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).     

An enhanced widely linear CDMA receiver with OQPSK modulation

This paper studies an enhanced widely linear (WL) receiver for direct-sequence code-division multiple-access (DS-CDMA) systems that employ aperiodic spreading sequences with offset quadrature phase-shift keying (OQPSK) modulation. The modulation scheme generates improper complex multiple-access interference (MAI) and necessitates the use of WL receivers. Focus is on bandlimited pulse shapes and the inherent cyclostationarity (CS) of the uncoded received signal. The enhanced WL receiver replaces the conventional chip-matched filter with new filters that exploit the CS of the received signal through frequency shifting. The proposed WL receiver is shown to outperform the classical strictly linear (SL) receiver when the interfering users are (quasi-)synchronous with respect to the user of interest. High-powered interfering users, that may exist to support high data rates, increase the performance improvement delivered by the WL receiver. Moreover, it is shown that MAI can become proper, either identically or asymptotically, when users are asynchronous and equally powered. This is despite the fact that individual interfering signals are improper. Numerical results demonstrate that the WL receiver can outperform the SL receiver by 1-3 dB under the examined scenarios with current CDMA standards settings. In asynchronous or quasi-synchronous transmission modes, performance gain of the WL receiver degrades unless the number of high-powered active users remains small. An example for implementation of the WL receiver is proposed and compared with that of the SL receiver when minimum-shift keying modulation, a special case of OQPSK, is used. The implementation is based on a fractionally spaced equalizer whose taps are updated by an adaptive algorithm. It is shown that the proposed structure is capable of delivering the maximum signal-to-noise ratio predicted by theory.     

Second order polynomial class of chip waveforms for band-limited DS-CDMA systems

The conventional frequency domain square-root raised cosine (Nyquist) chip waveform has much poorer anti-multiple-access-interference (anti-MAI) capability than the optimal band- limited waveform in direct sequence code division multiple access (DS-CDMA) systems. However, the digital implementation of the optimal chip pulse is very costly due to the slow decaying rate of the time waveform. In addition, its eye diagram and envelope uniformity are worse than the Nyquist pulse for a wide range of roll-off factor, which will incur performance degradation due to timing jitters and post non-linear processing. In this paper, based on an elementary density function of a second-order polynomial, a class of second-order continuity pulses is proposed. From this class of pulses, we can find some members having faster decaying rate, bigger eye opening, more uniform envelope and stronger anti-MAI capability than the Nyquist waveform. The normalized-band-width-pulse-shape-factor product, the decaying rate of the tail of the time waveform, the opening of the eye diagram, and the envelope uniformity of the second-order continuity pulses are addressed in the paper that provide the basic information for the selection of the chip pulse for CDMA systems.     

Direct sequence spread spectrum Walsh-QPSK modulation

We present Walsh-quadrature phase-shift keying (Walsh-QPSK) pseudonoise (PN) modulation schemes for both coherent and noncoherent direct-sequence code-division multiple-access (DS-CDMA) systems, wherein the PN spreading sequences for in-phase and quadrature data in a conventional QPSK PN modulation scheme are coded by Walsh sequences indexed by a special rule to reduce the envelope variation of the transmitted signal. The signal characteristics of the two schemes are analyzed when a rectangular-shaped PN chip pulse is used, and it is shown that the proposed coherent DS-CDMA system has a constant envelope even in the presence of a transmitted phase reference. We simulate the signals to obtain the envelope variations when a spectrally efficient shaped PN chip pulse is used, and compare the results with those of conventional QPSK and orthogonal QPSK (OQPSK) PN modulation schemes. The results show that both the noncoherent and coherent Walsh-QPSK schemes have smaller envelope variations than the conventional noncoherent QPSK and OQPSK PN modulation schemes, even though in the coherent Walsh-QPSK scheme the pilot channel is added to the signal channel     

Optimum Modulation and Channel Filters for Nonlinear Satellite Channels

This is a comparative study of three modulation schemes: QPSK, Offset QPSK(OQPSK), and MSK, in nonlinear satellite channels with adjacent channel interference. Two kinds of typical satellite channel models are used for performance evaluation: one is an INTELSAT type narrow band model and the other is a domestic type wide band model. The transmitter filter and receiver filter are optimized for each combination of modulation scheme, channel model, and an input back-off condition for nonlinear amplifiers. All the combinations considered here have the optimum division of the Nyquist shaping between transmitter filter and receiver filter in common. The filters are a wide band sharp cut-off transmitter filter with flat inband response and a gently rolled-off Nyquist receiver filter with an aperture equalizer (x/sin xor1-(2x)^{2}/cos xequalizer). With these optimized filters, comparisons are made with respect to the bit error rate (BER) performance and phase jitter of the recovered carrier. OQPSK and MSK show superior BER performance to QPSK in the wide band model. However, in the narrow band model, QPSK shows the best BER performance among the three modulation schemes. The phase jitter in the recovered carrier is small for all modulation schemes in the wide band model. But, in the narrow band model, the phase jitter in OQPSK and MSK is four times larger than in QPSK. Generally QPSK is the most preferable modulation scheme in the narrow band model: OQPSK and MSK are most preferable for the wide band model.     

