In this paper, the Nyquist criterion for ordinary linear modulation is generalized to the discrete-Fourier transform-spread (DFT-spread) orthogonal frequency-division multiplexing (OFDM). In particular, the DFT-spread OFDM of constellation-rotated PAM symbols is considered with frequency-domain spectrum shaping (FDSS). This includes the DFT-spread OFDM of π/2-BPSK symbols as a special case, which is supported by the 5th generation New Radio standard. Unlike the conventional Nyquist criterion with a linear receiver, the new criterion is to remove intersymbol interference in the output of a widely-linear receiver. It is shown that not only the folded spectrum but also the shifted and reverse-folded spectrum is crucial in the criterion, where the shift offset is determined by the rotation angle. As a design example, combinations of a constellation rotation angle and a square-root raised cosine pulse are proposed. It is shown that the proposed design can achieve better performance both in spectral efficiency and in peak-to-average power ratio than the conventional DFT-spread OFDM of π/2-BPSK symbols with FDSS.

In this paper, the Nyquist criteria for ordinary linear modulation are generalized to the discrete-Fourier transform-spread (DFT-spread) orthogonal frequency-division multiplexing (OFDM) of constellation-rotated PAM symbols. Unlike the conventional Nyquist criteria with a linear receiver, the new criteria are to remove intersymbol interference in the output of a widely-linear (WL) receiver. It is shown that not only the folded spectrum, but also the shifted and reverse-folded spectrum is crucial in the criteria, where the shift offset is determined by the rotation angle. As a design example, combinations of a constellation rotation angle and a square-root raised cosine pulse are proposed. It is shown that the proposed design can achieve better performance both in spectral efficiency and in peak-to-average power ratio than the conventional DFT-spread OFDM of π/2-BPSK symbols. The optimal one-tap frequency-domain equalizer is also derived under the WL zero-forcing (ZF) constraint. It is shown that, when the rotation angle is properly chosen, the proposed one-tap WL-ZF equalizer significantly outperforms the one-tap linear ZF equalizer in output signal-to-noise ratio. The proposed equalizer also outperforms the conventional equalizer in error vector magnitude measured at the output of a nonlinear power amplifier.

In this paper, single-carrier (SC) block transmission of improper-complex data symbols is considered over a multiple-input multiple-output (MIMO) frequency-selective channel with data-like cochannel interference (CCI). To exploit the cyclostationarity and impropriety of the desired and the interfering signals, an equalizer is designed that oversamples the received signal and then processes the sampled block by using widely-linear (WL) feedforward (FF) and noise-predicting feedback (NP-FB) filters. For the given equalizer structure, the minimum mean-squared error (MMSE)-optimal WL FF and NP-FB filters have high computational complexity due to the augmented correlation matrix of the data-like CCI in the received signal. Motivated by the asymptotic property of the correlation matrix, we approximate in the frequency domain the matrix by a block matrix with diagonal blocks. This leads to the low-complexity WL design of a frequency-domain FF filter and a causally noise-predicting FB filter. It is shown that this MIMO SC frequency-domain equalizer with noise prediction is asymptotically optimal in the sense that the average mean-squared error converges to that of the MMSE-optimal equalizer as the block length tends to infinity. Numerical results show that the proposed equalizer performs well even with a moderate block length.

In this paper, the design of a selfless overlay system is considered for a frequency-selective bandlimited linear time-invariant channel already occupied by a legacy system. It is assumed that the transmitted signal by the legacy system is well modeled by a zero-mean second-order cyclostationary (SOCS) Gaussian random process. It is also assumed that the legacy receiver employs a linear-conjugate linear (LCL) filter to capture possible impropriety of the signal. Our objective is to maximize the throughput of the overlay system under the constraint that no interfering signal component is observed at the output of the legacy LCL filter sampled at a uniform rate. A relevant problem of deriving the constrained capacity of a discrete-time vector Gaussian noise channel is first examined. Then, it is shown that the optimal input to the overlay channel must be a zero-mean SOCS Gaussian random process. Using these results, the optimization problem is formulated in the frequency domain, and the procedure named orthogonal cyclic water filling (O-CWF) is derived to find the optimal channel input distribution. Numerical results are provided to show that the proposed selfless overlay scheme enables reliable communication even over a channel fully occupied by a legacy system.

