a pure Gaussian noise channel are also given     

Multi-user performance of direct-sequence CDMA using combinedbinary PPM/orthogonal modulation

A new modulation format is proposed for cellular code-division multiple-access (CDMA) communications where binary pulse position modulation (PPM) is embedded in the chip waveform and combined with orthogonal modulation using Walsh/Hadamard codes. Compared to the conventional CDMA using orthogonal codes, this scheme allows reduction in receiver complexity by lowering the modulation level for the second-stage orthogonal modulation. The staggered (half-chip) quadrature direct-sequence signaling is adopted to uniformly distribute the transmit power and allow noncoherent detection at the receiver because carrier phase tracking is not feasible because of the binary PPM, suitable for the reverse link in cellular networks. Statistics of inter-user interferences are characterized, and then derive the symbol error probability for the proposed M-ary modulation format. It is shown that the advantage in view of receiver complexity can be achieved without deteriorating the multi-user performance in terms of the number of users affordable at a specified error rate     

Performance analysis of cellular CDMA networks overfrequency-selective fading channel

An effect of multipath fading on the performance of a cellular code-division multiple-access (CDMA) system is analyzed in this paper. A wide-sense stationary uncorrelated scattering (WSSUS) channel model and the coherent binary phase-shift keying (BPSK) with asynchronous direct-sequence (DS) spreading signal are assumed in the analysis. The average error probability for both the forward link and reverse link of a cellular CDMA system over a frequency-selective fading channel using a conventional correlation-type receiver and RAKE receiver are derived. The impact of imperfect power control and channel capacity of a cellular CDMA system is also investigated. The closed forms of average error probability derived in the paper can save a lot of computation time to analyze the performance and channel capacity of a cellular CDMA system. The analytical results show that the performance and maximum transmission rate of cellular CDMA systems degrade with an increase in the number of simultaneous users and the number of interfering cells. The signal-to-interface ratio (SIR) for the reverse link derived in this paper can directly describe the interrelationships among a number of paths, number of users, number of interfering cells, fading factors, and maximum variation of a received unfaded signal     

An efficient technique for evaluating direct-sequencespread-spectrum multiple-access communications

A technique is presented for obtaining bounds on the average probability of error for direct-sequence spread-spectrum multiple-access (DS/SSMA) communications. The technique is of interest because it yields arbitrarily right bounds, involves a small amount of computation, avoids numerical integrations, and applies to many types of detection. As an illustration, the technique is applied to binary DS/SSMA communications, an additive white Gaussian noise channel, and a coherent correlation receiver. It is assumed that all the signature sequences are deterministic. Each transmitter is assumed to have the same power, although the approach can accommodate the case of transmitters with unequal powers. Expressions are given for the density functions of the random variables that model the multiple-access interference. These expressions are used to obtain arbitrarily tight upper and lower bounds on the average probability of error without making a Gaussian approximation or performing numerical integrations to incorporate the effects of multiple-access interference     

Performance of Coherent 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.     

The effects of sequence selection on DS spread spectrum withselective fading and Rake reception

Error probabilities are evaluated for direct-sequence spread-spectrum communications and Rake reception over channels with doubly selective fading. The error probability for such a system depends on the spreading sequence, the autocorrelation function of the fading process, the received signal-to-noise ratio, and the number of taps in the Rake receiver. The focus of the paper is on the effect of the spreading sequence on the performance of each of two systems. One system employs noncoherent detection of differentially-encoded binary direct-sequence spread-spectrum signals and a post-detection diversity-combining Rake receiver which uses equal-gain combining. The other system employs coherent detection of binary direct-sequence spread-spectrum signals and a post-detection diversity-combining Rake receiver with perfect gain estimates for the channel. A simple sequence selection criterion is introduced, and the sensitivity of the performance of the system to the choice of the spreading sequence is examined. It is shown that significant performance differences result from different choices of the spreading sequence. It is also shown that, given a moderate range of delay spreads, sequences can be found that yield low bit error probabilities over that range. These are found to be robust with respect to the delay spectrum for the channel, the number of taps in the Rake receiver, the Doppler spread, and the signal-to-noise ratio     

Performance analysis of a DS/CDMA system with noncoherent M-aryorthogonal modulation in Nakagami fading

The probability of error performance of a direct sequence code-division multiple-access (DS/CDMA) system employing noncoherent M-ary orthogonal signaling in a Nakagami multipath fading channel is analyzed. A RAKE receiver structure with square-law demodulation is used at the receiver. The multiple-access interference are modeled as Gaussian and expressions derived for the exact probability of error. The performance is also evaluated in terms of the number of users that can be supported by the system at a given probability of error. The effect of correlated fading on system performance is also investigated by considering two correlation models, which can be characterized by a single correlation coefficient ρ. In the first model, the correlation coefficient between any two diversity branches is constant. In the second model, it is assumed that the correlation coefficient between any two diversity branches decreases exponentially as the separation between them increases. For both models, it is found that the presence of correlation deteriorates system performance. The use of larger signal alphabets than binary modulation in conjunction with diversity reception provides a considerable performance improvement even in the presence of correlated fading     