The search for optimized shaping filters suitable for vsat systems

The satellite communications industry has seen the emergence of VSAT (very small aperture terminal) systems with the promise of high growth in the next decade. The system design of the VSAT ground station has generally followed traditional satellite communication system design, namely featuring data transmission using QPSK (quadrature phase shift keying) or BPSK (binary phase shift keying) and 50 per cent raised cosine shaping filters with quasilinear transmission. Transmitter power is strictly limited and is at a premium for the VSAT transmitter which usually consists of a non-linear solid-state power amplifier (SSPA). Consequently it is important to operate the SSPA so that the maximum power is obtained, which means that the SSPA should be operated close to its saturation point. In so doing considerable distortion can be introduced, which leads to intersymbol interference (ISI) in the receiver and an associated degradation in error rate. Although constant envelope BPSK or QPSK solves the intersymbol interference problem and enables operation at the saturating point of the SSPA, the sinx/x spectral shape has unacceptable sidelobe levels. This paper gives results of a search for a pulse shaping filter characteristic that is bandlimited and yet has improved performance over the traditional root 50 per cent cosine roll-off filter when used in a VSAT ground station with a SSPA. The performance improvement due to improved shaping filtering is maintained over a range of output levels of the SSPA. Performance evaluation results using computer simulation are presented.     

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     

Chip Pulse Shaping in Asynchronous Chaos-Based DS-CDMA

This paper extends and fully formalizes some previous results by developing an analytical method to account for the general chip pulse for DS-CDMA systems in an asynchronous environment with an integrate-and-dump receiver, applying it to commonly used pulses. Given the pulse, such a formal method allows us to define the optimum spreading code autocorrelation to be used and the relative signal-to-interference ratio performance. A chaos-based spreading code is plugged into this model to show that such an optimum performance can be very well approximated by practical sequence generators. This is shown by analyzing some typical bandlimited and substantially bandlimited pulses and determining the optimum spreading for each of them. These results prove that the gain of chaos-based spreading over conventional i.i.d.-like spreading can reach 75% when practical bandlimited pulses are considered.     

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.     

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.     

基于并行干扰抵消的OFDM/OQAM系统中的信号检测方法

在多径衰落信道中,基于交错正交幅度调制的正交频分复用(OFDM with Offset QAM,OFDM/OQAM)系统使用迫零均衡器进行信号检测时,不能完全消除信道复数特性和滤波器实数正交特性引入的时域符号间干扰和频域子载波间干扰,及信道估计误差导致的误码率性能损失。该文利用对数据初始判决并重构相邻载波及符号间干扰的思想,通过分析采用迫零均衡信号检测时的残余干扰与信道估计误差干扰,提出了一种基于并行干扰抵消和迫零均衡器结合的OFDM/OQAM信号检测方法,并在IEEE 802.22技术标准的两种典型多径衰落信道中进行了计算机仿真与比较研究。仿真结果表明,与基于迫零均衡的检测方法相比,基于并行干扰抵消的迭代信号检测方法在误码率为1%时,可获得1 dB至2 dB的性能提升。     

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.     

Performance of coded OQPSK and MIL-STD SOQPSK with iterative decoding

We show that military standard (MIL-STD) shaped-offset quadrature phase-shift keying (SOQPSK), a highly bandwidth-efficient constant-envelope modulation, can be represented in the form of a cross-correlated trellis-coded quadrature modulation. Similarly, we show that offset QPSK (OQPSK) can be decomposed into a "degraded" trellis encoder and a memoryless mapper. Based on the representations of OQPSK and MIL-STD SOQPSK as trellis-coded modulations (TCMs), we investigate the potential coding gains achievable from the application of simple outer codes to form a concatenated coding structure with iterative decoding. For MIL-STD SOQPSK, we describe the optimum receiver corresponding to its TCM form and then propose a simplified receiver. The bit-error rate (BER) performances of both receivers for uncoded and coded MIL-STD SOQPSK are simulated and compared with that of OQPSK and Feher-patented QPSK (FQPSK). The asymptotic BER performance of MIL-STD SOQPSK is also analyzed and compared with that of OQPSK and FQPSK. Simulation results show that, compared with their uncoded systems, there are significant coding gains for both OQPSK and MIL-STD SOQPSK, obtained by applying iterative decoding to either the parallel concatenated coding scheme or the serial one, even when very simple outer codes are used.     