We consider the wireless relay network in which a base station communicates with multiple subscribers, each of which has the ability to act as a relay to forward information to a base station. Here, we propose an algorithm for joint optimization of power allocation, time scheduling, and relay selection when there is imperfect channel state information (CSI). We show that the algorithm converges with probability one to the optimal solution when a condition is satisfied. Otherwise, it converges with probability one to a solution in some neighborhood of the optimal solution.

An acquisition scheme, based on the least mean-squared error (LMSE), for the symbol timing, carrier phases, and multipath gains for multicarrier code-division multiple-access (MC-CDMA) systems is proposed. A new coefficient called the quasi-mean-squared accuracy coefficient (QMSAC) is introduced. This allows the search for multiple optimal parameters to be split into simpler single-parameter estimates. The symbol timing is acquired with a comparison of the QMSACs followed by a linear interpolation scheme or a search of a minimizing variable. Carrier phases and multipath gain coefficients are then estimated via some algebraic computations based only on the estimated symbol timing and the QMSACs. The spreading sequence of the desired user is the only prior knowledge required for the proposed approach. Simulation results demonstrate the near-far resistance of the approach and show that the error performance of minimum mean-squared error (MMSE) detection with acquired parameters is only a few decibels worse for the considered channel than the performance obtained with perfect knowledge about the channel impulse response.

The windows for achieving good multiple-access performance of multicarrier code-division multiple-access (MCCDMA) systems employing minimum mean-squared error receivers are studied. The mean-squared error (MSE) is used as the performance metric for the optimization. In a simplified two-user system, the rectangular window is found to be optimum while regarded as an inferior window in orthogonal frequency-division multiplexing systems because of its spectral inefficiency. Necessary conditions are given for improving the performances of spectrally efficient windows by exploiting the cyclic prefix and oversampling in the frequency domain.

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.

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.

Multiple-input, multiple-output (MIMO) techniques are considered in an asynchronous code-division multiple- access system with a flat fading channel. A unified maximum- likelihood receiver, based on chip-level oversampling, is proposed to jointly suppress the multiple-access interference and perform the space-time decoding. Analysis shows that the system performance is determined by the product measure of the space- time code and the effective signal-to-interference-plus-noise- ratio (SINR). Three expurgated union bounds are proposed to approximate the bit error rate for different MIMO schemes and SNRs. Next, spectral efficiency is analyzed by applying a Gaussian approximation to the multiple-access interference. Numerical results show that the chip-level oversampling, together with MIMO techniques, can effectively increase the spectral efficiency. The impact of channel estimation error on spectral efficiency is also investigated both analytically and numerically. Two tradeoffs are found in a lower bound of spectral efficiency. In the first tradeoff to optimize spectral efficiency, the increase of the number of users is shown to dominate the degradation of SINR. In the second tradeoff, increasing the number of training symbols in a fixed-length packet is shown to yield a higher SINR but a reduction in the amount of transmitted information. An optimal number of training symbols is found numerically as a function of the SNR and the packet length.

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 both large and small (in terms of the number of users) systems is considered. It is also shown that the proposed optimization technique is robust, and performs very well with nonlinear Tomlinson--Harashima precoding. Both coded and uncoded performances are considered.

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.

In this paper we develop optimization techniques for linear zero-forcing (ZF) 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 both large and small (in terms of the number of users) systems is considered. It is also shown that the proposed optimization technique is robust and performs very well with non-linear Tomlinson-Harashima precoding. Both coded and uncoded performances are considered

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.

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.

