A complexity-performance-balanced multiuser detector based on artificial fish swarm algorithm for DS-UWB systems in the AWGN and multipath environments
- Zhendong Yin^{1}Email author,
- Zhiyuan Zong^{1},
- Hongjian Sun^{2},
- Zhilu Wu^{1} and
- Zhutian Yang^{1}
DOI: 10.1186/1687-6180-2012-229
© Yin et al.; licensee Springer. 2012
Received: 21 February 2012
Accepted: 12 October 2012
Published: 30 October 2012
Abstract
In this article, an efficient multiuser detector based on the artificial fish swarm algorithm (AFSA-MUD) is proposed and investigated for direct-sequence ultrawideband systems under different channels: the additive white Gaussian noise channel and the IEEE 802.15.3a multipath channel. From the literature review, the issues that the computational complexity of classical optimum multiuser detection (OMD) rises exponentially with the number of users and the bit error rate (BER) performance of other sub-optimal multiuser detectors is not satisfactory, still need to be solved. This proposed method can make a good tradeoff between complexity and performance through the various behaviors of artificial fishes in the simplified Euclidean solution space, which is constructed by the solutions of some sub-optimal multiuser detectors. Here, these sub-optimal detectors are minimum mean square error detector, decorrelating detector, and successive interference cancellation detector. As a result of this novel scheme, the convergence speed of AFSA-MUD is greatly accelerated and the number of iterations is also significantly reduced. The experimental results demonstrate that the BER performance and the near–far effect resistance of this proposed algorithm are quite close to those of OMD, while its computational complexity is much lower than the traditional OMD. Moreover, as the number of active users increases, the BER performance of AFSA-MUD is almost the same as that of OMD.
Keywords
DS-UWB Multiuser detection (MUD) Artificial fish swarm algorithm (AFSA) Euclidean solution space1. Introduction
Ultrawideband (UWB) technology is attractive for its multiple-access (MA) applications in wireless communication systems owing to its high ratio of the transmitted signal bandwidth to information signal bandwidth (or pulse repetition frequency) [1]. Similarly, power can spread, because of its information symbols transmitted by short pulses, over the wide frequency band [2]. There are mainly two standard schemes formulated by IEEE 802.15 Task Group 3a, i.e., the multi-band-based orthogonal frequency division multiplexing (MB-OFDM) and single-band-based direct-sequence UWB (DS-UWB) [3]. The former is a carrier-based system that divides the wide bandwidth of UWB into many sub-bands, while the latter is a baseband system modulating its input information symbols with nanosecond pulses, which is different from conventional code division multiple access (CDMA) systems [1, 4, 5]. Compared with MB-OFDM, DS-UWB scheme has many advantages, which stem from its UWB nature, such as low peak-to-average power ratio, wide bandwidth, good information hidden ability, and less sensitivity to multipath fading [6, 7]. Our focus is thus on investigating the detection algorithms in multiuser DS-UWB communication systems.
Actually, the idea of UWB MA systems dates back to the original proposal put forward by Scholtz [8], and with subsequent analyses in [9–12]. However, as in conventional CDMA systems, these proposed UWB MA systems also suffer from the multiple-access interference (MAI) problem, which severely restricts their performance and system capacity. This is due to the crude assumption that the MAI can be modeled as a zero-mean Gaussian random variable (called “Gaussian approximation”) [13] for the conventional single-user matched receiver. Moreover, MAI even causes the near–far effect (NFE) [14], the case that the user with lower received signal power will be swamped by users with higher power. In order to solve these problems, multiuser detection (MUD) technology that can eliminate or weaken the negative effects of MAI was studied in [15–27]. Among them, the optimum multiuser detection (OMD), proposed for CDMA systems by Verdu [15], has the optimal BER performance [16] and the perfect NFE resistant ability [17]. But its computational complexity growing exponentially with the number of active users makes it impractical to use [18]. Yoon and Kohno [19] introduced this OMD algorithm to the UWB MA system; its high computational complexity problem is yet to be solved.
In recent years, many different sub-optimal MUD algorithms have been studied in literatures. In [20], a multiuser frequency-domain (FD) turbo detector was proposed that combines FD turbo equalization schemes with soft interference cancelation, but its BER performance is unsatisfactory. A blind multiuser detector using support vector machine on a chaos-based code CDMA systems was presented in [21], which does not require the knowledge of spreading codes of other users at the cost of training procedure. In [22], a low-complexity approximate SISO multiuser detector based on soft interference cancellation and linear minimum mean square error (MMSE) filtering was developed, but the performance of this detector is unfavorable at low SNR. As the swarm intelligence is one of the latest methods in the field of signal processing [23] (especially for combinatorial optimization problems [24]), several swarm-intelligence-based MUD algorithms have been considered in [25–27]. However, the tradeoff problem between computational complexity and BER performance still exists.
To solve these issues, we investigate a complexity-performance-balanced multiuser detector based on the artificial fish swarm algorithm (AFSA-MUD) for DS-UWB systems. As a kind of swarm intelligence methods, AFSA is selected here for its significant ability to search for the global optimal value and to adapt its searching space automatically [28, 29]. And its basic motivation is to find the global optimum by simulating the fish’s behaviors, such as preying, swarming, and searching.
