Synchronous CDMA Systems Research Articles

Signature sequence and training design for overloaded CDMA systems

The focus of this paper is on training and signature sequence design in an overloaded synchronous CDMA system. The channel fading gains are assumed to be unknown and are estimated using training sequences. We derive a maximum-likelihood (ML) estimator and design sequences to minimize the mean-squared error (MSE) of the estimate. Two design scenarios are considered. One case assumes that the spreading sequences are fixed due to existing system constraints and optimal training sequences are designed using an iterative algorithm in order to minimize the MSE of the estimate. Performance of the iterative algorithm is examined using Welch-bound equality (WBE) sequences as the pre-designed spreading sequences. In the other scenario, spreading sequences and training sequences are designed jointly to minimize the MSE of the estimate. The jointly designed training and spreading sequences achieve optimum performance in the sense of minimizing the MSE. It is observed that when WBE sequences are used as spreading sequences the performance of the iterative algorithm is close to optimum, or even optimum, in certain situations

A Joint Design of Complex Signatures Sets for Multicellular Synchronous CDMA Network

A design using total squared correlation (TSC) measure for the overloaded complex spreading sequence sets on the uplink of multicellular synchronous CDMA systems is introduced. For equal power users, the design provides orthogonal Welch Bound Equality (WBE) complex spreading sequences with constant chip magnitude. We developed an algorithm, which allows obtaining a structured Gram matrix having a particular pattern for cross correlations of the multicellular signature sequence sets without alphabet constraints. By using the proposed algorithm spreading sequences with maximum equicorrelated amplitude are also obtained. The mathematical formalism is supported with selected numerical examples in the multicellular S-CDMA context.

Iterative Equalization using Improved Block DFE for Synchronous CDMA Systems

Iterative equalization using optimal multiuser detector and optimal channel decoder in coded CDMA systems improves the bit error rate (BER) performance tremendously. However, given large number of users employed in the system over multipath channels causing significant multiple-access interference (MAI) and intersymbol interference (ISI), the optimal multiuser detector is thus prohibitively complex. Therefore, the sub-optimal detectors such as low-complexity linear and non-linear equalizers have to be considered. In this paper, a novel low-complexity block decision feedback equalizer (DFE) is proposed for the synchronous CDMA system. Based on the conventional block DFE, the new method is developed by computing the reliable extrinsic log-likelihood ratio (LLR) using two consecutive received samples rather than one received sample in the literature. At each iteration, the estimated symbols by the equalizer is then saved as a priori information for next iteration. Simulation results demonstrate that the proposed low-complexity block DFE algorithm offers good performance gain over the conventional block DFE.

Performance Analysis of Maximum-Likelihood Multiuser Detection in Space–Time-Coded CDMA With Imperfect Channel Estimation

In this paper, the performance of maximum-likelihood multiuser detection in space-time-coded code-division multiple-access (CDMA) systems with imperfect channel estimation is analyzed. A K-user synchronous CDMA system that employs orthogonal space-time block codes with M transmit antennas and N receive antennas is considered. A least-squares estimate of the channel matrix is obtained by sending a sequence of pilot bits from each user. The channel matrix is perturbed by an error matrix that depends on the thermal noise and the correlation between the signature waveforms of different users. Because of the linearity of the channel estimation technique, the characteristic function of the decision variable is used to obtain an exact expression for the pairwise error probability, and by using it, an upper bound on the bit error rate (BER) is obtained. The analytical BER bounds are compared with the BER obtained through simulations. The BER bounds are shown to be increasingly tight for large SNR values. It is shown that the degradation in BER performance due to imperfect channel estimation can be compensated by using a larger number of transmit/receive antennas

Low‐complexity linear group‐SIC detectors

AbstractIn this paper, we consider a linear group polynomial expansion successive interference cancellation (GPE‐SIC) detector in a synchronous CDMA system. It is a hybrid detector, which combines parallel and successive cancellation techniques in order to extract the advantages of both schemes. We use the fact that even if the cross‐correlation matrix of the system is not diagonal dominant, the sub‐matrices corresponding to different groups can be forced to be diagonal dominant by suitable grouping of users to approximate the decorrelator/MMSE detector by a low‐complexity polynomial expansion detector. The latter is computationally very efficient if the cross‐correlation matrix of users within the same group is diagonal dominant.Simulation results showed that the (GPE‐SIC) detector has the same performance as the linear group decorrelator successive interference cancellation (GDEC‐SIC) detector but with low‐computational complexity. Copyright © 2006 John Wiley & Sons, Ltd.

