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A throughput metric is considered for a multiple-input single-output (MISO) system with noisy feedback of channel state information (CSI). The goal is to optimize a precoding matrix with a medium-access control layer metric. The problem is a nonlinear multidimensional optimization. Results show that the optimal precoding turns into beamforming when the signal-to-noise ratio (SNR) of CSI feedback is sufficiently large. A necessary condition for the optimality of beamforming under the throughput metric is determined, and the necessary and sufficient condition is numerically found based on the Gauss-Chebyshev Quadrature method. Next, the rate allocation for beamforming and spatial diversity is analyzed. Then, a two-mode transmission scheme is proposed such that the transmitter is engaged in either the beamforming mode or the spatial diversity mode depending on the SNR of the CSI feedback. It is shown that at a fairly high SNR of CSI feedback, the rate allocation needs to be reduced, while at a low SNR of CSI feedback, the allocated rate should be increased. It is shown that when the SNR of CSI feedback is lower than a threshold, there always exists an SNR of the transmitted signal such that the CSI feedback can be viewed as the real CSI solely for the purpose of rate allocation. The result also shows that the throughput of two-mode transmission is almost the same as the throughput of the optimal precoding scheme, even with a low SNR and large feedback delay. Index Terms--Beamforming, multiple-input single-output (MISO), precoding, rate allocation, spatial diversity, throughput.

This correspondence examines the number of users that can be supported at a given signal-to-interference ratio in asynchronous direct-sequence code-division multiple-access (DS-CDMA) systems. It is shown that for many chip waveforms the user capacity for asynchronous systems is larger than for optimally designed synchronous systems. The degree to which the user capacity improves by exploiting asynchrony is characterized by defining the effective dimension of the chip waveform. Finally, simulation results are shown to verify the analysis. Index Terms--Code-division multiple access (CDMA), interference avoidance, user capacity.

In this paper, we develop optimization techniques for linear zero-forcing (ZF) multiple-input, multiple-output (MIMO) broadcast (BC) precoders. A computationally efficient technique based on QR-update algorithms for implementing this optimization is then proposed. The application of the proposed ZF precoders and decoders to systems with both large and small numbers of users is considered. The proposed optimization technique is also shown to perform very well in conjunction with nonlinear Tomlinson-Harashima precoding. Both coded and uncoded performances are considered. Index Terms--Broadcast channels, MIMO systems.

The significant loss in performance of multicarrier direct-sequence spread-spectrum multiple-access systems over fast-fading channels is investigated. First, the channel model for individual subchannels is obtained, using a canonical decomposition to a wide-sense stationary (WSS), uncorrelated scattering channel. Next, a receiver structure, which features both Doppler diversity and frequency diversity, is presented and analyzed. It is found that large Doppler spreads cause the average magnitude of the desired signals to diminish dramatically. Expressions for the bit-error rate are derived for both uncoded and coded systems by applying the standard Gaussian approximation. Numerical results, which show that Doppler diversity is preferable over frequency diversity in fast-fading channels, are provided for different combinations of the diversity orders. Numerical results, which show that the intersymbol and intersubchannel interference can be effectively suppressed, and the multiple-access interference tends to degenerate into a WSS process with the statistical periodicity destroyed by the fast-fading channels, are also provided. Index Terms--Doppler diversity, Doppler spread, doubly selective fading channels, frequency diversity, multicarrier direct-sequence spread-spectrum multiple access (MC/DS/SSMA).

A new asymptotic analysis is presented to establish whether or not commonly used techniques to approximate the performance of direct-sequence spread-spectrum multiple-access (DS/SSMA) systems still apply when the systems are strictly band limited. The results apply to any linear data modulation and spreading scheme. The interference components, including the interchip interference (ICI) of a linear receiver output, are shown to be asymptotically jointly Gaussian random variables conditioned on the phases and delays of the interfering signals. Expressions for the error probabilities of band-limited systems are also developed from this result. Index Terms--Approximation theory, asymptotic analysis, code-division multiple access, interference.