Error-rate evaluation of linear equalization and decision feedbackequalization with error propagation

We propose applying an approximate Fourier series to evaluate efficiently the bit-error-rate (BER) performance of finite-length linear equalization (LE) and decision feedback equalization (DFE). By extending the Fourier series, we enable BER calculations for quadrature phase-shift keying (QPSK) transmission on complex channels with in-phase and crosstalk intersymbol interference (ISI). The BER calculation is based on determining the residual ISI samples and background Gaussian noise variance at the equalizer output for static channels or for realizations of quasi-static fading channels. A simple bound on the series error magnitude in terms of the Fourier series parameters ensures the required accuracy and precision. Improved state transition probability estimates are derived and verified by simulation for an approximate Markov model of the DFE error propagation for the case in which residual ISI exists even when the previous decisions stored in the feedback filter (FBF) are correct. We demonstrate the ease and widespread applicability of our approach by producing results which elucidate a variety of equalization tradeoffs. Our analysis includes symbol-spaced and fractionally spaced minimum mean-square error (MMSE)-LE, zero-forcing (ZF)-LE, and MMSE-DFE (with and without error propagation) on static ISI channels and multipath channels with quasi-static Rayleigh fading; a comparison between suboptimum and optimum receiver filtering in conjunction with equalization; and an assessment of the accuracy of some widely used equalization BER approximations and bounds     

Downlink Specific Linear Equalization for Frequency Selective CDMA Cellular Systems

We derive and compare several linear equalizers for the CDMA downlink under frequency selective multipath conditions: minimum mean-square error (MMSE), zero-forcing (ZF), and RAKE. MMSE and ZF equalizers are designed based on perfect knowledge of the channel. The downlink specific structure involves first inverting the multipath channel to restore the synchronous multi-user signal transmitted from the base-station at the chip-rate, and then correlating with the product of the desired user's channel code times the base-station specific scrambling code once per symbol to decode the symbols. ZF equalization restores orthogonality of the Walsh-Hadamard channel codes on the downlink but often suffers from noise gain because certain channel conditions (no common zeros) are not met; MMSE restores orthogonality only approximately but avoids excessive noise gain. We compare MMSE and ZF to the traditional matched filter (also known as the RAKE receiver). Our formulation generalizes for the multi-channel case as might be derived from multiple antennas and/or over-sampling with respect to the chip-rate. The optimal symbol-level MMSE equalizer is derived and slightly out-performs the chip-level but at greater computational cost. An MMSE soft hand-off receiver is derived and simulated. Average BER for a class of multi-path channels is presented under varying operating conditions of single-cell and edge-of-cell, coded and un-coded BPSK data symbols, and uncoded 16-QAM. These simulations indicate large performance gains compared to the RAKE receiver, especially when the cell is fully loaded with users. Bit error rate (BER) performance for the chip-level equalizers is well predicted by approximate SINR expressions and a Gaussian interference assumption.     

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     

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.     

Adaptive MMSE maximum likelihood CDMA multiuser detection

The well-known code division multiple access maximum likelihood receiver (MF-ML) uses a bank of matched filters as a generator of sufficient statistics for maximum likelihood detection of users transmitted symbols. In this paper, the bank of matched filters is replaced by a bank of adaptive minimum mean squared error (MMSE) filters as the generator of sufficient statistics. This formal replacement of the MF bank by the adaptive MMSE filter bank has significant conceptual consequences and provides improvement by several performance measures. The adaptive MMSE-ML receiver's digital implementation is significantly computationally simplified. The advantages of the proposed adaptive MMSE-ML receiver over the MF-ML receiver are: (1) ability to perform joint synchronization, channel parameter estimation, and signal detection where the signal is sent over an unknown, slowly time-varying, frequency-selective multipath fading channel; (2) increased information capacity in a multicellular environment; and (3) significantly improved bit error rate (BER) performance in a multicellular mobile communications environment. The information capacity and the BER of the proposed MMSE-ML receiver are analyzed. Numerical results showing the BER performance of the MMSE-ML receiver in a multipath channel environment are presented     

Matched filters with interference suppression capabilities forDS-CDMA

This paper considers the design of near-far resistant matched filters (MFs) for direct-sequence code-division multiaccess (DS-CDMA) systems. We show how additional information on the individual powers and chip delays of locked users, that is available at the base station, can be exploited for the design of these MFs. The proposed receiver can specifically reduce the effects of the locked interferers at the expense of a partial increase in complexity over the conventional MF. Furthermore, this detection technique is a link between the linear minimum mean squared error (MMSE) centralized multiuser detector and the decentralized noise-whitening MF. Numerical results for the rectangular chip pulse illustrate the signal-to-noise ratio (SNR), near-far resistance, and bit-error rate (BER) improvement that the proposed MF yields over the conventional MF and noise-whitening MF     

Generalized raised-cosine filters

Data transmission over bandlimited channels requires pulse shaping to eliminate or control intersymbol interference (ISI). Nyquist filters provide ISI-free transmission. Here we introduce a phase compensation technique to design Nyquist filters. Phase compensation can be applied to the square-root of any zero-phase bandlimited Nyquist filter with normalized excess bandwidth less than or equal to one. The resulting phase compensated square-root filter is also a Nyquist filter. In the case of a raised-cosine spectrum, the phase compensator has a simple piecewise-linear form. Such a technique is particularly useful to accommodate two different structures for the receiver, one with a filter matched to the transmitting filter and one without a matched filter. We also use the phase compensation technique to characterize a more general family of Nyquist filters which subsumes raised-cosine spectra. These generalized raised-cosine filters offer more flexibility in filter design. For instance, the rate of asymptotic decay of the filter impulse response may be increased, or the residual ISI, introduced by truncation of the impulse response, may be minimized. Design examples are provided to illustrate these choices