On the construction of the unit tight frames in code division multiple access systems under total squared correlation criterion

We focus on the application of unit norm tight frames to design code division multiple (CDMA) systems spreading sequences with constant chip magnitude. An algorithm for the design of the overloaded real-valued signature sets with minimum total-squared-correlation equal to the Welch bound equality (WBE) set is presented. By using this algorithm we solved the open problem of existence of complex-valued WBE sequence sets with constant chip magnitude in the case when K = N + 1 , where K is the number of active users in the system and N is the processing gain. The normalized cross-correlation between any pair of signatures in a set obtained by the proposed algorithm is either 1 / ( K - 1 ) or - 1 / ( K - 1 ) corresponding to equiangular sequences. The results are derived in the context of synchronous CDMA systems. Numerical examples for K = 5 users for real WBE sequences and for K = 4 , 3 users for complex WBE sequences with constant chip magnitude are provided.

A New Ordering and Grouping Algorithm for the Linear Weighted Group Matched Filter Successive Interference Cancellation Detector

A linear group-wise successive interference canceller in a synchronous code-division multiple-access system (CDMA) is considered in this paper. The proposed hybrid detector that combines successive and parallel cancellation techniques makes use of advantages offered by the two techniques. The convergence of the hybrid interference cancellation (HIC) detector is guaranteed by an adjustable parameter that depends upon the largest eigenvalue of the system's transition matrix. Since the largest eigenvalue is difficult to estimate, an upper bound is necessary for successful convergence. For this reason, a new upper bound for the maximum eigenvalue of the system's transition matrix was developed. Moreover, a new ordering and grouping algorithm that results in a higher convergence speed is proposed. Simulation results show that a significant improvement in performance is obtained using this technique.

Iterative reduced-complexity multiuser detection based on Chase decoding for synchronous turbo-coded CDMA system

The conventional multiuser detector (MUD) based on the a posteriori probability (APP) algorithm has an exponential computational complexity in terms of the number of users. In this paper, we propose a low-complexity iterative multiuser receiver for synchronous turbo-coded code-division multiple-access (CDMA) systems. The proposed receiver is based on the Chase decoding algorithm that was previously used to decode turbo product codes. Simulation results show that the proposed receiver can significantly reduce the computational complexity with slight performance degradation compared with the APP MUD over highly correlated channels. Moreover, in this paper, we develop a numerical approach to analyze the convergence behavior of iteratively decoded CDMA channels based on density evolution technique. Analytical results are presented and shown to provide a reasonable match with what is observed in simulation.

A New Construction of Signature Waveforms for Synchronous CDMA Systems

We consider synchronous code-division multiple access (CDMA) systems over an additive white Gaussian noise (AWGN) channel, where all users are divided into groups of small size. The signature waveforms for users in each group are constructed from the same signature sequence but with different chip waveforms. To minimize the multiple access interference (MAI) at the output of the correlators, Welch-bound-equality (WBE) sequences and chip waveforms having optimal correlation property are employed. The main idea behind the proposed construction is to suppress the inter-group interference from users in different groups as much as possible (even to remove it completely) at the expense of introducing the intra-group interference among the users in the same group. The intra-group interference, however, can be easily handled by a low-complexity, optimal (or suboptimal) multiuser detector(s) if the group size is kept small enough. As special cases, the proposed constructions correspond to the optimal design of the signature waveforms and the conventional system that uses a single chip waveform, respectively. Thus the proposed construction offers a flexibility to trade performance for complexity. In particular, it is demonstrated that, while the conventional system's error performance is very sensitive to even a small amount of overload, the proposed system with two users per group can have up to 100% overload with an excellent error performance.