A technique for interference suppression in multicarrier code-division multiple-access (MC-CDMA) systems is proposed which exploits the structural differences in signals that arrive at the receiver with Doppler shifts or carrier offsets. Oversampling the received signal in the frequency domain and properly combining the samples provides the interference suppression. Frequency-domain oversampling is accomplished by using a time extension of the conventional MC-CDMA signal or unconsumed portions of the cyclic prefix. Furthermore, a receiver structure is introduced that despreads and combines groups of samples so that a linear minimum mean-squared error solution for combining the groups is easily found. This combining scheme increases the signal-to-interference ratio experienced by the desired user in the MC-CDMA system. In addition, the receiver performs well in severe near--far scenarios when there is sufficient frequency separation between the signals of the desired user and an interferer. Numerical results show that the proposed receiver significantly outperforms the conventional MC-CDMA receiver in many channel realizations. Index Terms--Code-division multiple access (CDMA), Doppler effect, interference suppression.

An unbiased, maximum-likelihood (ML), channel parameter-estimation algorithm for direct-sequence spread-spectrum systems with strong interference is discussed in this paper. The algorithm includes correcting terms to the extended Kalman filter (EKF) based on the gradient of the negative log-likelihood function of the output of a conventional matched filter. By an asymptotic analysis, the algorithm is shown to determine the actual parameters. A complete implementation of the algorithm is given, and its transient behavior is examined by computer simulations. Results show the ML algorithm, albeit optimal in the sense of unbiased parameter estimation, is less robust than the modified EKF described in the first reference. Index Terms--Identification, interference suppression, Kalman filtering, parameter estimation, pseudonoise coded communications.

Performance bounds on chip-matched-filter (CMF) receivers for bandlimited direct-sequence spread-spectrum multiple-access (BL-DS/SSMA) systems with aperiodic random spreading sequences are obtained. First, the optimum transmit-receive chip waveform pairs that maximize the conditional signal-to-interference ratio are derived. This leads to performance bounds on CMF receivers when the conditional Gaussian approximation for cyclostationary multiple-access interference (MAI) is exploited. The bounds are used to examine the dependence of the MAI suppression capability of the CMF receivers on the excess bandwidth of the system and the delay profile of multiple-access users. The system employing the flat-spectrum chip waveform pair is shown to have near-optimum average bit-error rate performance among the fixed CMF (FCMF) receiver systems. Numerical results are provided for an adaptive CMF receiver and for FCMF receivers employing several different fixed chip waveforms. Index Terms--Chip waveform, code-division multiaccess (CDMA), interference suppression, linear receiver, spread spectrum.

A new class of direct-sequence spread-spectrum multiple-access (DS-SSMA) systems with continuous phase modulation (CPM) is defined. The signals are unique in that the spreading is done by adding an extra phase term to the information phase while maintaining phase continuity, constant envelope, and efficient bandwidth usage. The spreading phase is formed from the spreading code and is independent of the information phase, which allows despreading to be done separately before data detection, which, in turn, allows a simple CPM detector to be employed for data detection. The information phase is considered in the minimum-shift keying (MSK) format, and a serial-MSK-type spread-spectrum receiver is considered for performance analysis. Expressions for the signal-to-noise ratio, the power spectral density, and the probability of bit error are developed, along with methods for computing their values to an arbitrarily close approximation. Numerical results show that the proposed system is an attractive alternative to the conventional DS-SSMA systems. Index Terms--Continuous phase modulation (CPM), multiple-access communication, spread spectrum.

Diversity combining of multiple time varying and correlated fading branches is investigated for direct-sequence spread-spectrum systems. The correlated branches are modeled and estimated jointly as a vector autoregressive (VAR) process. The joint estimation is shown to provide performance gain over separate estimation of the fading branches. The parameter matrices of the VAR model are estimated via the method of expectation maximization (EM) with two algorithms. The first algorithm, using results from Kalman smoothing, provides a closed-form solution to the maximization problem in the iterative EM procedure. However, the iterative EM-Kalman algorithm operates repeatedly on a batch of training data and results in large storage requirements and long processing delays. To overcome these disadvantages, a new algorithm with only forward-time recursions is proposed that approximates the iterative EM solution and efficiently adapts to slowly changing Doppler spreads. As a result, the new algorithm significantly reduces memory and training sequence requirements. Through computer simulations, a near ideal bit-error rate performance is found for both algorithms, and the efficacy of the new adaptive algorithm for channels with changing Doppler spreads is demonstrated. Index Terms--Autoregressive processes, correlated fading channels, direct-sequence spread-spectrum communication, diversity methods, expectation maximization method, maximum-likelihood estimation.

