Effect of chip waveform shaping on the performance of multicarrier CDMA systems

This paper studies the effect of chip waveform shaping on the performance of band-limited multicarrier direct-sequence code-division multiple-access (MC-DS-CDMA) systems. The performance criterion is the average multiple access interference at the output of a correlation receiver. A criterion based on the elementary density function is introduced for the performance comparison of various chip waveforms. It is demonstrated that the performance of MC-DS-CDMA systems is quite insensitive to the chip waveform shaping. Moreover, the optimum chip waveform for MC-DS-CDMA systems is practically the same as that of a single-carrier DS-CDMA system.     

An optimal signal design for band-limited asynchronous DS-CDMAcommunications

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     

Chip waveform design for DS/SSMA systems with aperiodic randomspreading sequences

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     

Asynchronous multiple-access interference suppression and chipwaveform selection with aperiodic random sequences

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     

Interference control and chip waveform design in multirate DS-CDMAcommunication systems

We study the interference effects in a multirate DS-code-division multiple-access (CDMA) system. Optimum chip waveform selection with arbitrary shapes is analyzed using a time domain approach. The problem is posed as an interference minimization problem under energy and time-bandwidth constraints and prolate spheroidal wave functions are used to arrive at a solution. Various factors affecting the interference are identified and the trade-off between competing factors is analyzed. The effect of the interchip interference on the optimum chip waveform design is also quantified under a practical bandwidth constraint. We study the benefits of employing two different chip waveforms for two classes of users. We compare the performance of systems employing two different chip waveforms with that of a single-chip waveform system such as IS-95. We show that when the power imbalance is large, it is advantageous to employ two different chip waveforms for different classes of users     

Performance Limits in DS-CDMA Timing Acquisition

This paper addresses timing acquisition aspects in direct-sequence code division multiple access (DS-CDMA) systems. Various chip waveform shaping schemes are considered, including both one-chip long full-response pulses, and partial-response ones occupying several chip periods. Different figures of merits are considered in a comparative analysis that seeks to establish performance limits in terms of correct timing detection capability, false alarm rate, bandwidth occupancy, multiple-access interference (MAI), and inter-chip interference (ICI). A waveform design algorithm is formulated to optimize system performance in terms of signal-to-interference-ratio (SIR) subject to other signalling constraints, and a solution based on the use of prolate spheroidal wave functions (PSWF) is derived. Numerous waveform design examples are then constructed to illustrate acquisition detection capability versus system load for both faded and unfaded cases. A comparative assessment of the performance of conventional signalling waveforms against the optimized ones is also presented. In particular, the numerical results show that the half-sine pulse used in minimum shift keying (MSK) is quasi-optimal within the full-response category, while root-raised cosine (RRC) Nyquist filtering with 22% rolloff (used in third generation CDMA standards) is also close to optimal when considering many-chip-long pulses.     

A Unified Analysis of Quaternary DS-CDMA Systems with Arbitrary Chip Waveforms and Its Applications

This paper is to present a systematic performance analysis of asynchronous quaternary direct sequence code division multiple access (DS-CDMA) systems using random signature sequences with arbitrary chip waveforms. The simplified improved Gaussian approximation method for bit error rate computation is extended to include arbitrary time-limited (full response or partial response) or band-limited chip waveforms with arbitrary receiver filters. As a time-limited partial response chip waveform modulation format, the well-known power and spectral efficient superposed quadrature amplitude modulation with matched filter or zero-forcing filter is evaluated, and the results show that the optimum zero-forcing filter will yield a performance better than the matched filter counterpart. For band-limited chip waveforms, based on an elementary density function of a second-order polynomial, a class of second-order continuity pulses is proposed for analysis. It is found that all common band-limited pulses are only its special cases. As a member of the class, the widely used frequency domain raised cosine pulse has the worst anti-multiuser-access-interference capability, which has been pointed out in (H. H. Nguyen, Proceedings of IEEE Canadian Conference on Electrical & Computer Engineering, 2002, pp. 1271–1275).     

Analysis and optimization of DS-CDMA systems with time-limited partial response chip waveforms

Conventional direct sequence code division multiple access systems (DS-CDMA) using offset quadrature phase shift key (OQPSK) usually employ a strictly bandlimited partial response square-root raised cosine pulse as the chip waveform. They have the disadvantage of large envelope fluctuation that will incur performance degradation due to the intermodulation and bandwidth enlargement caused by post nonlinear processing. To improve the performance of DS-CDMA systems, the chip waveform and receiver should be properly selected. This paper presents a systematic performance analysis of a matched filter receiver and zero-forcing filter (ZF) receiver for DS-CDMA using a time-limited partial response chip waveform. Nevertheless the systematic performance analysis is applicable to bandlimited chip pulse as well. For the zero-forcing filters, we propose to select the frequency responses that satisfy the first Nyquist criterion. With this class of filters, we can choose the roll-off factor to minimize the total power of multiple access interference and noise power. The zero-forcing filter with proper choice of roll-off factor, referred to as optimum ZF, yields a performance better than the matched filter counterpart. The bit error rate (BER) performance of the optimum ZF with superposed quadrature amplitude modulation signal as the time pulse waveform is evaluated. It is shown that the optimum ZF provides better BER performance than conventional OQPSK and minimum shift keying, and its envelope uniformity is much better than that of OQPSK.     

