Blind Decorrelating Detection Based on Particle Swarm Optimization under Spreading Code Mismatch

Jhih-Chung Chang and Chih-Chang Shen

Blind Decorrelating Detection Based on Particle Swarm Optimization under Spreading Code Mismatch

Jhih-Chung Chang and Chih-Chang Shen

—A way of resolving spreading code mismatches in blind multiuser detection with a particle swarm optimization (PSO) approach is proposed. It has been shown that the PSO algorithm incorporating the linear system of the decorrelating detector, which is termed as decorrelating PSO (DPSO), can significantly improve the bit error rate (BER) and the system capacity. As the code mismatch occurs, the output BER performance is vulnerable to degradation for DPSO. With a blind decorrelating scheme, the proposed blind DPSO (BDPSO) offers more robust capabilities over existing DPSO under code mismatch scenarios.

Index Terms—Code division multiple access, code mismatch, decorrelating detector, multiuser detection, particle swarm optimization.

1. Introduction

In a typical code division multiple access (CDMA) system, each user is distinguished by a unique spreading code. During transmission, the information from all users is modulated by the spreading codes and then mixed together. Therefore, in order to separate the information for each user at the receiver’s side, those spreading codes should ideally be orthogonal with each other. In practice, due to multipath fading, it is not possible to maintain the orthogonality of the spreading codes at the receiver in a mobile environment, and thus, multiple access interference (MAI) limits the capacity of the conventional detection[1]. Multiuser detectors (MUDs) are specifically designed to overcome the problem of MAI. The decorrelating detector (DD) eliminates the correlation between different users by restoring their orthogonality and by doing so they might amplify noise under the assumption that all active users’ true codes are known[2]. Although subspace based blind DD (BDD) can avoid the effect of code mismatches from strong interferers, it still cannot produce a sufficient performance in the presence of MAI and code mismatches[3].

In contrast to traditional computation systems which may be good at accurate and exact computation but have brittle operations, evolutionary computation provides a more robust and efficient approach for solving complex real world problem. Recently, particle swarm optimization (PSO)[4]has been proposed to solve complex optimization problems. In particular, many PSO algorithms based MUDs[5]-[6]are put forward to obtain a better bit error rate (BER) performance. It has been known that the decorrelating PSO (DPSO) MUD[7]can significantly improve BER and system capacity compared with the DD. However, one of the main disadvantages of DPSO is that it requires complete knowledge of CDMA systems, including the spreading sequences of all active users, the estimates of signals’ amplitudes, and noise variance, which are difficult to obtain in practice. Due to the fading channel and multipath problems, it is impossible to maintain the orthogonality of the spreading codes. Therefore, the performance of DPSO has also suffered from some deficiencies. To mitigate the effect of code mismatch problem, this letter presents a blind DPSO (BDPSO) MUD as the base of the fitness function to against the code mismatch. The contribution of this work is the development of a blind adaptive method for estimating the effective spreading codes, noise power, and signals’ amplitudes. Under the proposed scheme, the fitness function of DPSO can be obtained blindly, i.e., it can be estimated from the received signal with the prior knowledge of only the spreading codes and timing of the users of interest. Simulation results show that the proposed BDPSO obtained a significant improvement in the BER performance over the DPSO in the presence of spreading code mismatches.

2. Problem Formulation

2.1 Signal Model

Consider a baseband CDMA system withKsimultaneously active users. After being chip sampled, the received signal vector ()irin the thibit interval can be expressed as

In generally, we assume that the receiver has perfect knowledge of the spreading codes used to modulate the bits of all users, but this may not be true in practice. Because the actual received spreading codesof all users in the received data are mismatched with its counterpartCin the transmitter. It may include additional multipath components or other types of channel distortions[2]. Then, the users’codes with the mismatch may be represented aswhere the mismatch term ΔCis modeled as a zero mean Gaussian random matrix with variance2The output vector through the matched filter can be represented more compactly as

2.2 DPSO

The MUD problem in CDMA can be realized as a search problem in a noisy space of possible solutions. PSO is similar to the other evolutionary algorithms in that the system is initialized with a population of random solutions. Each potential solution, called particles, flies in theK-dimensional problem space with a velocity which is dynamically adjusted according to the flying experiences of its own and its colleagues. Thedth particle or solution is represented as, whereis the number of particles, andiNis the maximum number of iterations. Corresponding to each position, we have a particle velocity. Each particle keeps track of the position of its individual best performance, given asSimilarly, the swarm maintains the record of the position for the global best performance given as. The procedure of DPSO[7]is given as following steps.

