Synchronous CDMA Systems Research Articles

Method for Minimizing Total Generalized Squared Correlation of Synchronous DS-CDMA Signature Sequence Sets in Multipath Channels

We characterize the Total Generalized Squared Correlation (TGSC) for a given signature sequence set used in uplink synchronous code division multiple access (S-CDMA) when channel state information is known perfectly at bothtransmitter and receiver. We give a definition of the TGSC based on the eigenvalues of Gram matrix associated to signature sequences set for multipath channels in the presence of the colored noise. Total Squared Correlation (TSC) and Total Weighted Squared Correlation (TWSC) measures are particular cases of TGSC. We present a method for minimizing TGSC (TSC, TWSC) in multipath channels and in the presence of the colored noise. Numerical results for overloaded synchronous CDMA systems are presented in order to support our analysis.

Two dimension MDW OCDMA code cross-correlation for reduction of phase induced intensity noise

In this paper, we first review 2-D MDW code cross correlation equations and table to be improved significantly by using code correlation properties. These codes can be used in the synchronous optical CDMA systems for multi access interference cancellation and maximum suppress the phase induced intensity noise. Low Psr is due to the reduction of interference noise that is induced by the 2-D MDW code PIIN suppression. High data rate causes increases in BER, requires high effective power and severely deteriorates the system performance. The 2-D W/T MDW code has an excellent system performance where the value of PIIN is suppressed as low as possible at the optimum Psr with high data bit rate. The 2-D MDW code shows better tolerance to PIIN in comparison to others with enhanced system performance. We prove by numerical analysis that the PIIN maximally suppressed by MDW code through the minimizing property of cross correlation in comparison to 2-D PDC and 2-D MQC OCDMA code.scheme systems.

Novel Hybrid Orthogonal Large Set Code Sequence for High Density Wireless Networks

CDMA technique has been successfully employed to implement high capacity mobile networks with optimum channel bandwidth utilization. The two most coveted criteria for the spreading codes used in such network are, the number of codes in the set and the code orthogonality, in order to ensure accommodation of large number of users and as well as minimal interference between the users. Walsh code has proved to be a popular orthogonal code, whereas m-sequence, Gold code and Kasami code have established themselves as popular non-orthogonal binary codes. Small set Orthogonal Kasami code has been proposed and evaluated by researchers for CDMA applications. In this paper the authors report the design of hybrid orthogonal large set (HOLS) code for synchronous CDMA systems. The HOLS code was evaluated in a synchronous CDMA system over different channel conditions. The authors also demonstrate that the BER performance of the HOLS code is comparable to that of the existing orthogonal codes, but outperforms Gold and large set Kasami code sequences. The HOLS code sequence is also shown to outperform the existing code sequences in the number of cells it can support. In terms of multiple access interference (MAI), the cross-correlation function (CCF) of the HOLS code sequence is comparable to that of Walsh and orthogonal small set Kasami codes, and much better than those of Gold and large set Kasami code sequences. HOLS code sequence has comparable auto-correlation function (ACF) with that of Gold, large set Kasami and orthogonal small set Kasami code sequences and a much better ACF than that of Walsh code sequence.

Multi-User Detection Based on Quasi-Synchronous CDMA Systems

Multi-user detection is one of the key technologies of CDMA systems. Its basic idea is that, all user signals are considered as useful signals. Then, we can use them to eliminate multiple access interference (MAI). This paper presents an improvement of multi-user detection based on QS-CDMA systems. By the improving, computational complexity is lower, and performances approach synchronous CDMA systems.

Uniquely Decodable Codes with Fast Decoder for Overloaded Synchronous CDMA Systems

In this paper, we introduce a new class of signature matrices for overloaded synchronous CDMA systems that have a very low complexity decoder. While overloaded systems are more efficient from the bandwidth point of view, the Maximum Likelihood (ML) implementation for decoding is impractical even for moderate dimensions. Simulation results show that the performance of the proposed decoder is very close to that of the ML decoder. Indeed, the proposed decoding scheme needs neither multiplication nor addition and requires only a few comparisons . Furthermore, the computational complexity and the probability of error vs. Signal to Noise Ratios (SNR) are derived analytically.

Multiuser detection based on modified PSO algorithm for synchronous CDMA systems

The computational complexity of the optimum maximum-likelihood detector does not allow its utility for multiuser detection (MUD) in code-division multiple-access (CDMA) systems. In this paper, a novel particle swarm optimization (PSO) algorithm is suggested to carry out MUD for synchronous CDMA systems. This work considers two new aspects, namely an adaptive velocity updating mechanism based on Newton method and a dynamic inertia weight into the standard PSO. These mechanisms can provide more diversity to help avoiding premature convergence and significantly improve the bit error rate performance. Several computer simulation results demonstrate that the proposed modified PSO detector significantly outperforms the decorrelating detector, the linear minimum mean square error detector, and the standard PSO-based detector.

