On adaptive minimum probability of error linear filter receiversfor DS-CDMA channels

Receiver architectures in the form of a linear filter front-end followed by a hard-limiting decision maker are considered for DS-CDMA communication systems. Based on stochastic approximation concepts a recursive algorithm is developed for the adaptive optimization of the linear filter front-end in the minimum BER sense. The recursive form is decision driven and distribution free. For additive white Gaussian noise (AWGN) channels, theoretical analysis of the BER surface of linear filter receivers identifies the subset of the linear filter space where the optimal receiver lies and offers a formal proof of guaranteed global optimization with probability one for the two-user case. To the extent that the output of a linear DS-CDMA filter can be approximated by a Gaussian random variable, a minimum-mean-square-error optimized linear filter approximates the minimum BER solution. Numerical and simulation results indicate that for realistic AWGN DS-CDMA systems with reasonably low signature cross-correlations the linear minimum BER filter and the MMSE filter exhibit approximately the same performance. The linear minimum BER receiver is superior, however, when either the signature cross-correlation is high or the background noise is non-Gaussian     

Design and analysis of receiver filters for multiple chip-rateDS-CDMA systems

As multimedia applications proliferate, there is a desire to provide wireless transport to information streams with inherently different data rates. Direct-sequence code division multiple access (DS-CDMA) is a natural multiple-access strategy for multiple data-rate systems. Previous work on multirate DS-CDMA receivers has focused on signal-processing techniques, which detect all users of all rates simultaneously. In the current work, multirate users have multiple bandwidths. Thus, it is proposed to exploit bandwidth differences to achieve frequency-based rate separation followed by single-rate detection schemes. Such a methodology enables a tradeoff between receiver complexity and performance. The performance of the proposed filters and receivers are derived for both a modified matched filter and modified decorrelator employing rate separation. The performance of a multirate CDMA overlay system is evaluated. In addition, chip pulse shaping for wide-band users is developed to improve performance for narrow-band users for the overlay system     

MMSE multiuser detection for array multicarrier DS-CDMA in fading channels

Reception of asynchronous, multicarrier direct-sequence-code division multiple access (DS-CDMA) in time-varying, multipath radio channels with use of a receiving antenna array is investigated. Interference reducing minimum mean squared error (MMSE) receivers are discussed, and by considering the time-variation of the channel, a modified structure is derived which is efficient for channels experiencing small-scale fading. A blind implementation of this receiver is then proposed. Subspace concepts are applied to formulate a tracking, composite channel vector estimator which operates effectively in fading situations, even when high levels of interference are present. Both the modified MMSE weight matrix and diversity combining weights are generated from these channel estimates. Simulations of the proposed receiver show it to have superior performance over a standard MMSE receiver which is periodically re-evaluated to permit it to follow the channel variations due to small-scale fading. Furthermore, a hybrid MMSE receiver is proposed which applies different processing methods depending on each transmitters mobility, resulting in improved performance.     

Comparison of MC-CDMA with DS-CDMA using frequency domain and time domain RAKE receivers

In this paper a multicarrier CDMA (MC-CDMA) system with a soft decision differential phase shift keying (DPSK) frequency domain RAKE receiver is described. We compare a MC-CDMA system with a direct sequence CDMA system using RAKE receivers. In contrast with previous MC-CDMA systems, guard intervals are not used and the carriers are spaced at the reciprocal of the bit rate, optimising the usage of the bandwidth. In this way a comparison can be made between the multicarrier CDMA system described and a direct sequence (DS-CDMA) system with the same bandwidth. The results presented are received bit error rates from Monte Carlo simulations. The simulations are conducted in a multipath channel with Rayleigh fading and 300 Hz Doppler spectrum with additive white Gaussian noise. It is shown that the multicarrier CDMA matched filter receiver performs favourably compared to the direct sequence CDMA matched filter receiver for 1 -path fading. For a single user at a receive bit error rate of 1×10^–3 in the 4-path fading channel the multicarrier RAKE receiver requires no knowledge of the channel delay spread and performs 3 dB worse than the DS-CDMA RAKE receiver simulated. The performance of the MC-CDMA RAKE receiver for a single user increases with increasing channel dispersion. The performance of the DS-CDMA RAKE receiver for multiple user is superior to that of the MC-CDMA RAKE receiver.     