User capacity in synchronous CDMA systems has been well characterized and is fixed by the processing gain and target SIR required by each user. Asynchronous systems have not been as well studied. This paper examines the user capacity of asynchronous CDMA systems. It is shown that the user capacity can be increased over synchronous systems by allowing the users to be chip asynchronous and adapting their spreading codes to decrease interference. The degree to which the system experiences a gain by asynchrony is characterized by the effective dimension of the chip waveform. Simulation results are provided to verify that the user capacity is improved by allowing asynchrony when interference avoidance algorithms are employed.

In this paper, a linear receiver is proposed and its performance is analyzed for direct-sequence spread-spectrum communications with wideband data-like interference. Two groups of communicators employing generalized random spreading are considered, and the signals are assumed to have harmonically related cyclostationarity periods. First, the output signal-to-interference ratio (SIR) of a general correlation receiver is derived in the frequency domain, and the key system parameters that affect the structure of the interference are identified. Then, a linear interference suppression scheme based on the maximum SIR (MSIR) criterion is proposed, and a receiver structure similar to the cyclic Wiener filter is derived. Numerical results show that the proposed linear MSIR receiver significantly outperforms the conventional correlation receiver by effectively suppressing the wideband data-like 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.

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.

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.

Full-rate, full-diversity space-time codes are consid- ered in the framework of asynchronous direct-sequence code- division multiple access with aperiodic random spreading se- quences. The system is described in a multiuser uplink channel with multiple transmit and receive antennas. Chip-level oversam- pling is used to exploit the cyclostationarity of multiple-access interference. A sphere decoder is employed to jointly decode the space-time codes and suppress the interference. Simulation is performed to show the validity of applying the sphere decoder to multiple-access interference suppression. The performance im- provement of the sphere decoder over the conventional minimum- mean-square-error detector is also studied.

Gaussian approximations to the overall interference at the output of linear receivers are commonly used to analyze the performance of asynchronous DS/SSMA communication systems. In this paper, a new asymptotic analysis is presented to establish the validity of Gaussian approximations for the systems employing more general chip waveforms of interest, which include strictly band-limited waveforms. The transmit and receive chip waveforms, can be either time-limited or band-limited with their energy normalized to unity.

A simple transmit diversity method for asynchronous direct-sequence CDMA systems is proposed. In addition, a receiver structure that can effectively suppress multiple-access interference and exploit transmit diversity is examined. The proposed system is shown to perform well even when there are severe impairments to the desired user from high-power interferers. Finally, an adaptive implementation of the receiver is proposed, and its performance is evaluated with simulations.

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.

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.

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.

An optimal signal design for band-limited, asynchronous, direct-sequence code-division multiple-access (DS-CDMA) communications with aperiodic random spreading sequences and a 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.

The dependence of the error performance and spectral efficiency of direct-sequence spread-spectrum multiple-access (DS/SSMA) systems with matched filter receivers on the chip waveform is examined. The actual shape of the chip waveform, as well as its energy, is found to influence the statistical properties of the multiple-access interference (MAI). An approach to design waveforms that may result in interchip interference (ICI) is proposed and a criterion for design based on the conditional Gaussian approximation of the MAI for systems with aperiodic random spreading sequences is derived. For a simplified system, a closed-form solution for optimal band-limited waveforms is obtained for excess bandwidth less than or equal to one by using a performance metric that includes the effect of ICI. Numerical results, based on an analytical method, as well as Monte Carlo simulations, are provided to evaluate the performance of the proposed waveforms in general systems with conventional matched filter receivers.

Multicarrier direct-sequence spread-spectrum multiple-access systems in frequency-selective fading channels are investigated. A consistent channel model is used for each system. First, the tapped delay line (TDL) channel model with uniformly spaced, uncorrelated taps is investigated to model a complex Gaussian, wide-sense stationary, uncorrelated scattering channel. An approximate average bit-error-rate expression is obtained for the receiver with RAKE fingers on each subcarrier branch, whose outputs are combined according to the maximum signal-to-noise ratio criterion. Various system configurations are examined for the same TDL channel model, data rate, total system bandwidth, and excess bandwidth of the chip waveform. All the systems compared employ the same number of correlators. The numerical results show that, given a contiguous spectrum, the systems with more fractionally-spaced RAKE fingers per subchannel are more robust than the systems with more subcarriers.

