A simple and accurate method of probability of bit error analysisfor asynchronous band-limited DS-CDMA systems

This paper considers probability of bit error (P_e) analysis in asynchronous band-limited direct-sequence code-division multiple-access (DS-CDMA) systems. It presents a simple and accurate method of P_e analysis. The proposed method can serve as an attractive alternative to the only two techniques currently available for band-limited systems: the standard Gaussian approximation (SGA) and the characteristic function method. The former is prone to inaccuracy while the latter, large computational complexity. The method generalizes the simplified improved Gaussian approximation (SIGA) derived previously for rectangular pulses. This paper also outlines a generalization of another method referred to as the improved Gaussian approximation (IGA). Numerical examples demonstrate the far greater accuracy of the generalized SIGA with respect to the SGA. The examples consider the IS-95 and square-root raised cosine (Sqrt-RC) pulses as well as uniform and nonuniform received power conditions     

The error performance of CD900-like cellular mobile radio systems

The symbol error performance of CD900-like digital cellular mobile radio systems over narrowband and urban wideband transmission channels was investigated. The basic performance is presented for Gaussian, flat-fading Rayleigh, and log-normal channels in the presence of selection and ratio combining space diversity schemes. For wideband channels having more than one resolvable fading path, a CD900-like system without diversity reception suffers from large residual symbol error probabilities P_R(≈10^-1). The introduction of adaptive correlation diversity (ACD) mitigates the effects of multipath, yielding a P_R of 6×10^-5. Although this P_R value is relatively low, the probability of symbol error (P_e) versus signal-to-noise ratio (SNR) is significantly poorer than for the Gaussian channel. By combining the ACD scheme with space diversity, the P_R is eliminated by P_e >10^-5, and the channel SNR is within 5 dB of the Gaussian channel performance when P_e is 10^-10     

BER Performance of Bandlimited DS-CDMA Systems in Nakagami Fading

Accurate average bit-error rate analysis of asynchronous bandlimited binary direct-sequence code-division multiple-access (DS-CDMA) systems in Nakagami-m fading is studied. The fading is assumed to be flat and slow. The spectrum raised-cosine (SRC) and Beaulieu-Tan-Damen (BTD) pulse-shapes are employed. A new method which combines the characteristic function (CF) method with the improved Gaussian approximation (GA) is proposed for evaluating the BER of bandlimited DS-CDMA. A substantial computational complexity reduction is achieved. The well-known standard GA, Holtzman's simplified improved GA, and improved Holtzman's GA methods are also considered. The accuracies of the approximation methods are assessed using Monte Carlo simulation. For a system employing a deterministic sequence for the desired user and random sequences for the active interfering users, a CF method is employed to derive precise BER results. The new BTD pulse outperforms the SRC pulse in all situations     

Accurate computation of bit error probabilities of band-limited asynchronous DS-CDMA systems using higher order moments

An existing method called the simplified improved Gaussian approximation (SIGA) was previously applied to compute the bit error probabilities (BEPs) of band-limited asynchronous direct sequence code division multiple access (DS-CDMA) systems employing general pulse shaping (IEEE Trans. Commun., vol. 50, p. 656, 2002). The SIGA method uses moments up to the second order and is more accurate than the standard Gaussian approximation (SGA) (IEEE Trans. Commun., vol. 50, p. 656, 2002). In this paper, a new method that uses moments up to the fourth order is proposed for computing the BEP. The method is derived from a five-point Chebyshev interpolation formula and is inherently more accurate than the SIGA. Like the SIGA, the new method requires the evaluation of only closed-form expressions and the error function. The new method achieves higher accuracy with a modest increase in computational complexity.     

An Exact Error Analysis for Low-Duty Pulsed DS-CDMA Systems in Flat Nakagami Fading

Based on the characteristic function method, an exact error analysis is presented for low-duty pulsed direct sequence code division multiple access (DS-CDMA) systems in flat Nakagami fading channel. The presented method is simple and good for any arbitrary pulse shape. The computational involvement of the method is simpler than the method based on improved Gaussian approximation (IGA), which is the only reliable method currently available for calculating error probabilities of such systems     

Average bit-error-rate performance of band-limited DS/SSMA communications

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.     