On the performance of band-limited asynchronous DS-CDMA over nakagami-m channels

In this paper we investigated the BER performance of DS-CDMA using various chip-waveforms, which include three time-limited chip-waveforms and two band-limited chip-waveforms. Closed-form formulae were derived for evaluating the achievable bit-error rate performance with the aid of the standard Gaussian approximation, when communicating over a Nakagami-m channel. The time-limited waveforms impose a low implementational complexity, since they maybe over sampled and read from a look-up table. However, they are outperformed by the frequency-domain raised-cosine waveform as well as the optimum waveform specifically designed by Cho and Lehnert for achieving the lowest possible bit error rate     

Performance bounds on chip-matched-filter receivers for bandlimited DS/SSMA 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.     

On the use of interference suppression to reduce intermodulationdistortion in multicarrier CDMA systems

This paper presents a coded multicarrier direct-sequence code-division multiple-access (DS-CDMA) system that, by the use of a minimum mean-squared-error receiver, achieves frequency diversity (instead of path diversity as in a conventional single-carrier RAKE DS-CDMA) and has the ability to suppress the intermodulation distortion and partially compensate for the signal distortion introduced by a nonlinear amplifier at the transmitter. A frequency-selective Rayleigh fading channel is decomposed into M frequency-nonselective channels, based on the channel coherence bandwidth. A rate 1/M convolutional code, after being interleaved, is used to modulate M different DS-CDMA waveforms. The new system is shown to effectively combat intermodulation distortion in the presence of multiple-access interference     

A method using optimized combinations based on energy spectrum extension factor to reduce MAI in asynchronous DS-CDMA systems

The principle to suppress multiple access interference (MAI) using double chip waveforms (DCW) in asynchronous DS-CDMA systems is analyzed in the paper. Based on the principle, a new method adopting optimized combinations of chip waveforms (CCW) to reduce MAI is proposed. The energy spectrum extension factor (ESEF) of equivalent chip waveform is introduced to optimally select CCW to reduce MAI, improve the signal to interference plus noise ratio (SINR) and bite error rate (BER) performance of asynchronous DS-CDMA users. The general closed form expression of SINR for asynchronous DS-CDMA users with CCW is obtained. The BER is also derived by improved Gaussian approximation (IGA). The theoretical analysis and numerical simulation results show that the optimized CCW using ESEF can effectively suppress MAI better, achieve higher SINR and BER performance compared with DCW. Moreover, the overlap between the simulation and IGA BER curves verifies the theoretical derivation.     

Error probabilities for generalized quadriphase DS/SSMAcommunication systems with random signature sequences

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     

Convolutionally coded multicarrier DS-CDMA systems in a multipathfading channel. I. Performance analysis

This paper presents a multicarrier asynchronous direct-sequence code-division multiple-access (DS-CDMA) system wherein the output of a convolutional encoder modulates multiple band-limited DS-CDMA waveforms, which are transmitted in parallel at different carrier frequencies. The receiver detects and combines signals for the desired user and feeds a soft-decision Viterbi decoder. The performance of this system is compared to that of a conventional single-carrier DS-CDMA system with a RAKE receiver, assuming a slowly varying frequency-selective Rayleigh fading channel and assuming the presence of additive white Gaussian noise and multiple-access interference. Results will demonstrate similar performance at roughly equal receiver complexity     

Performance evaluation for band-limited DS-CDMA systems based on simplified improved Gaussian approximation

The standard Gaussian approximation (SGA) for error analysis of direct-sequence code-division multiple-access (DS-CDMA) systems is very optimistic in many cases. Improved Gaussian approximation (IGA) is a technique that produces accurate error probabilities, but is still computationally intensive. Simplified IGA (SIGA) has complexity similar to that of SGA and, at the same time, provides sufficient accuracy. In this paper, we consider SIGA for DS-CDMA systems employing random sequences in a band-limited scenario. The validity of IGA for band-limited systems is established in a rigorous mathematical sense. Then a key parameter in SIGA is derived via a frequency-domain approach. Applications to a number of typical chip waveforms, including the popular sinc and raised-cosine pulses, are investigated. Performance comparison with IGA-based lower and upper bounds shows that SIGA yields very accurate probability of error.     