In this paper, maximum a posteriori (MAP) detection is applied to a direct-sequence code-division multiple-access (DS-CDMA) system jointly with identification and estimation of time-selective fading channels. By sampling the outputs of the matched filter and combining antenna array elements, strong and time-varying multiple-access interference (MAI) is characterized and suppressed instantaneously. The decision statistics for MAP detection are obtained from the conditional probability density function of the prediction error. The prediction is accomplished by approximating the fading channel with a constrained nonlinear state model. Unknown parameters such as auto-regressive (AR) process coefficients, noise covariance matrices, and the antenna array vector are estimated based on received sample vectors only. Also, differential modulation is applied to eliminate the need for pilot insertion. Through computer simulations, near-optimum bit error rates (BERs) are found.

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.

The problem of selecting the processing gain and the chip waveform of a band-limited, direct-sequence spread-spectrum multiple-access communication system with aperiodic random spreading sequences and conventional matched filter receiver is considered when given the system bandwidth and the symbol transmission rate. The average probability of bit error is used as the objective function of the optimization. The signals are constrained to be strictly band-limited and to produce zero interchip interference. With a technique to characterize a band-limited chip waveform with a finite number of parameters, a sufficient condition for a system to have lower average probability of bit error is found. Some design strategies are derived that are based on the sufficient condition. Design examples are also provided using analytical methods and Monte-Carlo simulations.

Three methods of determining the Erlang capacity of a cellular CDMA uplink system are presented. The first method decouples the analysis of blocking and outage performance, and avoids iterative search. Based on two approximations regarding the mobile traffic and the interference, the second method jointly examines the blocking and outage performance. The third, more detailed, method considers the mobile traffic characteristics and the interference with mobile traffic fluctuations. The Erlang capacity of a cellular CDMA uplink system using a power control scheme called truncated channel inversion is calculated with each of the methods. The methods are also used to compare the Erlang capacities for different power control schemes.

A spatio-temporal matched filter receiver for direct-sequence spread-spectrum multiple-access (DS/SSMA) communications with aperiodic random quadriphase spreading sequences is derived, and the system performance is analyzed. It is shown with the method of characteristic functions that the cross-correlation coefficients between the desired user's and the interfering users' spreading sequences tend, in distribution, to independently and identically distributed circularly symmetric complex Gaussian random variables as the processing gain goes to infinity. Based on this Gaussian approximation, the structure of the spatio-temporal matched filter receiver is derived and a bit error rate formula is obtained. Using Monte-Carlo simulations, as well as analytical methods, it is shown that the spatio-temporal matched filter receiver achieves a significant performance improvement over the conventional, temporal, and spatial matched filter receivers by effectively suppressing the multiple access interference.

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.

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.

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.

In this paper, we consider the transmitter optimization problem in direct-sequence spread-spectrum multiple-access (DS/SSMA) communications with random spreading sequences and a matched filter receiver. A chip waveform optimization is performed under strict-sense bandwidth and zero interchip interference (ICI) conditions. Optimum chip waveforms are found for the excess bandwidth 0/spl les//spl beta//spl les/1, and are shown to achieve the minimum average bit error probability (BEP) for any distribution of the power and delay profiles of users. A simple efficiency measure is derived to assess how efficiently a chip waveform utilizes the excess bandwidth, and it is shown that the square-root raised cosine chip waveforms have only 50% efficiency. Numerical examples including BEP performance of the optimum chip waveforms are also provided.

In this paper, we consider the problem of fitting two users into a channel normally occupied by one user. The users share the same physical channel, but crosstalk is controlled. A linear receiver, which maximizes the signal-to-noise ratio (SNR) is employed, and several well known time-limited symbol waveforms are tested. Performance analysis shows that two users can be easily accommodated in a single-user channel with slight degradation of bit error rate (BER), and furthermore, near single-user performance is achievable by properly selecting the symbol waveform. A simple LMS-type algorithm is also discussed for adaptive implementation.