Direct-sequence spread-spectrum multiple-access (DS/SSMA) communications, strictly band-limited transmitter chip waveforms with excess bandwidth in the interval between zero and one, pseudo-random spreading sequences, an additive white Gaussian noise channel, and matched filter receivers are considered. First, a new expression for the average bit error rate (BER) is derived for systems with quaternary phase-shift keying (QPSK) spreading, the conventional matched filter receiver, a coherent detector for binary phase-shift keying (BPSK) data symbols, and chip waveforms that result in no interchip interference. The expression consists of a well known BER expression based on the Standard Gaussian Approximation to multiple-access interference and a few correction terms. It enables accurate BER evaluations without any numerical integration for various choices of system parameters of interest. The accuracy of the expression is guaranteed as long as the Conditional Gaussian Approximation to the cross-correlation coefficients between the desired user's spreading sequence and the interfering users' spreading sequences is valid. The expression well reflects the effect of filtering on the system performance. Extensions of the expression are discussed for systems with QPSK spreading and different detection schemes, systems with BPSK spreading, and systems with different transmit and receive filters. Monte Carlo simulation results are also provided to verify the accuracy. Index Terms--Approximation theory, bandlimited communication, code division multiple access, performance evaluation, pulse shaping, spread spectrum communication.

An optimal signal design for band-limited, asynchronous, direct-sequence code-division multiple-access (DS-CDMA) communications with aperiodic random spreading sequences and the conventional matched filter receiver is considered in an additive white Gaussian noise (AWGN) channel. With bandwidth defined in the strict sense, two optimization problems are solved under finite bandwidth and zero interchip interference constraints. First, a chip waveform optimization is performed given the system bandwidth, the data symbol transmission rate, and the processing gain. A technique to characterize a band-limited chip waveform with a finite number of parameters is developed, and it is used to derive optimum chip waveforms which minimize the effect of multiple-access interference (MAI) for any energy and delay profile of users. Next, a joint optimization of the processing gain and the chip waveform is performed, given the system bandwidth and the data symbol transmission rate. A sufficient condition for a system to have lower average probability of bit error for any energy profile is found, and it is used to derive some design strategies. It is shown that the flat spectrum pulse with the processing gain leading to zero excess bandwidth results in the minimum average probability of bit error. Design examples and numerical results are also provided. Index Terms--Chip waveform, code division multiple access (CDMA), matched filter, optimal signal design, random spreading sequence.

Byline: Shiauhe Tsai (1), Wen Gao (1), James S. Lehnert (1) Keywords: maximum a posteriori (MAP) detection; channel estimation; interference suppression; time-varying fading channel; matched filter; code-division multiple-access (CDMA); direct-sequence spread-spectrum (DS-SS); conditional Gaussian approximation Abstract: An adaptive maximum a posteriori (MAP) receiver withmultiple-access interference (MAI) mitigation is proposed for DS-CDMAsystems in frequency-flat, time-varying fading channels. The receiverconsists of a sequence matched filter (MF), an adaptive channelestimator, and a MAP demodulator. By oversampling the MF output, thereceiver can characterize the MAI symbol-by-symbol to suppress thestrong and time-varying MAI. Without any pilot insertion and apriori knowledge, the channel estimator can adapt to various fadingchannels using a general, model-based approach. For practicalimplementations, a reduction in complexity is introduced and is shownto have a negligible effect on both uncoded and decoded bit errorrates (BER's). Author Affiliation: (1) School of Electrical and Computer Engineering, Purdue University, 1285 EE Building, West Lafayette, IN, 47907-1285, U.S.A Article History: Registration Date: 04/10/2004

In this paper, we consider signal reception in multicarrier code-division multiple-access (MC-CDMA) systems. A blind adaptive algorithm is proposed to determine a weight vector which optimally combines the desired signal contributions from different carriers while suppressing noise and interference. No knowledge of the channel conditions (fading coefficients, signature sequences and timing of interferers, statistics of other noises, etc.) nor any training sequence is required. The performance is examined for Rayleigh fading channels. Results show that the proposed algorithm performs well and is robust to the near-far problem. Hence, the results show that MC-CDMA systems are attractive candidates for future CDMA systems. Index Terms - Adaptive signal detection, code-division multiple access, fading channels, interference suppression, multicarrier modulation.