A comparison of long versus short spreading sequences in codedasynchronous DS-CDMA systems

The performance of turbo-coded asynchronous direct sequence code division multiple access (DS-CDMA) using long and short spreading sequences is compared by both analysis and simulation. For coded systems with a conventional matched filter (MF) receiver, three analytical methods with different complexity are compared: the standard Gaussian approximation, the improved Gaussian approximation (IGA), and the density function approach. It is shown that while the standard Gaussian approximation is fairly accurate for the long sequences, it is too optimistic for the short sequences. For the short-sequence systems, the IGA gives an accurate estimate for the performance with much less complexity than the density function approach. The analysis shows that for either the additive white Gaussian noise (AWGN) channel or the flat Rayleigh fading channel and a MF receiver, there is a degradation in the average performance of the turbo-coded short-sequence systems compared to the long-sequence systems due to the fact that the cross-correlations are not time-varying. However, the short-sequence systems are amenable to the use of an interference suppression technique designed to minimize the mean square error. Such a minimum mean square error (MMSE) receiver in the turbo-coded system is shown to outperform the long-sequence system with the MF receiver, especially when there is a near-far problem, as previously observed in a convolutionally-coded system. Finally, similar results are obtained by computer simulations for the turbo-coded CDMA systems on a frequency-selective Rayleigh fading channel     

Performance of coded DS‐CDMA system using reduced rank MMSE receiver in Rayleigh fading channels

This paper examines the performance of a reduced rank minimum mean square error (MMSE) receiver‐based direct sequence code division multiple access (DS‐CDMA) system. For such system, when a large processing gain is employed, substantial time is consumed in computing the filter tap weights. Many schemes for reducing the complexity of the MMSE have been proposed in recent years. In this paper, computational complexity reduction of the MMSE receiver is achieved by using the K‐mean classification algorithm. The performance of the uncoded and coded systems are investigated for the full rank MMSE receiver and reduced rank MMSE receiver and results are compared in terms of bit error rate at different loading levels in both AWGN and fading channels. A system with the matched filter (MF) receiver is also presented for the purpose of comparison and an analytical pair‐wise error bound for the coded system is derived. In the adaptive implementation of the receivers, results show that good performance is achieved for the reduced rank receiver when compared to the full rank receiver in both coded and uncoded systems, while in the optimum implementation of the tap weights, the reduced dimension receiver performance experiences degradation when compared to the full rank scheme. Over the band‐limited channels considered, results for the reduced rank receiver also reiterate the fact that higher code rates tend to yield lower BER than that of low rate codes. Copyright © 2006 John Wiley & Sons, Ltd.     

Reduced-rank interference suppression for DS-CDMA based on interpolated FIR filters

Reduced-rank receivers based on interpolated finite impulse response (FIR) filters for direct sequence code division multiple access (DS-CDMA) systems are proposed and a novel scheme where the interpolator is rendered time-varying is introduced. The interpolated minimum mean squared error (MMSE) and constrained minimum variance (CMV) solutions are derived for both receiver and interpolator to mitigate multiple access interference (MAI) and intersymbol interference (ISI) in a downlink scenario.     

Filter Bank Channelizers for Multi-Standard Software Defined Radio Receivers

The ability to support multiple channels of different communication standards, in the available bandwidth, is of importance in modern software defined radio (SDR) receivers. An SDR receiver typically employs a channelizer to extract multiple narrowband channels from the received wideband signal using digital filter banks. Since the filter bank channelizer is placed immediately after the analog-to-digital converter (ADC), it must operate at the highest sampling rate in the digital front-end of the receiver. Therefore, computationally efficient low complexity architectures are required for the implementation of the channelizer. The compatibility of the filter bank with different communication standards requires dynamic reconfigurability. The design and realization of dynamically reconfigurable, low complexity filter banks for SDR receivers is a challenging task. This paper reviews some of the existing digital filter bank designs and investigates the potential of these filter banks for channelization in multi-standard SDR receivers. We also review two low complexity, reconfigurable filter bank architectures for SDR channelizers based respectively on the frequency response masking technique and a novel coefficient decimation technique, proposed by us recently. These filter bank architectures outperform existing ones in terms of both dynamic reconfigurability and complexity.     

