An improved design of chip waveforms for band-limited DS-CDMA systems

This paper introduces an efficient and improved design of chip waveforms to minimize the multiple-access interference in band-limited direct-sequence code-division multiple-access (DS-CDMA) systems. For ease of implementation, the DS-CDMA system employs a time-limited chip waveform, whereas its band limitation is ensured by the low-pass filters at both the transmitter and receiver ends. The design uses sinusoids to synthesize the time-limited chip waveform so that the portion of its spectrum across the specified bandwidth is as flat as possible. It is shown that by using a simple series expansion (with only a few terms) the synthesized chip waveforms significantly outperform the spreading/despreading waveforms previously proposed, particularly for large values of the chip duration-bandwidth product.     

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     

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     

Bit-to-bit error dependence in slotted DS/SSMA packet systems withrandom signature sequences

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     

On the use of a suppression filter for CDMA overlay

This paper is concerned with a direct-sequence code-division multiple-access (DS-CDMA) system operating over a Rayleigh fading channel and sharing a common spectrum with a narrow-band waveform. A suppression filter at the receiver is employed to reduce the narrow-band interference. We evaluate the average up-link bit error rate (BER) performance and investigate how the performance is influenced by various parameters, such as the number of taps of the suppression filter, the number of multiple-access users, the ratio of narrow-band interference bandwidth to the spread-spectrum bandwidth, the interference power to signal power ratio, the ratio of the offset of the interference carrier frequency from the spread-spectrum carrier frequency to the half spread-spectrum signal bandwidth, and so on     

一种并行传输的时频域扩频多载波DS-CDMA系统性能分析

提出了一种并行传输的时频域扩频多载波DS-CDMA系统,它先将传输数据进行串并转换而后经过时域和频域两次扩频。在不改变传输数据速率和扩频增益的情况下,并行传输可以增大符号时间和降低码片速率,从而提高信号的抗频率选择性衰落的能力和实现低速率信号处理。采用码片匹配滤波的方式对信号进行接收,分析了高斯信道下的单用户检测性能并推导了误比特率表达式。研究表明,在此系统中串并转换比与码片速率的降低和子载波个数成正比,而与误比特率无关;不存在比特间干扰;多用户干扰只存在于同一子载波传输的不同用户的数据比特之间,且可通过采用正交时域扩频码来消除;误比特率随用户数量的增加而增加,而随每比特信噪比和扩频增益的增加而降低;在带宽受限的情况下,可通过合理设置串并装换比、时域和频域扩频增益参数来简化系统实现,满足误比特率的性能需求。     

Protection of a Narrow-Band BPSK Communication System with an Adaptive Array

This paper describes the performance of an adaptive array when used with narrow-band BPSK communication signals; A previous paper [11] described the performance of an adaptive array with a standard BPSK signal when the array bandwidth is several times the signal bandwidth. These earlier results are extended to the case where the array bandwidth is as small as possible, equal to the desired signal symbol rate. To realize such a bandwidth reduction, it is necessary to reshape the BPSK signaling waveform before transmission to prevent intersymbol interference. This is done by passing the BPSK signal through a pulseshaping filter at the transmitter. The performance of the optimal detector for the narrow-band BPSK signal is determined when this detector operates behind an adaptive array that is subjected to CW interference. The bit error probability is obtained as a function of the desired signal and interference powers and arrival angles as well as the array bandwidth.     

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.     

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.     

Subspace multiuser detection for multicarrier DS-CDMA

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 non 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.     

The effect of low SNR in phase estimation in wideband CDMA

In wideband code-division multiple-access (CDMA) systems, where large diversity gains are used to mitigate the effects of multipath fading, system performance is increasingly limited by channel estimation error. In a packet-based system, the estimation error can be reduced by increasing the header length; however this, for a fixed bandwidth, reduces the amount of transmit energy available to the data symbols and reduces the processing gain of the system. To determine the allocation of the transmit energy between the data and estimation symbols in order to minimize the probability of bit error, we use an approximate upper bound on the probability of bit error for a RAKE receiver operating with imperfect phase estimates     

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.     

TCM/SSMA communication systems with cascaded sequences and PAM/QAMsignal sets

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     

MMSE detection in asynchronous CDMA systems: an equivalence result

The analysis of linear minimum mean-square error (MMSE) detection in a band-limited code-division multiple-access (CDMA) system that employs random spreading sequences is considered. The key features of the analysis are that the users are allowed to be completely asynchronous, and that the chip waveform is assumed to be the ideal Nyquist sinc function. It is shown that the asymptotic signal-to-interference ratio (SIR) at the detector output is the same as that in an equivalent chip-synchronous system. It is hence been established that synchronous analyses of linear MMSE detection can provide useful guidelines for the performance in asynchronous band-limited systems.     