Arbitrarily tight upper and lower bounds on the pairwise error probability (PEP) of a trellis-coded or convolutional-coded direct-sequence spread-spectrum multiple-access (DS/SSMA) communication system over a Rayleigh fading channel are derived. A new set of probability density functions (pdf's) and cumulative distribution functions (cdf's) of the multiple-access interference (MAI) statistic is derived, and a modified bounding technique is proposed to obtain the bounds. The upper bounds and lower bounds together specify the accuracy of the resulting estimation of the PEP, and give an indication of the system error performance. Several suboptimum decoding schemes are proposed and their performances are compared to that of the optimum decoding scheme by the average pairwise error probability (APEP) values. The approach can be used to accurately study the multiple-access capability of the coded DS/SSMA system without numerical integrations. Index Terms - Code division multiaccess, error correction coding, error analysis, fading channels.

The capacity of direct-sequence spread-spectrum modulation to reject narrow-hand interference can be significantly improved by eliminating narrow-band energy at the receiver in a process called frequency excision. This paper considers several algorithms that operate on the real-time discrete Fourier transform (DFT) of the received signal to perform frequency excision. The case in which only the signal and additive white Gaussian noise (AWGN) are present at the receiver is considered as a means of comparing the relative performance of different algorithms that operate without knowledge of the power spectral density of the interference. An approach for analysis, using tile postcorrelation signal-to-noise ratio (SNR) as the figure of merit, is presented that is valid for a broad class of spreading modulations. First, the algorithm that sets a fixed fraction of the frequency domain record to zero is examined using rank-order statistics as an analytical tool. This result is then generalized to confirm previous estimates of SNR degradation for the algorithm that sets all values that exceed a threshold to zero. These results are again generalized to apply to the algorithm that sets a fixed fraction of the hand to a fixed amplitude while retaining phase information in an algorithm called fraction clip. The relative performances of several clip algorithm options are derived as special casts. Finally, a performance measure of the algorithms in the presence of multiple narrow-band interference is provided and illustrated with an example. Index Terms - Code-division multiaccess, discrete Fourier transforms, interference suppression, pseudonnise coded communication, spread-spectrum communication.

Throughput, delay, and stability for two slotted ALOHA packet radio systems are compared. One system is a slotted direct-sequence spread-spectrum multiple-access (DS/SSMA) network where each user employs a newly chosen random signature sequence for each bit in a transmitted packet. The other system is a multiple-channel slotted narrow-band ALOHA network where each packet is transmitted over a randomly selected channel. Accurate packet success probabilities for the code-division multiple-access (CDMA) system are computed using an improved Gaussian approximation technique which accounts for bit-to-bit error dependencies. Average throughput and delay results are obtained for the multiple-channel slotted ALOHA system and CDMA systems with block error correction. The first exit time (FET) is computed for both systems and used as a measure of the network stability. The CDMA system is shown to have better performance than the multiple-channel ALOHA system in all three areas. Index Terms - Access protocols, code-division multiaccess, packet radio, pseudonoise coded communication, stability.

A conditional probability density function of the multiple-access interference (MAI) in direct sequence/spectrum-spreading multiple access (DS/SSMA) systems with complex modulation (e.g., M-ary and continuous phase) is derived from a geometric viewpoint. A method to efficiently calculate the two-dimensional (2-D) convolutions of a number of circularly symmetric densities is presented. The utility of these methods is then illustrated by evaluating a noncoherent DS/SSMA system.

Methods to determine the average error probabilities in quadriphase direct-sequence spread spectrum multiple-access (DS/SSMA) communication systems are proposed. The systems being considered employ random signature sequences and arbitrary chip waveforms that are time-limited to one chip interval. The methods range from an algorithm that determines upper and lower bounds with arbitrary accuracy, to simple formulas that provide accurate estimates efficiently. Each method will find applications in different areas. Numerical examples are provided to illustrate each of the methods.