SINR maximizing space-time filtering for asynchronous DS-CDMA

Direct sequence code division multiple access (DS-CDMA) is a core technology for wireless access that is proposed for future generation (3G) mobile and personal communication systems. The use of a base-station antenna array is strongly endorsed in these systems, because of its capabilities of filtering out the interference in the space domain. This paper considers space-time one shot single user receivers for DS-CDMA, based on a multiple input single output time invariant linear filter. The optimization of the filter response is performed jointly in the space and time domains yielding maximal signal-to-interference-plus-noise ratio. Using this framework, a space-time noise whitening matched filter (ST-NWMF) for DS-CDMA demodulation is introduced. It is shown that combined spatio-temporal filtering, taking advantage of the fact that the multiple access interference is colored in the space as well as time domains, can reduce the effects of strong interference components and improves the performance. Simpler suboptimal space-time linear receivers, consisting of a single temporal LT filter following the antenna array, are also considered. It is shown that such a filter approaches the ST-NWMF in the limit, when the M chip waveform has a flat spectrum with no excess bandwidth and N the observation interval is infinite. These schemes, optimal as well as suboptimal, for large observation intervals are suitable also for DS-CDMA systems employing long sequence spreading     

Design of reduced-rank MMSE multiuser detectors using random matrix methods

Reduced-rank minimum mean-squared error (MMSE) multiuser detectors using asymptotic weights have been shown to reduce receiver complexity while maintaining good performance in long-sequence code-division multiple-access (CDMA) systems. In this paper, we consider the design of reduced-rank MMSE receivers in a general framework which includes fading, single and multiantenna receivers, as well as direct-sequence CDMA (DS-CDMA) and multicarrier CDMA (both uplink and downlink). In all these cases, random matrix results are used to obtain explicit expressions for the asymptotic eigenvalue moments of the interference autocorrelation matrix and for the asymptotic weights used in the reduced-rank receiver.     

Performance of coded DS-CDMA with pilot-assisted channel estimationand linear interference suppression

We consider a direct sequence (DS-) code division multiple access (CDMA) system with orthogonally multiplexed pilot signals and minimum mean squared error (MMSE) data and channel estimation. Both flat and frequency-selective fading channels are considered. Large system analysis is used to optimize the pilot-to-data power ratio (PDR) and the code rate for a fixed bandwidth expansion. Specifically, the PDR is selected to minimize the probability of error subject to a constraint on transmitted power. When the MMSE filter estimates the channel of the desired user, but averages over the channels of the interferers (corresponding to an adaptive filter in moderate to fast fading), the optimal PDR is less than that for the matched filter (MF). That is, the MMSE filter benefits from allocating more power to the data. When the MMSE filter directly incorporates estimates of all users' channel coefficients, the optimal PDR is greater than that for the MF. System performance as a function of code rate is characterized through both probability of error and cutoff rate. The optimal code rate for the MMSE receiver is generally higher than that for the MF, and increases with load and E_b/N₀. In the presence of fading, and with channel estimation, the optimal code rate approaches zero for both MMSE and MF receivers, but the MMSE filter is more robust with respect to a suboptimal choice of code rate     

Bandwidth-constrained signature waveforms and Walsh signal space receivers for synchronous CDMA systems

Synchronous CDMA systems whose transmission bandwidth is quantified through the fractional out-of-band energy (FOBE) constraint are considered. Either a conventional matched filter (MF) receiver or a minimum mean-square error (MMSE) receiver is employed for users' data detection. The total squared correlation (TSC) and the total mean-square error (TMSE) are proposed as the performance parameters for the MF and MMSE receivers respectively. These parameters need to be minimized in order to maximize the signal-to-interference ratios (SIRs) at the receivers' outputs. For a given FOBE bandwidth constraint, the sets of signature waveforms that minimize either TSC or TMSE are obtained from the prolate spheroidal wave functions (PSWFs). Furthermore, if the number of users is the size of a Hadamard matrix, then optimal signature waveforms can be obtained to maximize the individual SIR for every user. Due to the complicated nature of the PSWFs, simplified MF and MMSE receivers based on the Walsh signal space are developed.     