We consider subspace-based MMSE multiuser detection for multicarrier code division multiple access (MC-CDMA) in Rayleigh fading channels. The knowledge of the fading coefficients for all the carriers and the timing delay of the desired user is needed to construct the MMSE detector. A subspace-based channel estimation technique is developed to obtain the required information. Numerical results show that the proposed algorithm is robust to fading and moderate near-far situations.

The application of maximum a posteriori (MAP) detection to DS-CDMA systems in time-selective fading channels is investigated. By sampling the outputs of a matched filter and combining antenna array elements, strong multiple-access interference (MAI) is estimated and suppressed. By incorporating channel approximations, Kalman filtering, and the probability density of the prediction error, a joint channel estimation and MAP detection algorithm is developed. Unknown channel parameters are identified by using an algorithm similar to the extended Kalman filter (EKF). Also, differential modulation is applied to eliminate the need for pilot insertion. Through computer simulations, a near-optimum bit-error-rate (BER) performance is found.

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.

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.

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 dynamics. 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.

The stability of a slotted direct-sequence spread-spectrum multiple-access (DS-SSMA) packet radio network employing a type-II hybrid automatic-repeat-request (ARQ) protocol is considered. The equilibrium point analysis (EPA) technique is employed to approximately compute the system throughput and delay, and to analyze the system stability. It is found that the system exhibits bistable behavior in some situations. With this information, a desirable region of operation for the DS-SSMA network employing the type-II hybrid ARQ protocol is obtained.

An expression in matrix form for the multiple-access interference (MAI) in an asynchronous direct-sequence spread-spectrum multiple-access (DS/SSMA) communication system with cascaded sequences (CVs), arbitrary chip waveforms, and trellis-coded modulation (TCM) with a pulse amplitude modulation (PAM) or quadrature amplitude modulation (QAM) signal set is obtained. TCM provides significant coding gain while the CVs decrease the correlation between the MAI of adjacent data intervals. The expression is used to calculate arbitrarily accurate probability density functions (PDFs) of the MAI in the TCM system and to derive an accurate approximation of the MAI variance. It also helps illustrate some properties of the MAI by separating contributing parameters into different matrices. We derive an approximation of the upper union bound on the bit-error probability and investigate its applicability. The results show that CV schemes can greatly reduce the pairwise error probabilities (PEPs) until the length of the CV becomes greater than that of the error weight sequence (EWS) under consideration.

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 (PDFs) and cumulative distribution functions (CDFs) 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.

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.

A class of spread-spectrum systems with continuous-phase spreading signals is proposed. We present a characterization of the spectral-spreading signals that allows computation of various measures of the system performance, such as the signal-to-noise ratio (SNR), spectral density, and average bit-error probability. The error probability can be evaluated if the distributions of the multiple-access interferences (MAIs) are available. We obtain the conditional distributions of random variables that characterize the MAI given the time delays. These conditional distributions are used to compute vectors, allowing the average bit-error probability to be computed with arbitrary accuracy. Since most of the computations only involve array additions and multiplications, these operations can be performed efficiently on array processors.

The capacity of direct-sequence spread-spectrum modulation to reject narrow-band 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 the 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 band 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 cases. Finally, a performance measure of the algorithms in the presence of multiple narrow-band interference is provided and illustrated with an example.

We investigate direct-sequence spread-spectrum multiple-access (DS/SSMA) communication systems with general linear modulation and error control coding. By the central limit theorem for martingale difference arrays, it is proved that under general conditions, the overall multiple-access interference (MAI) across different symbol intervals tends to a jointly complex Gaussian random vector as both the number of chips per symbol interval and the number of interferers tend to infinity. The result allows the calculation of the limiting exact error probabilities, and justifies the use of the popular standard Gaussian approximation. The asymptotic properties of the MAI from each individual interferer are also examined. The results lead to another approximation, the conditional Gaussian approximation, which provides better estimates to the error probabilities, especially in near-far situations.