Binary orthogonal signaling over the Gaussian channel with unknownphase/fading: new results and interpretations

The problem of binary orthogonal signaling over a Gaussian noise channel with unknown phase/fading is considered. By viewing the problem in a rotated coordinate system, the orthogonal signal structure is considered as the combination of an antipodal signal set and a pilot tone for channel measurement. For data detection the optimum matched-filter envelope-detector is shown to be identical to a novel detector-estimator receiver in which the detector performs partially coherent detection, using an absolute coherent reference generated by the estimator from the channel measurement provided by the pilot-tone component of the orthogonal signal structure. This detector-estimator interpretation shows that it is incorrect to refer to the optimum receiver as a noncoherent receiver. It also leads to the development of new approaches for analyzing the error probability of the receiver. An exponential Chernoff upper bound is obtained for the Rician channel     

Probability-of-error bounds for binary transmission on the slowly fading Rician channel

Chernoff bounds and tilted distribution arguments are applied to obtain error probability bounds for binary signaling on the slowly-fading Rician channel with L diversity. For the maximum likelihood receiver, the CB-optimum [optimum in the sense of minimizing the Chernoff (upper) bound on error probability] signal correlation is determined and plotted; it is found that antipodal signals should be used ifa > b^{2}(1 + b), where a is the signal-to-noise ratio of the specular components andbis that of the fading components. The CB-optimum number of diversity paths is then obtained. Ifa/b > 0.2, antipodal signaling with unlimited diversity is CB-optimum; whereas, ifa/b < 0.2, orthogonal signaling with properly chosen diversity is very nearly CB-optimum. If restricted to orthogonal signaling, unlimited diversity is CB-optimum whenevera/b > 1.0. Similar results are obtained for the generally nonoptimum square-law-combining receiver. In this case, orthogonal signaling with finite diversity is always CB-optimum.     

Selection of spreading sequences for direct-sequencespread-spectrum communications over a doubly selective fading channel

Error probabilities are evaluated for direct-sequence spread-spectrum communications over channels with doubly selective fading. The error probability for such a system depends on the spreading sequence, the autocorrelation function of the fading process, and the receiver signal-to-noise ratio. The focus of this paper is on the effect of the spreading sequence on the performance of differentially coherent detection of binary direct-sequence spread-spectrum signals using a correlator receiver. It is shown that significant performance differences result from different choices of spreading sequence. It is also shown that, given a moderate range of delay and Doppler spreads, sequences can be found which yield low bit error probabilities over the entire range. These are found to be robust with respect to a variety of shapes for the channel autocorrelation function and the full range of signal-to-noise ratios     

Worst interference for coherent binary channel (Corresp.)

For a coherent channel transmitting binary digits, a worst distribution under an average power constraint can be defined. A solution for the very noisy channel is found to be Gaussian, and the minimax demodulator utilizes correlation detection to guarantee an exponential bound on probability of error.     

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.     

Performance comparison of different spread-spectrum signalingschemes for cellular mobile radio networks

Different spread-spectrum signaling schemes in a cellular mobile radio network are compared in terms of throughput and packet error probability. Bounds on the bit and packet error probabilities are derived for data modulation schemes with binary phase shift keying with noncoherent demodulation. Reed-Solomon coding is employed for error-correction purposes. In all cases, the effect of varying interference power (according to some inverse power of distance) of the desired signal, of the interfering signals, and of Rayleigh nonselective channel fading is accurately taken into account. The throughput in the mobile-to-base transmission mode is evaluated for the above data modulation, demodulation, and forward-error-control coding schemes. The comparison shows that, under the varying interference power model, the frequency-hopped scheme performs best among all schemes with the same bandwidth. Power control mechanisms are required to improve the performance of direct-sequence systems     

An Analytical Expression for the BER of an Individually Optimal Single Cochannel Interferer BPSK Receiver

An analytical expression for the bit-error rate (BER) of an individually optimal receiver in a two-user synchronous channel is derived. The desired signal is a binary phase-shift keying (BPSK) signal corrupted by a like-modulated interference and additive white Gaussian noise (AWGN). The BER expression decomposes into the probability of error of BPSK in AWGN plus an interference term which tends to zero when either the interferer power or the interferer signal correlation with the desired signal approaches zero     

Optimum Detection of Quantized PAM Data Signals

The degree of complexity of a digital signal processor is closely related to the precision with which samples of an incoming analog waveform are represented. There is considerable interest in determining how coarse this representation can be without seriously degrading performance from that of an ideal processor of unquantized samples. This question is examined for a receiver of noisy, linearly distorted pulse amplitude modulation (PAM) signals. An optimum [maximum likelihood (ML)] detector, analogous to the Viterbi detector for unquantized samples, is derived for the case of a quantized sample sequence. Performance is evaluated under the assumption of high signal-to-noise ratio (SNR), and the resultant error probability is a good approximation for coarse quantization, and an upper bound for any degree of quantization. For a specified error probability, the degree of quantization suggested by this approach is conservative. Since receiver complexity is closely associated with the length of the digital representation of an input sample, an upper bound on receiver complexity is also suggested. Numerical evaluation of the error probability is quite tedious for an arbitrary channel; however, system performance may be readily evaluated for partial-response (PR) signaling. For the PR channels     