Forward-link performance of satellite CDMA with linear interference suppression and one-step power control

Wideband direct-sequence (DS)-code-division multiple-access (CDMA) is a strong candidate for both terrestrial and satellite components of UMTS. The forward-link capacity of a satellite DS-CDMA system with a conventional matched filter (MF) receiver is limited by interference from adjacent beams and possibly overlapping beams from multiple satellites. In this paper, we study the performance of the linear minimum mean squared error (MMSE) receiver for the satellite forward link. System constraints are long propagation delay, which prevents accurate closed-loop power control, and low on-board power consumption, which implies a low received bit energy to noise density ratio at the mobile receiver. We consider a "one-step" power adjustment algorithm which attempts to compensate for random shadowing and path loss, and compare the associated performance of the MMSE and MF receivers. Dual-satellite diversity is also considered. The effect of code rate on performance is studied through the use of punctured convolutional codes and the evaluation of random coding bounds. Our results indicate that linear MMSE interference suppression can improve the quality of service and increase system capacity significantly.     

Signal Processing by Generalized Receiver in?DS-CDMA Wireless Communication Systems with?Frequency-Selective Channels

The generalized receiver (GR) based on a generalized approach to signal processing (GASP) in noise is investigated in a direct-sequence code-division multiple access (DS-CDMA) wireless communication system with frequency-selective channels. We consider four avenues: linear equalization with finite impulse response (FIR) beamforming filters; channel estimation and spatially correlation; optimal combining; and partial cancellation. We investigate the GR with simple linear equalization and FIR beamforming filters. Numerical results and simulation show that the GR with FIR beamforming filters surpasses in performance the optimum infinite impulse response beamforming filters with conventional receivers, and can closely approach the performance of GR with infinite impulse response beamforming filters. Channel estimation errors are taken into consideration so that DS-CDMA wireless communication system performance will not be degraded under practical channel estimation. GR takes an estimation error of a maximum likelihood (ML) multiple-input multiple-output (MIMO) channel estimation and GR spatially correlation into account in computation of minimum mean square error (MMSE) and log-likelihood ratio (LLR) of each coded bit. The symbol error rate (SER) performance of DS-CDMA employing GR with a quadrature sub-branch hybrid selection/maximal-ratio combining (HS/MRC) scheme for 1-D modulations in Rayleigh fading is obtained and compared with that of conventional HS/MRC receivers. Procedure of selecting a partial cancelation factor (PCF) for the first stage of a hard-decision partial parallel interference cancellation (PPIC) of the GR employed in DS-CDMA wireless communication system is proposed. A range of optimal PCFs is derived based on the Price’s theorem. Computer simulation results show superiority in bit error rate (BER) performance that is very close to that potentially achieved and surpasses the BER performance of the real PCF for DS-CDMA systems discussed in literature.     

Optimal and suboptimal receivers for code‐multiplexed transmitted‐reference ultra‐wideband systems

In this study, optimal and suboptimal receivers are investigated for code‐multiplexed transmitted‐reference (CM‐TR) ultra‐wideband systems. First, a single‐user scenario is considered, and a CM‐TR system is modeled as a generalized noncoherent pulse‐position modulated system. Based on that model, the optimal receiver that minimizes the bit error probability is derived. Then, it is shown that the conventional CM‐TR receiver converges to the optimal receiver under certain conditions and achieves close‐to‐optimal performance in practical cases. Next, multi‐user systems are considered, and the conventional receiver, blinking receiver, and chip discriminator are investigated. Also, the linear minimum mean‐squared error (MMSE) receiver is derived for the downlink of a multi‐user CM‐TR system. In addition, the maximum likelihood receiver is obtained as a performance benchmark. The practicality and the computational complexity of the receivers are discussed, and their performance is evaluated via simulations. The linear MMSE receiver is observed to provide the best trade‐off between performance and complexity/practicality. Copyright © 2011 John Wiley & Sons, Ltd.     

A low complexity reduced-rank MMSE receiver for DS/CDMA communications

The minimum mean squared error (MMSE) receiver is a linear filter which can achieve optimal near-far resistance in direct-sequence code-division multiple-access communications. However, one of the main problems of this receiver is the required number of filter taps, which is typically large. This is especially true in systems with a large processing gain in which case the receiver's computation burden becomes very high. As a result, methods for reducing the complexity of the MMSE receiver have been of great interest in recent years. We propose an efficient partitioned MMSE receiver based on a classification algorithm. It is shown that the computational complexity (in terms of the filter taps) of the proposed receiver can be reduced significantly while good performance is maintained. Based on the special structure of our proposed receiver, we also propose a release-merge adaptive partition algorithm which can update the partition and the receiver's coefficients simultaneously. In particular, it is demonstrated that the proposed receiver can perform much better than previously proposed reduced-rank MMSE receivers, such as the partial despreading MMSE receiver and the cyclically shifted filter bank receiver, with even a smaller number of taps.     