SSFBG-based decorrelator for MUI rejection in synchronous optical CDMA systems

A superstructured fibre Bragg grating (SSFBG) decorrelator for rejecting multi-user interference (MUI) in a synchronous optical code division multiple access (OCDMA) system is proposed and investigated. The decorrelator is formed by appropriately defining the superstructure of a weak fibre Bragg grating. Theoretical results arrived at using coupled mode theory show that it is possible to make the MUI practically zero at the sampling instant provided there is perfect bit synchronisation among the users accessing the OCDMA system. A theoretical investigation on the degradation of optical signal to interference ratio (OSIR) is also conducted by statistically modelling the jitter likely to result in the bit synchronisation mechanism of the system.

An Iterative ICI Cancellation and Decoding Scheme for Coded OFDM Systems in Mobile Channels

Recently, it has been shown that the received signal in the orthogonal frequency-division multiplexing (OFDM) systems can be viewed as the synchronous code-division multiple access (SCDMA) signal in receiver after some mathematical manipulation, and the ICI term in the OFDM system is equivalent to the multiple access interference (MAI) term in SCDMA system. They proposed a successive interference cancellation multicarrier detector and it performs better than the conventional single-carrier detection schemes. To further improve the performance of OFDM systems in the presence of ICI, we propose to use a soft-in soft-out (SISO) multicarrier detector and a SISO convolutional decoder in an iterative (turbo) way. Note that full-complexity turbo multicarrier detector and turbo decoder are not used to strike a balance between performance and complexity of OFDM systems. And the transmitter structure of OFDM systems is unchanged. The simulation results show that the first iteration of the proposed scheme demonstrates 2--3 dB gain compared to the previous multicarrier detection schemes. The second and third iterations improve the performance further.

Achievable Information Rates and the Coding–Spreading Tradeoff in Finite-Sized Synchronous CDMA Systems

In this letter, we compute achievable information rates for finite-sized synchronous code-division multiple-access (CDMA) systems, and low-density parity-check (LDPC) codes are adopted to approach the achievable rates. The associated coding-spreading tradeoff problem is also considered using these results. We assume binary random spreading sequences, and the computed achievable rates are averaged over ensembles of spreading sequences. Unlike most prior papers, which analyze the spectral efficiency of large CDMA systems under Gaussianity assumptions (channel inputs and/or multiple-access interference), we make no such assumptions. In order to display the coding-spreading tradeoff, we plot the minimum required signal-to-noise ratio for reliable transmission as a function of information rate. It is shown that the coding-spreading tradeoff favors all coding (i.e., no spreading) when the optimal joint multiuser detector/decoder is employed, whereas for systems with a suboptimal multiuser detector and single-user decoders, there generally exists an optimal balance between coding and spreading. We also provide simulation results on the performance of LDPC-coded synchronous CDMA systems which approach the information-theoretic limits we have computed.

An Iterative Multiuser Detector for Turbo-Coded DS-CDMA Systems

We propose an iterative multiuser detector for turbo-coded synchronous and asynchronous direct-sequence CDMA (DS-CDMA) systems. The receiver is derived from the maximum a posteriori (MAP) estimation of the single user's transmitted data, conditioned on information about the estimate of the multiple-access interference (MAI) and the received signal from the channel. This multiple-access interference is reconstructed by making hard decisions on the users' detected bits at the preceding iteration. The complexity of the proposed receiver increases linearly with the number of users. The proposed detection scheme is compared with a previously developed one. The multiuser detector proposed in this paper has a better performance when the transmitted powers of all active users are equal in the additive white Gaussian noise (AWGN) channel. Also, the detector is found to be resilient against the near-far effect.

Novel Sequence Pair and Set with Three Zero Correlation Windows

In this paper, we present a set of sequence pairs which produce zero correlation windows not only in the middle part of the sum of aperiodic correlation functions, but also in the two terminal parts. We name it Ear Windows. In approximately synchronous CDMA communication system, this set of sequences is able to completely remove the inter-symbol interference (ISI) and multi-user interference (MUI) caused by the multipath effect if the maximum delay is shorter than the length of the Ear windows. In addition, it is also feasible in M-ary modulation. The intercede interference will be mitigated drastically.

User capacity for synchronous multirate CDMA systems with linear MMSE receivers

The performance of linear minimum mean-square error (MMSE) multiuser receivers in a dual-rate synchronous direct-sequence code-division multiple-access (DS-CDMA) system is investigated using the random spreading sequence analysis. Multicode (MC) systems and different variants of variable spreading length (VSL) systems are studied. User capacity regions are obtained for these systems.