Step 1 : Run the DD.

Step 2: Initialization. The output result of DD is taken as the input first particleThe rest of population is randomly generated as either 1 or -1. Thus, the initial position of the particle is represented asThe initial velocityis randomly chosen in the interval [-1, 1].

Step 3: The DD is utilized as the base of the fitness functionF. That is to find the particle positionand maximize the following fitness function:

Step 4: Update the inertia weightwith α＜ 1.

where1μand2μare the weights of the stochastic acceleration constants that pull each particle towards thepositions, respectively.are the random numbers that are uniformly distributed between 0 and 1. The particle velocity is limited by the maximumvelocityFinally, updateto obtain next position:

Step 6: First, update the individual best particle position by following rule: ifOtherwise, set the global particle position as: ifFinally, the decision to be made for the particle position to be (1)± depends onbestsign( )g.

Step 7: The above steps are repeated until the minimum error condition is satisfied.

In practice, the output result of DD is taken as the initial position of the first particleinstead of using the trueWhen DPSO provides a good initialization,can maximize the fitness functionFat iteration 0. Unfortunately, with even a small code mismatch, the output BER of DPSO may be seriously degraded.

3. Blind DPSO (BDPSO)

In this section, a blind scheme combining with PSO is presented to enhance the robustness against the code mismatch. The autocorrelation matrix of ()iris

It is easy to see that rangeunder the case of perfect channel, where range{·} is the spanned subspace. First, the received signal ()iris projected onto the signal subspace to get awhich clearly is a sufficient statistic for demodulating theKusers’ data bits. The spreading code matrixCis also projected onto the signal subspace to obtain. By utilizing the output of the BDD to provide a good initialization to the PSO, the initial position of the first particle is set asTherefore, the projection of the linear MUD in the signal subspace is obtained by projecting the signature waveform of the users of interest onto the signal subspace, followed by scaling the thkcomponent of this projection with a factor ofthe precise spreading vector by projecting the assumed spreading vector into the signal subspace can be obtained. Therefore, the corrected spreading code matrix is given by

which lies in the signal subspace and the problem of suppressing the desired user signal can be avoid. Then, the output signal of all active users isovercome the effect of code mismatches, the matrixQin fitness function for implementing BDPSO is given by

It is noted that the noise powerused for constructingMcan be estimated priori by numerical technique, which is to compute the eigenvalues ofrrRand identify those“smallest” eigenvalues. Then, the noise power is estimated according to

wherelπ is the eigenvalue ofrrR. In addition, the estimate of the thkuser’s signal amplitude for constructingin the fitness function is given by

where D is the samples of the received signal within each observation vector. Note that the BDPSO chooses the matrixinstead of usingQin (3). Finally, the blind fitness function for implementing the BDPSO is given by

Due to the effect of code mismatches, the performance degradation is occurred when the noise power increases. The orthogonality property between spreading codes of different users is lost, which will cause the poor cross-correlation properties of signatures of different users. The signatures cannot be used as a reference signature to find the desired users’ bits and the desired user is hard to be recovered. The BDPSO optimizes a fitness function incorporating the BDD to detect the received data bits. At the termination of optimization, the received binary data bit is set equal tobestsign( )g.