Partial zero-forcing adaptive MMSE receiver for DS-CDMA uplink in multicell environments

Adaptive multi-user detection techniques for interference suppression in direct-sequence code division multiple access (DS-CDMA) systems have gained much attention since they do not require any information on interfering users. In the uplink of DS-CDMA systems, however, the base station receiver typically knows the spreading waveforms of the users within its cell but does not know those of the users in other cells. We propose a partial zero-forcing adaptive minimum mean squared error (MMSE) receiver for the DS-CDMA uplink utilizing the spreading waveforms known at the base station as well as training data. The proposed receiver first removes the intracell interference using a linear filter based on the knowledge of the spreading waveforms of the interfering users within the cell. Then the intercell interference remaining in the output of the linear filter is mitigated by adaptive MMSE detection. To speed up the convergence of the adaptive filter weights without loss of the steady-state performance, we develop a modified least mean square (LMS) algorithm based on the canonical representation of the filter weights. It is shown through analysis and simulation results that the proposed receiver improves the convergence speed and the steady-state performance.     

Convolutionally coded multicarrier DS-CDMA systems in a multipathfading channel. II. Narrow-band interference suppression

For pt.I see ibid., vol.47, p.1570-92 (1999). In Rowitch and Milstein (1999), a convolutionally encoded multicarrier asynchronous direct-sequence code-division multiple-access (DS-CDMA) system was proposed and compared to a classical single-carrier DS-CDMA system employing a RAKE receiver and the same convolutional code, in the presence of additive white Gaussian noise and multiple-access interference. This paper considers the additional impact of various forms of narrow-band interference on the performance of these two systems and the ability of the multicarrier system to effectively suppress the interference using the innate structure of its receiver. At roughly equivalent receiver complexity, results demonstrate superior performance of the multicarrier system in the presence of such interference, without requiring the addition of a front-end interference suppression filter     

Asymptotic Performance Analysis of Blind Minimum Output Energy Receivers for Large DS-CDMA Systems

The random matrix theory is used to analyze the asymptotic performance of the blind minimum output energy (MOE) receiver in direct-sequence code division multiple-access (DS-CDMA) systems in the presence of unknown multipath channel under the condition that the spreading factor and the number of users go to infinity with the same rate. As a special case, the asymptotic properties of the blind Capon receiver are also studied and the conditions of convergence of the signal-to-interference-plus-noise ratio (SINR) of this receiver to that of the optimal minimum-mean-square error (MMSE) receiver are discussed. In particular, it is shown that the SINR performances of the Capon and MMSE receivers are nearly identical in the uplink scenario, while the performance of the Capon receiver may be considerably inferior to that of the MMSE receiver in the downlink transmission case. As the performance of the Capon receiver is closely related to the performance of the Capon channel estimator, the asymptotic properties of the latter estimator are also studied and the conditions of convergence of the Capon channel estimate to a scaled version of the channel vector of the user-of-interest are obtained.     

An improved blind adaptive MMSE receiver for fast fading DS-CDMAchannels

Blind adaptive minimum mean-squared errors (MMSE) receivers for multiuser direct-sequence code-division multiple access (DS-CDMA) systems that assume knowledge of the steering vector, i.e., the cross-correlation between the desired output and the input signal, are known for their robustness against channel fading as they do not attempt to explicitly track the channel of the user of interest. However, these receivers often have higher excess mean squared error and, hence, poorer performance than training-sequence based adaptive MMSE receivers. In this paper, an improved correlation matrix estimation scheme for blind adaptive MMSE receivers is provided. The new scheme takes advantage of the fact that the desired linear receiver can be expressed as a function of the interference correlation matrix only, rather than the total data correlation matrix. A theoretical analysis is performed for the flat fading case which predicts that the new estimation scheme will result in significant performance improvement. Blind adaptive MMSE receivers with the new estimation scheme appear to achieve performance comparable to the training-sequence based adaptive MMSE receivers. Detailed computer simulations for the fast multipath fading environment verify that the proposed scheme yields strong performance gains over previous methods