A proposition that is useful for studying multiple-access interference (MAI) in generalized quadriphase spread-spectrum systems is established. The proposition provides the conditional density functions and the conditional cumulative distribution functions of random variables that characterize the MAI. It is shown that these characterizing random variables converge almost surely to the true MAI. The proposition provides a method to study the effect of the chip waveform on the performance of the system and provides a means for the design and analysis of spectrally efficient systems with continuous-phase or M-ary phase-shift-keyed modulation. The proposition allows the evaluation of the average error probability with arbitrary accuracy without making a Gaussian approximation for the MAI and is also useful for studying systems that send data in packets, where the delays of the interferers are often fixed for the duration of a packet. For illustration, the proposition is applied to computing the average error probability of generalized quadriphase direct-sequence spread-spectrum multiple-access communication systems with various chip waveforms and offset parameters corresponding to commonly used modulation schemes.

An expression for the decision statistic of the receiver in a noncoherent DS/SSMA communication system is obtained, and conditions are identified that allow key parameters in the expression to be modeled as a set of Gaussian random variables. The decision statistic is then characterized as an inhomogeneous quadratic form in Gaussian random variables. An applicable theorem is applied to obtain a new expression, a function of a set of independent Gaussian random variables, with the same distribution as the decision statistic. The results are used to determine the distribution for the decision statistic and to compute the average probability of error for the system. The effects of the length of the signature sequences and the number of interfering transmitters are illustrated.

Packet throughput figures are obtained for DS/SSMA slotted ALOHA radio systems where all users employ random signature sequences from bit-to-bit within all transmitted packets. These calculations use an improved Gaussian approximation technique which gives accurate bit error probabilities and also incorporates the effect of bit-to-bit error dependence within each packet in the multiple-access interference environment. Numerical results are given for packets which employ varying amounts of block error control, and a comparison is made with results obtained by other methods which ignore the effects of bit-to-bit error dependence and/or employ less-accurate Gaussian approximations to the probability of data bit error. Maximum throughput per unit bandwidth figures are calculated which compare favorably to similar figures for narrow-band signaling techniques.

A serial mininum-shift-keyed (MSK) direct-sequence spread-spectrum multiple-access (DS/SSMA) communication system is described and analyzed to obtain the signal-to-noise ratio. The single-channel system generates the same transmitted signals as a corresponding parallel MSK/DS/SSMA system. Hence, the transmitted signals have a constant envelope and desirable spectral properties. However, hardware is required for only one channel, and the multiple-access capability of the system compares favorably with a standard binary DS/SSMA system.

A new spreading scheme and an accompanying blind adaptive receiver structure are proposed for direct-sequence spread-spectrum multiple-access communications in a slowly-varying, frequency-selective fading channel. Each user's spreading sequence is given by the Kronecker product of a long-period pseudonoise (PN) sequence, which is accurately modeled by a random sequence, and a short-length deterministic signature code. This spreading scheme bridges the gap between pure PN spreading and pure short-code spreading schemes. It is shown that with this spreading scheme, the channel response to the desired signal component is easily estimated without relying on the spectral decomposition of the signal correlation matrix. With the estimate of the channel response, the receiver suppresses interference based on the maximum signal-to-interference ratio criterion. The blind adaptive receiver requires only coarse timing information and a priori knowledge of the desired user's PN sequence for adaptation. Numerical results show that the adaptive receiver significantly suppresses interference by successfully estimating the channel response and the interference statistics with a low computational complexity. An extension to spatio-temporal processing using an array antenna is also discussed. Index Terms--Code-division multiple access, fading channels, interference suppression, modulation, spread-spectrum communications.

A power control scheme, called truncated channel inversion, in which a mobile suspends transmission when the wireless channel is in a bad condition in order to reduce out-cell interference is examined. It is found that capacity is improved and battery power consumption is reduced as a consequence of suspending transmission, but extra queuing delay is introduced. It is shown that the extra queuing delay depends on how fast the channel characteristics change and that the truncated scheme works well, even for moderate mobile velocities. Index Terms--Code division multiple access, Markov processes, personal communication networks, power control.