A linear receiver for direct-sequence spread-spectrum multiple-access communication systems under the aperiodic random sequence model is considered. The receiver consists of the conventional matched filter followed by a tapped delay line with the provision of incorporating the use of antenna arrays. It has the ability of suppressing multiple-access interference (MAI) and narrowband interference in some weighted proportions, as well as combining multipath components without explicit estimation of any channel conditions. Under some specific simplified channel models, the receiver reduces to the minimum variance distortionless response beamformer, the RAKE receiver, a notch filter, or an MAI suppressor. The interference rejection capability is made possible through a suitable choice of weights in the tapped delay line. The optimal weights can be obtained by straightforward but computationally complex eigenanalysis. In order to reduce the computational complexity, a simple blind adaptive algorithm is also developed.

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 conditional probability density function of the multiple-access interference (MAI) in direct-sequence spread-spectrum 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.

Direct-sequence spread-spectrum multiple-access (DS/SSMA) communication systems with random m-phase sequences, for even m, are considered. By examining the asymptotic behavior of the normalized multiple-access interference (MAI), the authors find that a system with random m-phase sequences, for m>4, should have the same performance as one with random quadriphase sequences asymptotically. However, a system, with random m-phase sequences, for m/spl ges/4, may perform better than one with random binary sequences when the number of simultaneous users is relatively small. A new Gaussian approximation is proposed to estimate the probabilities of error in these systems. In two cases, the new approximation reduces to established results which have been shown to provide close estimates to the probabilities of error.

A direct-sequence spread spectrum multiple access (DS/SSMA) communication system employing continuous phase modulation (CPM) and trellis coding is described and analyzed to obtain an estimate of the error probability. The trellis code provides significant coding gain while the CPM signal format gives desirable spectral properties. The analysis shows that significant improvement in error probability over the standard binary DS/SSMA system can be achieved with relatively simple codes.>

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.>

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.>

A serial minimum-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.>

Packet throughput figures are obtained for direct sequence spread spectrum multiple access (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 multiaccess 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 within each packet in the multiaccess interference environment. Numerical results are given for packets which employ varying amount of block error control, and a comparison is made with results obtained by other methods which ignore the effects of bit-to-bit error 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 narrowband signaling techniques.>

Progress is reported in the design and analysis of spread-spectrum packet radio networks for the factory of the future. This progress includes the accurate analysis of the probability of packet success in a direct-sequence spread-spectrum communication channel and analytical results on the transient behavior of packet radio networks. The first use of these networks will be to provide communications between a transport system controller and a fleet of autonomous guided vehicles.>

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.>

A technique is developed to find an accurate approximation to the probability of data bit error and the probability of packet success in a direct-sequence spread-spectrum multiple-access (DS/SSMA) packet radio system with random signature sequences. An improved Gaussian approximation to the probability of data bit error is performed. Packet performance is analyzed by using the theory of moment spaces to gain insight into the effect of bit-to-bit error dependence caused by interfering signal relative delays and phases which are assumed constant over the duration of a desired packet. Numerical results show that if no error control exists in the desired packet or if block error control is used when multiple-access interference is high, the error dependence increases the average probability of packet success beyond that predicted by models which use independent bit errors. However, when block error control is used and the multiple-access interference is low, the bit error dependencies cause a reduction in packet error performance.>

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 analysis of a multipath-combining receiver for directsequence spread-spectrum communications through a specular multipath channel is developed. The analysis applies to systems that use quadriphase-shift-keyed, offset quadriphase-shift-keyed, minimum-shiftkeyed, or binary phase-shift-keyed modulation. The measures of performance are the signal-to-noise ratio and approximations to the error probability involving the signal-to-noise ratio. The performance of a multipath-combining receiver is determined not only for the case of a single transmitter, but also for the case of multiple interfering transmit, ters. Furthermore, the performance of the system is determined in terms of parameters of the signature sequences. These parameters can be used as guides in selecting signature sequences for the system. Results are also given for the case of randomly generated signature sequences.