Combined power control and error-control coding in multicarrier DS-CDMA systems

We propose truncating the transmission power (allocating no power) for symbols with low channel gain, and tagging erasures on the corresponding symbols at the receiver. The motivation is that symbols with low channel gain are highly likely to be in error and yet, if transmitted, consume the energy resource and generate interference to other users. Truncating the power for those symbols has the effect of reducing the interference to other users and allocating more power on symbols with high channel gain (thereby reducing the error probability). Since block codes can correct twice as many erasures as errors, the coded performance can be improved by properly combining the power control with the error-control coding. In this letter, we analyze the performance of the Reed-Solomon-coded multicarrier direct-sequence code-division multiple-access systems with two power-control schemes. We show that the probability of incorrect decoding can be significantly improved by properly combining the power control with the error control coding.     

On orthogonal signaling over the slow nonselective Rician fadingchannel with unknown specular component

Orthogonal signaling over the slow nonselective Rician fading channel is considered. Previous receiver designs have all assumed the amplitude and phase of the specular component of the received carrier to be known completely, but this assumption is entirely unrealistic. The problem is reformulated with unknown random amplitude and phase of the specular component. The optimum maximum likelihood receiver is obtained for equally likely equal-energy orthogonal signals and is shown to be identical to the quadratic receiver for the purely unknown phase channel and the pure Rayleigh fading channel. The error probability performance is analyzed for a fixed known specular amplitude. When specialized to the binary signaling case this error probability result exhibits a performance that is very close to and asymptotically approaches that of the conventional coherent-specular-component case for high SNR. Thus, knowledge of the specular component phase is not important to the optimum receiver     

Multiple-access capability of frequency-hopped spread-spectrumrevisited: an analysis of the effect of unequal power levels

A method for the evaluation of the probability of error of uncoded asynchronous frequency-hopped spread-spectrum multiple-access communications is presented. For systems with binary FSK modulation this method provides an accurate approximation and a tight upper bound to the bit error probability; for systems with M-ary FSK modulation, it provides tight upper bounds to the symbol error probability. The method enables the computationally efficient averaging of the error probability with respect to the delays, phase angles, and data streams of the different users. It relies on the integration of the product of the characteristic function of the envelope of the branch of the BFSK demodulator, which carries the desired signal, and of the derivative of the characteristic function of the envelope of the other branch. For sufficient frequency separation between the BFSK tones, the method can achieve any desirable accuracy. Moreover, the computational effort required for its evaluation grows linearly with the number of interfering users. In the M-ary case, tight upper bounds based on the union bound and the results of the binary case are derived. The method allows the effect of unequal power levels on other-user interference in FH/SSMA systems to be quantified accurately for the first time. The results indicate that the FH/SSMA systems suffer from the near-far problem, although less seriously than direct-sequence SSMA systems     

Analysis of Rake reception with multiple symbol weight estimation for antipodal signaling

Consider a Rake receiver for coherent binary antipodal signaling with: 1) a delayed received signal configuration; 2) weight estimation by matched filtering using the reference signal along with the decisions of the previous M symbol intervals; and 3) predetection maximal-ratio combining (MRC). The weight estimation errors here are not independent of the additive noise, and do not fit into the Gaussian weighting error model for MRC. Here we analyze the error performance of the receiver by obtaining the conditional symbol error probability, conditioned on past decisions, from the characteristic function of the decision variable, and getting the unconditional error probability (UEP) for a block of M consecutive symbols using a Markov model of the decision process. The channel is Rayleigh fading with independent and identically distributed branch gains. Results show that the error performance of the Gaussian distributed weighting error model is a bound for that of multiple symbol weight estimation by matched filtering, and the steady state UEP decreases with increase of M, but the amount of decrease reduces as M increases.     

Direct-Sequence Spread-Spectrum Receiver for Communication on Frequency-Selective Fading Channels

The reception of direct-sequence spread-spectrum signals on frequency-selective fading communication channels is considered. The fading statistics are described using the wide-sense-stationary uncorrelated-scattering (WSSUS) channel model. It is shown that, under certain assumptions about this channel such as time-invariance over the duration of a data symbol, an orthogonal representation for the received distorted signal can be found. The optimum incoherent receiver can then be realized with reasonable complexity. The analysis shows that exploiting the inherent diversity of a frequency-selective channel can reduce the receiver error probability by several orders of magnitude. The optimum selective channel and the jamming susceptibility of the receiver are discussed.