A subspace-based linear minimum mean-squared error (MMSE) multiuser detection scheme is proposed for a multicarrier direct-sequence code-division multiple-access (MC-DS-CDMA) system. Typically, a MC-DS-CDMA system employs a band-limited chip waveform. The band-limited nature of the chip waveform causes problem in applying standard subspace techniques because no nonnull noise subspace can be formed. It is shown that channel and timing information needed for the construction of the linear MMSE detector can be identified by a multiple-signal-classification-like algorithm based on a finite-length truncation approximation of the chip waveform. In practice, since perturbed versions of the subspaces assumed in the finite-length truncation approximation are actually observed, and because of the band-limited property of the chip waveform, the accuracy of the channel estimation and, hence, the performance of the MMSE detector are degraded. This effect is investigated in this paper. Index Terms--Code-division multiple access, multicarrier system, multiuser detection, subspace-based estimation.

In this paper, the design of decision-feedback multiuser (DFM) receivers for asynchronous code-division multiple-access (CDMA) systems over a mismatched flat Rayleigh fading channel is studied, and tight upper and lower bounds on the pair-wise symbol-error probability, which has been averaged over the channel fading, time delays, and phase angles, are derived for some of the DFM detection schemes. The performance bounds, which are computed by efficient analytic techniques, can serve as reliable references for CDMA system design. It is shown that the proposed system, which takes into account the effect of mismatched fading on the system design, has some gain over the system where the estimation of fading is assumed to be exact. Index Terms--Decision feedback, fading, multiuser detection, spread spectrum.

A decision-feedback maximum a posteriori (MAP) receiver is proposed for code-division multiple-access channels with time-selective fading. The receiver consists of a sequence-matched filter and a MAP demodulator. Output samples (more than one per symbol) from the matched filter are fed into the MAP demodulator. The MAP demodulator exploits the channel memory by delaying the decision and using a sequence of observations. This receiver also rejects multiple-access interference and estimates channel fading coefficients implicitly to give good demodulation decisions. Moreover, computer simulations are performed to evaluate the bit-error rate performance of the receiver under various channel conditions. Index Terms--Code-division multiaccess, fading channels, feedback communication, linear prediction, MAP estimation.

A theoretical framework for evaluating the performance of alternative combinations of time weighting functions, frequency domain mapping algorithms and fractions of overlap in overlap-and-add architectures is presented. The proposed algorithm is based on real-time discrete Fourier transform and aims to minimize the sensitivity loss caused by frequency excision. The sensitivity loss due to time weighting is described for variable overlaps and several different windows.

In this paper, the application of a type-II hybrid ARQ protocol in a slotted direct-sequence spread-spectrum multiple-access (DS-SSMA) packet radio system is investigated. Both the static performance and the dynamic performance of such a system are analyzed. In the physical layer, packet error and packet success probabilities are computed using the improved Gaussian approximation technique, which accounts for the bit-to-bit error dependence within a packet. In the data-link layer, two-dimensional Markov chains are employed to model the system dynamic. Based on this model, the performance of the type-II hybrid ARQ protocol is upper and lower bounded by considering, respectively, a superior scheme and an inferior scheme. Steady state throughput and delay performances of the two bounding schemes are obtained. Moreover, it is shown that for each fixed input load, there is an optimal retransmission probability under the finite user population assumption. Bounds on this optimal retransmission probability are also given. Index Terms - Automatic repeat request, code division multiaccess, Markov processes, networks, packet radio, spread spectrum communication.

A linear decentralized receiver capable of suppressing multiple-access interference (MAI) for asynchronous direct-sequence code-division multiple-access (DS-CDMA) systems with aperiodic random signature sequences is proposed. Performance bounds on this receiver are also obtained. Using them as performance measures, the problem of chip waveform selection in DS-CDMA systems with the proposed receiver under the near-far scenario is investigated. In particular, the performance of several practical chip waveforms is compared. An LMS-type adaptive algorithm is developed to obtain the parameters needed in the receiver, which only requires the signature sequence and coarse timing information of the desired user. Index Terms - Adaptive signal detection, chip waveform, code division multiaccess, interference suppression, spread spectrum.