A Hybrid Interference Cancellation technique for overloaded CDMA with timing offset error

A novel method of Hybrid Parallel/Successive Interference Cancellation (HIC) for Overloaded Direct Sequence Code Division Multiple Access (OCDMA) system involving two groups of users is proposed in this paper. The impact of timing synchronization error on acceptable channel load in a synchronous binary spread CDMA system is studied by mitigating the effect of multi-access interference (MAI). A small timing synchronization error is introduced in the DS-CDMA system under study to disturb the orthogonality of group-1 users and group-2 users. This orthogonality loss leads to Multi User Interference (MUI) in group-1 users and it is cancelled using Parallel Interference Cancellation (PIC). The interference of group-2 users on group-1 users is cancelled using Successive Interference Cancellation (SIC). The analytical expressions of the Bit Error Rate (BER) are derived. The simulation results prove that the BER performance of the proposed HIC method is better than the conventional PIC and SIC.

The Construction of Orthogonal Variable Spreading Factor Codes from Semi-Bent Functions

In a recent paper spreading codes for CDMA systems were constructed based on Hadamard matrices and semi-bent functions. These codes were applicable to synchronous CDMA systems and to quasi-synchronous CDMA systems when a loosely-synchronized code is used. The codes consist of the union of rows of four Hadamard matrices. The codes can be assigned to a regular tessellation of hexagonal cells in such a way that the correlation between codewords assigned to adjacent cells is zero, while the correlation between codewords assigned to non-adjacent cells is small. The use of codewords from four Hadamard matrices allows greater codeword re-use distances than the use of codewords from a single Hadamard matrix. This has advantages for both satellite and terrestrial systems. These codes only support a single data rate. The current paper shows how orthogonal variable spreading factor codes can be created from them by a careful selection of the semi-bent functions used.

A review on synchronous CDMA systems: optimum overloaded codes, channel capacity, and power control

This paper is a tutorial review on important issues related to code-division multiple-access (CDMA) systems such as channel capacity, power control, and optimum codes; specifically, we consider optimum overloaded codes that achieve errorless transmission in the absence of noise for the binary and nonbinary cases. A survey of lower and upper bounds for the sum channel capacity of such systems is given in the presence and absence of channel noise. The asymptotic results for the channel capacity are also investigated. The channel capacity, errorless transmission codes, and power estimation for near-far effects are also explored. The emphasis of this tutorial review is on the overloaded CDMA systems.

Multiuser receiver scheme for full-rate space-time coded CDMA system with imperfect estimation

By introducing a full-rate space–time coding (STC) scheme, a synchronous CDMA (code division multiple access) system with full-rate STC is given, and the corresponding uplink performance is investigated in Rayleigh fading channel with imperfect estimation. Considering that existing STC-CDMA system has high decoding complexity, low-complexity multiuser receiver schemes are developed for perfect and imperfect estimations, respectively. The schemes can make full use of the complex orthogonality of STC to reduce the high decoding complexity of the existing scheme, and have linear decoding complexity compared with the existing scheme with exponential decoding complexity. Moreover, the proposed schemes can achieve almost the same performance as the existing scheme. Compared with full-diversity STC-CDMA, the given full-rate STC-CDMA can achieve full data rate, low complexity, and partial diversity, and form efficient spatial interleaving. Thus, the concatenation of channel coding can effectively compensate for the performance loss due to partial diversity. Simulation results show that the full-rate STC-CDMA has lower bit error rate (BER) than full-diversity STC-CDMA systems under the same system throughput and concatenation of channel code. Moreover, the system BER with imperfect estimation are worse than that with perfect estimation due to the estimation error, which implies that the developed multiuser receiver schemes are valid and reasonable. Copyright © 2010 John Wiley & Sons, Ltd. (Based on the imperfect estimation information, a multiuse receiver scheme for full-rate space-time coded CDMA system with estimation error is developed in Rayleigh fading channel. This scheme includes perfect estimation as a special case. It has a lower implement complexity than the existing scheme, and can obtain almost the same performance.)