4. Simulation Results

The simulation results are obtained to evaluate the BER performance of the BDPSO MUD under the additive white Gaussian noise (AWGN) channel. Comparison results of the average BER of conventional detector (CD), DD, subspace based BDD[3], and DPSO[7]are also presented. Each simulation result is averaged overbits, and 100 independent runs are simulated. The PSO starts with a random initialization, and is terminated when the global best particle position is not updated in 20 successive iterations. The parameters of PSO chosen for the simulations are described as follows. The acceleration constants1μ and2μ are equal to 2. The population size is set asand the maximum number of iterationsis 100. In addition, the initial inertia weightand the decreased constantAll CDMA signals with the number of active usersK=15 are generated with binary phase-shift keying (BPSK) modulation and the PN codes of processing gainL=31. The signal-to-noise ratio (SNR) of a desired signal is set as 15 dB. The all uncorrelated interferers are set to the equal power with interference-to-noise ratio (INR)=10 dB.

Fig. 1 plots the BER performance of the proposed BDPSO versus the variance of code mismatches from -30 dB to 0 dB. It is clear that other detectors are quite sensitive to code mismatches. As the code mismatch increases, the performance degradation of others detectors become relatively worse. It is also shown that the conventional detector has a poor performance when the code mismatch is exist. Although the BDD has a better capability to alleviate the effect of code mismatches than the DPSO, it suffers from the suppression of desired signal in the weak or equal power interferers’ environments[3]. However, the proposed BDPSO is robust against the signature waveform mismatch though the noise subspace of the mismatched signature waveform is null out. Fig. 2 shows that the BER performance versus different SNRs of the desired user underFrom Fig. 2, it is shown that the BDPSO has minimum BER under the same SNR. This is to say, the BDPSO has a better capability against BER than the DPSO and BDD. It is seen that by employing the DD and DPSO, more performance degradation is incurred when the signal is distorted by the code mismatch and noise enhancement. But, the proposed technique can project onto the signal subspace to produce more correct matrixwhich can efficiently eliminate the effect of

Fig. 1. Output BER versus variance of code mismatch.

Fig. 2. Output BER versus SNR of the desired user.

5. Conclusions

In this paper, we have developed a blind adaptive multiuser detection technique based on DPSO. Compared with the previous DPSO and BDD, it is seen that the proposed method with few attendant increases in complexity has a better BER performance under spreading codes mismatches. Computer simulations have demonstrated the effectiveness of the proposed scheme.

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Jhih-Chung Changwas born in Taiwan in 1965. He received the B.S. and M.S. degrees both in information engineering and computer science from Feng Chia University, Taichung in 1987 and 1990, respectively, and the Ph.D. degree in information management from National Yunlin University of Science and Technology, Yunlin in 2007.

Dr. Chang was a lecturer with the Department of Information Network Center at Ling Tung University, Taichung from 1994 to 2004. From 2004 to 2007, he was a lecture with the Department of Information Technology, Ling Tung University, Taichung. He became an associate professor with the Department of Information Technology, Ling Tung University in 2007. His research interests include artificial intelligence algorithm, array signal processing, and web technique.

Chih-Chang Shenwas born in Taiwan in 1977. He received his B.S. degree in information management form Chang Jung Christian University, Tainan in 2001, the M.S. degree in information management from Shu-Te University, Kaohsiung in 2003, and the Ph.D. degree in information management from National Yunlin University of Science and Technology, Yunlin in 2008.

Dr. Shen joined the Department of Information Technology, Ling Tung University as an assistant professor in 2008. His research interests include wireless sensor network, orthogonal frequency-division multiplexing (OFDM), and mobile location for wireless communications.

Manuscript received December 4, 2013; revised March 10, 2014. This work was supported by the NSC under Grant No. NSC 101-2221-E-275-007.

J.-C. Chang is with the Department of Information Technology, Ling-Tung University, Taichung 40852 (e-mail: changjc@mail.ltu. edu.tw).

C.-C. Shen is with the Department of Information Technology, Ling-Tung University, Taichung 40852 (Corresponding author e-mail: huntsam@teamail.ltu.edu.tw).

Digital Object Identifier: 10.3969/j.issn.1674-862X.2014.03.009