A noise whitening approach to multiple-access noise rejection .II.Implementation issues

Several practical methods are proposed for the implementation of linear filters that reject multiple-access noise in direct sequence code-division multiple-access (DS-CDMA) receivers. These methods rely on taking advantage of variations in the received chip spectrum, and do not require locking and despreading multiple signals. The resulting structures are simple, and some can operate at a high chip rate. Adaptive structures are also proposed. It is shown that a close relationship exists between noise whitening and chip-equalization for a DS-CDMA receiver. System issues affecting the choice of the chip spectrum, and thus the applicability of these methods, are described     

A DS-CDMA system using despreading sequences weighted by adjustablechip waveforms

This paper evaluates the performance of a direct-sequence code-division multiple-access system using coherent receivers in which the despreading sequences are weighted by adjustable chip waveforms. The chip weighting waveforms under consideration are designed for multiple-access interference (MAI) rejection. Assuming that the received chip waveforms are rectangular, new expressions for the signal-to-interference-plus-noise ratio (SINR) of the decision variable are derived when different weighted despreading sequences (WDSs) are used in the receiver. The novelty of the derived expressions is that each of the expressions, when the system parameters are given, is determined only by one parameter of the adjustable chip waveforms employed. As a result, we can simply tune the parameter to its optimal value in real-time for MAI rejection without knowing the other users' spreading codes, timing, and phase. The criterion for tuning the parameter is to maximize the SINR of the decision variable based on the relative strength between the additive Gaussian white noise and the MAI. Numerical results show that when the multiple-access interference is significant, the receivers using WDSs outperform significantly the conventional receiver using a rectangular despreading sequence. Brief analysis for bandlimited spreading signals is also provided to reveal the practical implications of the proposed technique     

DS-CDMA chip waveform design for minimal interference underbandwidth, phase, and envelope constraints

This paper investigates the effect of chip waveform shaping on the error performance, bandwidth confinement, phase continuity, and envelope uniformity in direct-sequence code-division multiple-access communication systems employing offset quadrature modulation formats. An optimal design methodology is developed for the problem of minimizing the multiple-access interference power under various desirable signal constraints, including limited 99% and 99.9% power bandwidth occupancies, continuous signal phase, and near-constant envelope. The methodology is based on the use of prolate spheroidal wave functions to obtain a reduced-dimension discrete constrained optimization problem formulation. Numerous design examples are discussed to compare the performance achieved by the optimally-designed chip waveforms with other conventional schemes, such as offset quadrature phase-shift keying, minimum-shift keying (MSK), sinusoidal frequency-shift keying (SFSK), and time-domain raised-cosine pulses. In general, it is found that while the optimized chip pulses achieved substantial gains when no envelope constraints were imposed, these gains vanish when a low envelope fluctuation constraint was introduced. In particular, it is also shown that MSK is quasi-optimal with regard to the 99% bandwidth measure, while the raised-cosine pulse is equally good with both the 99% and 99.9% measures, but at the expense of some envelope variation. On the other hand, SFSK is quasi-optimal with regard to the 99.9% bandwidth occupancy, among the class of constant-to-low envelope variation pulses     

Chip-delay locked matched filter for DS-CDMA systems using longsequence spreading

This paper considers an improved single-user detection technique for asynchronous direct-sequence code-division multiple-access (DS-CDMA) systems using long sequence spreading (random-CDMA) Most of the known detection schemes for DS-CDMA suffer from either poor performance under power-imbalance (near-far like) conditions, excessive complexity, or incompatibility with systems employing long sequence spreading. To address these problems, this paper considers a signal-to-noise ratio maximizing linear time-invariant filter for one-shot bit symbol detection exploiting some information about the interferers. This filter, referred to as the chip-delay locked matched filter (CLMF), exploits the cyclostationarity in multiple-access interference, and it can offer good near-far resistance while remaining suitable for systems with long sequence spreading. The CLMF requires knowledge of interferers chip delays and signal powers; however, knowledge of their pseudonoise sequences is unnecessary. This paper also demonstrates the improvement in performances offered by the CLMF over other single-user receivers such as the conventional matched filter and noise-whitening matched filter performance is evaluated in terms of probability of outage for single-rate and dual-rate DS-CDMA systems using bandwidth-efficient chip pulses, over a single-path additive white Gaussian noise channel. Errors in the interferer chip delay estimates degrade the CLMF performance. However, if the root-mean-square value of these errors is less than 5% of the chip interval, then this degradation is small     

Effect of tap spacing on the performance of direct-sequencespread-spectrum RAKE receiver

The effect of tap spacing on the performance of a RAKE receiver is analyzed analytically in a frequency-selective fading channel. A continuous time multipath fading channel model is used for the analysis, and the expression of the correlation between the desired signals, interference signals, and noise signals at the output of each branch of the RAKE receiver is derived for various chip waveforms. Since the noise components of each branch signal are correlated to each other, an optimum combining rule based on the maximum-likelihood criterion is derived to gain utmost performance. It is shown that the performance of the system can be improved by setting the tap spacing of the RARE receiver below the chip duration when the bandwidth of the transmitted signal is larger than the inverse of the chip duration. Also, it is shown that the normalized capacity of the system can be increased by using a chip waveform occupying wider bandwidth, which takes advantage of the increased diversity gain merits of a wide-band code-division multiple-access system at the same chip rate. It is noted that the derived combining rule gives diversity gain against the fading process as well as noise whitening processing gain against multiple-access interference at the same time