SINR-maximizing spreading code allocation for non-linear serial interference cancellation

This paper considers the issue of spreading code allocation and receiver optimization in a CDMA-based multiuser data network. Assuming that non-linear serial interference cancellation is performed at the receiver, the problem of noncooperative SINR maximization with respect to each user's spreading code and uplink receiver is first considered. It is shown that iterative SINR maximization converges in a finite number of steps, and that the equilibrium resulting from noncooperative behavior is also Pareto-optimal. Next, the problem of optimal multiuser detection for a system using the above optimal spreading codes is also considered, and it is shown that, for such a system, maximum likelihood detection entails a computational complexity that is exponential in the ratio between the number of users and the system processing gain, thus providing huge savings with respect to the general case wherein the optimal receiver has a complexity exponential in the number of users. While initially considering a simple frequencyflat synchronous CDMA system, the obtained results are then extended to more general scenarios, such as asynchronous CDMA systems, multipath CDMA channels, and multiuser multiantenna systems. Finally, the issue of non-cooperative power minimization and choice of the spreading code subject to a QoS constraints is also considered, and comparisons with the corresponding cooperative solution are also discussed. Numerical results corroborate the validity of the theoretical analysis, and show that the use of non-linear interference cancellation coupled with waveform adaptation brings remarkable performance gains with respect to linear multiuser receivers.

A Class of Errorless Codes for Overloaded Synchronous Wireless and Optical CDMA Systems

In this paper, we introduce a new class of codes for overloaded synchronous wireless and optical code-division multiple-access (CDMA) systems which increases the number of users for fixed number of chips without introducing any errors. Equivalently, the chip rate can be reduced for a given number of users, which implies bandwidth reduction for downlink wireless systems. An upper bound for the maximum number of users for a given number of chips is derived. Also, lower and upper bounds for the sum channel capacity of a binary overloaded CDMA are derived that can predict the existence of such overloaded codes. We also propose a simplified maximum likelihood method for decoding these types of overloaded codes. Although a high percentage of the overloading factor degrades the system performance in noisy channels, simulation results show that this degradation is not significant. More importantly, for moderate values of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> (in the range of 6-10 dB) or higher, the proposed codes perform much better than the binary Welch bound equality sequences.

An Iterative Soft Bit Error Rate Estimation of Any Digital Communication Systems Using a Nonparametric Probability Density Function

In general, performance of communication system receivers cannot be calculated analytically. The bit error rate (BER) is thus computed using the Monte Carlo (MC) simulation (Bit Error Counting). It is shown that if we wish to have reliable results with good precision, the total number of transmitted data must be conversely proportional to the product of the true BER by the relative error of estimate. Consequently, for small BERs, simulation results take excessively long computing time depending on the complexity of the receiver. In this paper, we suggest a new means of estimating the BER. This method is based on an estimation, in an iterative and nonparametric way, of the probability density function (pdf) of the soft decision of the received bit. We will show that the hard decision is not needed to compute the BER and the total number of transmitted data needed is very small compared to the classical MC simulation. Consequently, computing time is reduced drastically. Some theoretical results are also given to prove the convergence of this new method in the sense of mean square error (MSE) criterion. Simulation results of the suggested BER are given using a simple synchronous CDMA system.

A New Construction Method of Zero-Correlation Zone Sequences Based on Complete Complementary Codes

In approximately synchronous CDMA (AS-CDMA) systems, zero correlation zone (ZCZ) sequences are known as the sequences to eliminate co-channel and multi-path interferences. Therefore, numerous constructions of zero correlation zone (ZCZ) sequences have been introduced e.g. based on perfect sequences and complete complementary codes etc. However, the previous construction method which based on complete complementary code is lacking for merit figures when none of whose elements are zero. In this paper, a new construction method of ZCZ sequences based on complete complementary codes is proposed. By proposed method, non zero elements ZCZ sequences whose merit figure is greater than 1/2 are constructable.

Multiple-Access Interference Plus Noise-Constrained Least Mean Square (MNCLMS) Algorithm for CDMA Systems

Since multiuser code-division multiple-access (CDMA) communications systems suffer significantly from multiple-access interference (MAI) and from classical white Gaussian noise, it is therefore necessary to consider their impact on the performance of these systems. It is well known that the learning speed of any adaptive filtering algorithm is increased by adding a constraint to it. In this paper, a constrained least-mean-square (LMS) algorithm, which incorporates the knowledge of the number of users, spreading sequence length, and additive noise variance, is developed subject to the new combined constraint comprising the MAI and noise variance for a synchronous downlink direct-sequence CDMA system. The novelty of this constraint resides in the fact that the MAI variance was never used as a constraint. In our approach, a Robbins-Monro algorithm is used to minimize the conventional mean-square-error criterion subject to the variance of the new constraint (MAI plus noise). This constrained optimization technique results in an (MAI plus noise)-constrained LMS (MNCLMS) algorithm. The MNCLMS algorithm is a type of variable step-size LMS algorithm where the step-size rule arises naturally from the constraints on MAI and noise variance. Convergence and tracking analysis of the proposed algorithm are carried out in the presence of MAI. Finally, a number of simulations are conducted to compare the performance of the MNCLMS algorithm with other adaptive algorithms.