Performance analysis of synchronous optical CDMA systems with EWO signaling

AbstractThe EWO signaling scheme has been proposed as an optical CDMA system. In this scheme, two orthogonal codewords with equal weights are assigned to a set of users. Depending on the transmitted information, one is selected for code spreading. Unlike the OOK signaling scheme, which is the fundamental optical CDMA system, the scheme is superior because the receiver threshold at the time of decoding need not be estimated dynamically. The EWO signaling scheme has been evaluated in an asynchronous system with OOC and PSC as the signature code. Although its error rate characteristic depends on the code used, there is no significant improvement over that of the OOK signaling scheme, and in fact the error rate may be worse depending on the conditions. This paper evaluates the error rate when the EWO signaling scheme is applied to a synchronous system. MPSC is used as the signature code. An ideal link is assumed in which all causes of noise other than interference from other channels can be neglected. Analytical evaluations and computer simulations are carried out. It is found that the EWO signaling scheme has much better error rate characteristics than the OOK system. In particular, by engineering the assignment of the codewords to each user, the EWO signaling scheme achieves an error rate of 0 regardless of the number of multiple users. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(12): 37–48, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10164

User Capacity of Asynchronous CDMA Systems With Matched Filter Receivers and Optimum Signature Sequences

For a symbol-asynchronous (but chip-synchronous) single-cell code-division multiple-access (CDMA) system, we define a system-wide quantity called the total squared asynchronous correlation (TSAC) which, for arbitrary signature sets, depends on the users' delay profile. We develop a lower bound for TSAC that is independent of the users' delays. We show that if the signature set achieves this TSAC lower bound, then the user capacity of the asynchronous CDMA system using matched filters becomes the same as that of a single-cell synchronous CDMA system; in this case, there is no loss in user capacity due to asynchronism. We present iterative signature adaptation algorithms, which, when executed sequentially by the users, appear to converge to these optimum signature sequences; however, the existence, for all user delay profiles, of signature sequences achieving this lower bound remains a significant open problem.

Speed and Accuracy Comparison of Techniques for Multiuser Detection in Synchronous CDMA

In this letter, we compare the complexity and efficiency of several methods used for multiuser detection in a synchronous code-division multiple-access system. Various methods are discussed, including decision-feedback (DF) detection, group decision-feedback (GDF) detection, coordinate descent, quadratic programming with constraints, space-alternating generalized EM (SAGE) detection, Tabu search, a Boltzmann machine detector, semidefinite relaxation, probabilistic data association (PDA), branch and bound (BBD), and the sphere decoding (SD) method. The efficiencies of the algorithms, defined as the probability of group detection error divided by the number of floating point computations, are compared under various situations. Of particular interest is the appearance of an of algorithms, primarily composed of DF detector, GDF detector, PDA detector, the BBD optimal algorithm, and the SD method. The efficient frontier is the convex hull of algorithms as plotted on probability of error versus computational demands axes: algorithms not on this efficient frontier can be considered dominated by those that are.

A new CDMA/SDMA structure with transmit diversity

Space division multiple access (SDMA) is a technique which can be used to increase the capacity of mobile communication systems by exploiting the spatial separation between different users. Space-time block codes can provide good performance in wireless fading channels through spatial diversity. Here these two techniques are combined to produce a new cooperative diversity architecture for code division multiple access (CDMA)/SDMA cellular systems using a space-time block code. An analysis of the system performance is given for a Rayleigh fading channel. This analysis can easily be generalized to similar systems. The bit error rate performance for this architecture with the Universal Mobile Telecommunications System, UMTS Terrestrial Radio Access, time-division duplex (UMTS UTRA TDD) and time-division synchronous CDMA (TD-SCDMA) systems is presented.

Binary CDMA signatures for M + N users in N -dimensional global signal space

Binary signatures are constructed for M+N users in N-dimensional signal space. Proposed signatures preserve the minimum Euclidean distance between signals inherent in an N-dimensional orthogonal signal set. They are easily generated with Hadamard matrices, and they can be applied in oversaturated synchronous CDMA systems.