Influence of guard times on the performance of slottedfrequency-hopped spread spectrum multiple access systems

A number of authors have examined the problem of determining the codeword error probability, P_e, in an asynchronous frequency-hopped spread spectrum multiple access (FH-SSMA) communication system. In this letter, we present a method for determining P_e in a time-slotted system which incorporates a guard time and study the effect of the guard time on P_e and some other performance measures     

Performance analysis of a linear MMSE receiver for bandlimited random-CDMA using quadriphase spreading over multipath channels

This paper analyzes the bit-error-rate (P/sub e/) performance of a linear minimum mean-square error (LMMSE) receiver for bandlimited direct-sequence code-division multiple-access systems which use quadriphase spreading with aperiodic pseudonoise (PN) sequences. The analysis is based on the improved Gaussian approximation (IGA) with focus on chip pulse shaping. It shows that the IGA reduces to the standard Gaussian approximation (SGA) if 1) random quadriphase spreading is employed, 2) the spreading factor takes moderate to large values, and 3) the chip pulse excess bandwidth (BW) is zero. Hence, the SGA, known for its inaccuracy in low regions of P/sub e/, remains an accurate approximation even when the number of active users in the system is small as long as the aforementioned conditions are met. The analysis holds for either matched or different transmit and receive filters. Consequently, closed form conditional P/sub e/ expressions are derived for the coherent selective RAKE and the LMMSE receivers and verified with Monte Carlo simulations. Numerical results are presented to illustrate the performance improvement achieved by the LMMSE receiver which, in contrast to the coherent selective RAKE receiver, not only suppresses interference when the excess BW of chip pulse is nonzero, but also harnesses the energy of all paths of the desired user. Under the examined scenarios tailored toward current narrowband system settings, the LMMSE receiver achieves 60% gain in capacity over the selective RAKE receiver. A third of the gain is due to interference suppression capability of the receiver while the rest is credited to its ability to collect the energy of the desired user diversified to many paths. Future wideband systems will yield an ever larger gain.     

An efficient simulation of multiple correlated Rayleigh fading envelopes

In order to better assess the performance of wireless communication systems, it is desirable to produce multiple Rayleigh fading envelopes with specified correlations. In this paper, we analyze theoretically a procedure which generates correlated Gaussian random variables from independent Gaussian random variables and give a physical explanation for the limitation of this procedure. Then, based on some uncorrelated Rayleigh fading envelopes, a simple but efficient procedure for generating an arbitrary number of cross-correlated Rayleigh fading envelopes is proposed. Simulation results and computational complexity analysis are presented, which show that the proposed method has some advantages, such as high accuracy, low computational complexity and easy implementation, over the conventional simulation method.     

基于奇异值分解的直扩信号伪码序列及信息序列盲估计方法

针对非合作扩频通信中直扩信号伪码序列的盲估计问题,在已知码片速率和伪码周期的前提下,该文提出一种基于奇异值分解的直扩信号伪码序列及信息序列的盲估计方法。该方法对接收信号构成的观测矩阵进行奇异值分解,通过左奇异向量实现伪码序列估计的盲估计。同时,通过右奇异向量可以在信号序列未同步和伪码序列未知的情况下实现信息序列的盲估计。仿真实验结果表明该算法具有精确度高、稳定性高、计算量小和观测时间短等优点。     

Quadriphase DS-CDMA with pulse shaping and the accuracy of the Gaussian approximation for matched filter receiver performance analysis

Probability of bit-error (P/sub e/) performance of asynchronous direct-sequence code-division multiple-access (DS-CDMA) systems is analyzed. In particular, the effects of pulse shaping, quadriphase (or direct-sequence quadriphase shift keying (DS-QPSK)) spreading, aperiodic spreading sequences and the coherent correlator or, equivalently, the matched filter (MF) receiver are considered. An exact P/sub e/ expression and several approximations: one using the characteristic function (CF) method, a simplified expression for the improved Gaussian approximation (IGA) and the simplified improved Gaussian approximation (SIGA) are derived. Two main results are presented. Under conditions typically satisfied in practice and even with a small number of interferers, the standard Gaussian approximation (SGA) for the multiple-access interference component of the MF statistic and for MF P/sub e/ performance is shown to be accurate. Moreover, the IGA is shown to reduce to the SGA for pulses with zero excess bandwidth. Second, the P/sub e/ performance of quadriphase DS-CDMA is shown to be superior or equivalent to that of biphase DS-CDMA. Numerical examples with Monte Carlo simulation are presented to illustrate P/sub e/ performance for square-root raised-cosine (Sqrt-RC) pulses and spreading factors of moderate to large values.     