Average of Product of Two Gaussian Q-Functions and its Application to Performance Analysis in Nakagami Fading

The average of the product of two Gaussian Q- functions having arguments as different scaled versions of the same Nakagami distributed fading gain magnitude is derived in closed-form. Both the cases when (1) the fading parameter is an integer, and (2) the fading parameter is an odd multiple of one-half, are considered. The results are applied to evaluating in closed-form (a) the symbol error probability (SEP) of rectangular quadrature amplitude modulation with maximal-ratio combining in independent Nakagami fading, and (b) the outage probability of a two-user synchronous code-division multiple-access system having signal-to-noise ratio (SNR) imbalance among users in Nakagami fading. It is found in application (a) that with increase in the degree of fading, the robustness to decision distance imbalance between in-phase and quadrature signals increases. In addition, there exists an optimum decision distance ratio at which the SEP has a minimum. In application (b), we find that the outage probability increases sharply with SNR imbalance factor at low SNR imbalance and tends to reach saturation as the imbalance increases.

Effects of Spreading and Training on Capacity in Overloaded CDMA

We address the issue of sum-capacity in an overloaded, uplink, synchronous CDMA system in a quasi-static fading environment. Part of each fading block is reserved for channel training and the remainder of the block is used for data transmission. We evaluate bounds on sum-capacity using the estimates from channel estimation, and consider the effects on the lower bound caused by the spreading-coding-training tradeoff.

Directional Diversity of Smart Antenna in LAS CDMA Systems

The performance of code division multiple access (CDMA) systems can be affected by small scale fading such as Rayleigh fading channel. In this paper, the application of smart antenna and Large Area Synchronous CDMA (LAS CDMA) systems, which introduce directional diversity channel, is presented. A novel interference cancellation scheme through dynamic space code (DSC) algorithm is briefly described. The directional diversity can be realized from the directional gain of smart antenna system. It can be found that when the number of elements in smart antenna is increase the directional gain of antenna system is much higher than single antenna. The system performance analysis in term of error probability is compared between traditional and LAS CDMA systems in both single and smart antenna systems. From the performance analysis it is found that CDMA system is more susceptible to multipath fading channel than interferences from existing users.

A Unified Approach to BER Analysis of Synchronous Downlink CDMA Systems with Random Signature Sequences in Fading Channels with Known Channel Phase

A detailed analysis of the multiple access interference (MAI) for synchronous downlink CDMA systems is carried out for BPSK signals with random signature sequences in Nakagami-m fading environment with known channel phase. This analysis presents a unified approach as Nakagami-m fading is a general fading distribution that includes the Rayleigh, the one-sided Gaussian, the Nakagami-q, and the Rice distributions as special cases. Consequently, new explicit closed-form expressions for the probability density function (pdf) of MAI and MAI plus noise are derived for Nakagami-m, Rayleigh, one-sided Gaussian, Nakagami-q, and Rician fading. Moreover, optimum coherent reception using maximum likelihood (ML) criterion is investigated based on the derived statistics of MAI plus noise and expressions for probability of bit error are obtained for these fading environments. Furthermore, a standard Gaussian approximation (SGA) is also developed for these fading environments to compare the performance of optimum receivers. Finally, extensive simulation work is carried out and shows that the theoretical predictions are very well substantiated.

On the Optimal Sequences and Total Weighted Square Correlation of Synchronous CDMA Systems in Multipath Channels

We generalize the total square correlation and the total weighted square correlation (TWSC) for a given signature set used in synchronous code division multiple access (S-CDMA) systems. We define the extended TWSC measure for multipath channels in the presence and the absence of the colored noise. The main results of this paper are the following: 1, the necessary and sufficient conditions of the received Gram matrix to maximize the sum capacity in the presence of multipath; 2, the conditions on the channel such that the received multipath sequences in the presence of the colored noise are Welch bound equality (WBE) sequences; 3, a decentralized method for obtaining generalized WBE sequences that minimize the TWSC in the presence of multipath and colored noise. Using this method, the optimal sequences, which achieve sum capacity for overloaded S-CDMA systems, in the presence of multipath are obtained. Numerical examples that illustrate the mathematical formalism are also included.