Performance of ultrawideband SSMA using time hopping and M-ary PPM

Wireless spread spectrum multiple access (SSMA) using time hopping and block waveform encoded (M-ary) pulse position modulated (PPM) signals is analyzed. For different M-ary PPM signal designs, the multiple-access performance in free-space propagation renditions is analyzed in terms of the number of users supported by the system for a given bit error rate, signal-to-noise ratio, bit transmission rate, and number of signals in the M-ary set. The processing gain and number of simultaneous users are described in terms of system parameters. Tradeoffs between performance and receiver complexity are discussed. Upper bounds on both the maximum number of users and the total combined bit transmission rate are investigated. This analysis is applied to ultrawideband impulse radio modulation. In this modulation, the communications waveforms are practically realized using subnanosecond impulse technology. A numerical example is given that shows that impulse radio modulation is theoretically able to provide multiple-access communications with a combined transmission capacity of hundreds of megabits per second at bit error rates in the range 10^-4 to 10^-7 using receivers of moderate complexity     

Interference suppression for DS/CDMA

A direct-sequence spread spectrum (DS/SS) receiver for suppressing multiple-access interference in direct-sequence code-division multiple-access (DS/CDMA) communication systems is introduced. The proposed receiver does not require knowledge of other users' spreading codes, timing, or phase information. Moreover, the receiver allows the number of taps to be chosen independently of the processing gain and, hence, is easily applicable to CDMA systems employing either a small or a large processing gain. Performance analysis, including average probability of error and signal-to-noise ratio, is provided, and results are presented for systems varying from lightly loaded (for example, eight user/255 chip) to heavily loaded (for example, 50 user/200 chip). Performance results indicate that the proposed receiver outperforms the linear correlation receiver and, in many cases, it does so by a considerable margin     

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     

Hybrid DS/SFH spread-spectrum multiple access with predetectiondiversity and coding for indoor radio

The authors derive close upper and lower bounds on the average bit error probability for hybrid direct-sequence/slow-frequency-hopped spread-spectrum multiple-access (DS/SFH-SSMA) systems with noncoherent DPSK demodulation, using predetection diversity (selection combining and equal gain combining) in conjunction with interleaved channel coding (Hamming (7,4) code and BCH (15,7) code) operating through indoor radio channels. A multipath Rayleigh fading model is assumed for the indoor radio channel. The results show that the DS portion of the modulation combats the multipath interference, whereas the FH portion is a protection against large multiaccess interference. It is shown that, for the considered types of channel coding, the use of predetection diversity is still essential for obtaining satisfactory error performance     

Performance analysis of time-hopping spread-spectrum multiple-access systems: uncoded and coded schemes

An ultra-wide bandwidth time-hopping spread-spectrum code division multiple-access system employing a binary PPM signaling has been introduced by Scholtz (1993), and its performance was obtained based on a Gaussian distribution assumption for the multiple-access interference. In this paper, we begin first by proposing to use a practical low-rate error correcting code in the system without any further required bandwidth expansion. We then present a more precise performance analysis of the system for both coded and uncoded schemes. Our analysis shows that the Gaussian assumption is not accurate for predicting bit error rates at high data transmission rates for the uncoded scheme. Furthermore, it indicates that the proposed coded scheme outperforms the uncoded scheme significantly, or more importantly, at a given bit error rate, the coding scheme increases the number of users by a factor which is logarithmic in the number of pulses used in time-hopping spread-spectrum systems.     

Multi-user performance of direct-sequence CDMA using combinedbinary PPM/orthogonal modulation

A new modulation format is proposed for cellular code-division multiple-access (CDMA) communications where binary pulse position modulation (PPM) is embedded in the chip waveform and combined with orthogonal modulation using Walsh/Hadamard codes. Compared to the conventional CDMA using orthogonal codes, this scheme allows reduction in receiver complexity by lowering the modulation level for the second-stage orthogonal modulation. The staggered (half-chip) quadrature direct-sequence signaling is adopted to uniformly distribute the transmit power and allow noncoherent detection at the receiver because carrier phase tracking is not feasible because of the binary PPM, suitable for the reverse link in cellular networks. Statistics of inter-user interferences are characterized, and then derive the symbol error probability for the proposed M-ary modulation format. It is shown that the advantage in view of receiver complexity can be achieved without deteriorating the multi-user performance in terms of the number of users affordable at a specified error rate