TH-CDMA/PPM的比特误码率分析与研究

对采用二元脉冲位置调制的超宽带跳时多路无线电网络的误码率进行了分析。在矩形脉冲的前提下,可以得到关于TH-CDMA/PPM信号在高斯白噪声信道存在k个干扰时错误比特的概率。通过概率的表达式来评定类高斯噪声的准确性,从而可以对超宽带脉冲无线电网络的类高斯噪声性能进行分析。通过大量的仿真结果可以看到,由类高斯噪声产生的比特误码率要低于高斯噪声产生的。对于每个信息比特有较少的脉冲的系统来说,类高斯噪声所产生的错误就变得非常重要。     

Performance of binary and quaternary direct-sequencespread-spectrum multiple-access systems with random signature sequences

The performance of synchronous and asynchronous, binary and quaternary (with and without offset) direct-sequence spread-spectrum multiple-access (DS/SSMA) communication systems using random signature sequences and arbitrary chip waveforms is investigated. The average probability of error at the output of the correlation receiver is evaluated using a characteristic-function approach for these systems. Numerical results are presented that illustrate performance comparisons between systems using random and deterministic signature sequences, synchronous and asynchronous systems, systems with rectangular or sinewave chip waveforms, and binary and quaternary systems with the same data rates and bandwidth. In all cases, the accuracy of the Gaussian approximation is also examined     

Performance evaluation of TH-PPM UWB systems in the presence of multiuser interference

This letter presents a new method for the evaluation of the bit error probability of a time hopping binary pulse position ultra-wideband modulation scheme, in the presence of multiuser interference. The technique permits to predict the system performance with high accuracy and reasonable complexity. A perfect agreement with simulation results is shown, and a comparison with the Gaussian approximation is presented.     

Iterative demodulation/decoding methods based on Gaussian approximations for lattice based space-time coded systems

In this letter, we study iterative demodulation and decoding methods for lattice based space-time coded systems concatenated with convolutional codes. We first apply the optimal MAP demodulation and the suboptimal linear MMSE methods to lattice based space-time demodulation and decoding. We then propose two other methods based on the idea of soft interference cancellation and in one method vector Gaussian approximation is used and in the other method scalar Gaussian approximation is used. We also present the EXIT chart analyses for the performance analyses for these iterative methods. Both theoretical and simulation results show that the performance of the vector Gaussian approximation method is the same as that of the linear MMSE method but in some cases the vector Gaussian approximation method has lower complexity. The complexity of the scalar Gaussian approximation method is the lowest among these different methods and grows linearly with the transmission rate while it still has an acceptable performance. Full diversity and full rate lattice based space-time coding is compared with the BLAST scheme and simulations show that the former has a better performance than the later even with the proposed suboptimal iterative demodulation and decoding methods.     

Successive interference cancelation for space-time block codes over time-selective channels

In this letter, we propose a very simple successive interference cancelation (SIC) based signal detector for space-time block codes (STBC) to combat time-selective fading. The main idea is to treat un-detected symbols as noise using a Gaussian approximation. Simulation results show that our scheme can provide performance very close to ML decoding with extremely low computational complexity     

Artificial Bee Colony and Tabu Search Enhanced TTCM Assisted MMSE Multi-User Detectors for Rank Deficient SDMA-OFDM System

In this paper, we present a generalized accurate methodology to predict the bit error rate performance for non-coherent chaos-based communication systems. The Gaussian approximation approach, which is widely used to compute the performance of such systems, leads to inaccurate results, especially with respect to low spreading factors. Our new approach based on the chaos bit energy distribution gives accurate results even for low spreading factors. The system is studied and simulated under an additive white Gaussian noise, Rice and Rayleigh channels. Finally, we compare our approach to the Gaussian approximation approach. Computer simulations shows a high accuracy for our method, especially for small spreading factors.     

Accurate DS-CDMA bit-error probability calculation in Rayleighfading

A binary direct-sequence spread-spectrum multiple-access system with random sequences in flat Rayleigh fading is considered. A new explicit closed-form expression is obtained for the characteristic function of the multiple-access interference signals. It is shown that the overall error rate can be expressed by a single integral whose integrand is nonnegative and exponentially decaying. Bit-error rates (BERs) are obtained with this expression to any desired accuracy with minimal computational complexity. The dependence of the system BER on the number of transitions in the target user signature chip sequence is explicitly derived. The results are used to examine definitively the validity of three Gaussian approximations and to compare the performances of synchronous systems to asynchronous systems     

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).     

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.