In this proposed AFSA-MUD algorithm, a simplified Euclidean solution searching space is constructed by the use of the solutions of sub-optimal multiuser detectors, which are MMSE detector, decorrelating (DEC) detector, and successive interference cancellation (SIC) detector. Specifically, the center of this space is the result judged in terms of the average value of all these sub-optimal solutions, while its radius is defined as the maximum distance between this center and these sub-optimal solutions. Then, AFSA is applied in this simplified solution space and these sub-optimal solutions are considered as the initial states for the artificial fishes (AFs). Simulation results show that the BER performance and the NFE resistance capability of this proposed algorithm are comparable to those of OMD, and significantly better than those of matched filter (MF), SIC, DEC, and MMSE detectors. Besides, its computational complexity is much lower than that of OMD, indicating a better efficiency.
The remainder of this article is organized as follows. In Section 2, the general multiuser DS-UWB system and some typical MUD algorithms are described, including OMD, MMSE, DEC, and SIC. And in Sections 3 and 4, the basic principles of AFSA and the proposed AFSA-MUD algorithm are discussed, respectively. In Section 5, simulation experiments that compare the performance of different MUD algorithms are made, followed by conclusions given in Section 6.
2. Multiuser DS-UWB system model and some classical MUD algorithms
2.1. Multiuser DS-UWB system model in additive white Gaussian noise and IEEE 802.15.3a channels
where τ_{ m } is the parameter that determines the width of the pulse.
where A_{ k } is the amplitude of the k th received signal and n(t) represents the received noise modeled as a normal distribution N(0, σ_{ n }^{2}) [4].
where X is the lognormal shadowing factor, {α_{m,l}} are the multipath gain coefficients, T_{ l } is the delay of the l th cluster, τ_{m,l} represents the delay of the m th multipath component (called “ray”) relative to the l th cluster arrival time (T_{ l }), i.e., τ_{0,l} = 0. L and M denote the number of clusters and its rays, respectively. In addition, the amplitude |α_{m,l}| has a lognormal distribution while the phase ∠ α_{m,l} is equal to {0, π} with equiprobability [30].
According to the conclusions in [32], there are four typical multipath channel models of different channel characteristics, namely CM1–CM4. CM1 represents a line-of-sight (LOS) propagation case with 0–4-m propagation distance, while CM2–CM4 denote three different non-LOS propagation cases with different propagation distance or delay spread. The detailed characteristics of these models are summarized in [32].
where the symbol ⊗ denotes the convolution operation. Furthermore, in this case, the pulse repetition period T_{ c } is chosen large enough to preclude intersymbol and intrasymbol interference [10]. With the help of Rake receivers, the MUD algorithms discussed in the AWGN case can be applied to the multipath case easily.
2.2. Classical multiuser detectors
2.2.1. Single-user MF
2.2.2. OMD
It is known that the selection of this optimal solution $\widehat{b}$ in the K-dimensional Euclidean solution space is generally a non-deterministic polynomial (NP) hard problem [18]. For this reason, the computational complexity of OMD grows exponentially with the number of active users.
2.2.3. MMSE detector
2.2.4. DEC detector
where the interference caused by other users is eliminated completely, but that of background noise is amplified.
2.2.5. SIC detector
Notice that all these MUD algorithms introduced above can be applied to the multipath situation easily by Rake receivers with channel estimators [33] (which is outside the scope of this article).
3. The basic principles of AFSA
AFSA is a random-searching optimization algorithm inspired by fish’s behaviors, such as searching for food, swarming, and following others. It is good at avoiding the local optimum and searching for the global optimum owing to its adaptive capacity in the parallel search of solution space through simulating these behaviors in nature [27–29]. In this section, the general AFSA is discussed below.
3.1. Some definitions for AFSA
where x_{ i } (i = 1, 2, …, K) is the i th component of X. Moreover, Y = f(X) denotes the food concentration level of this state, where f(.) is also called the fitness function or the objective function for specific issues.
In addition, Visual denotes the local visual (or search) distance of AFs, δ is the factor of crowdedness that affects the number of AFs in the local space, step is the movement size of AFs, and try _number is the random-searching times in searching behavior described below.
3.2. The behavior descriptions of AFSA
3.2.1. Searching behavior
3.2.2. Swarming behavior
3.2.3. Following behavior
Otherwise, the searching behavior is executed.
3.3. Bulletin board
The bulletin board is designed to prevent the optimization results from degradation, that is, it is used to record and renew the best food concentration and its corresponding state during the iteration of AFSA. After the maximum number of iterations has been achieved, the final records on this bulletin board will be output as the result of AFSA.
3.4. The selection of different behaviors for AFs
4. The proposed AFSA-MUD algorithm
4.1. The AFSA for MUD problem
- (1)
The expression of AF’s state. In this solution space, the state of each AF is encoded by −1 or +1. If there are K active users in this DS-UWB MA system, thus the state is a K-dimensional vector, like X _{0} = (x _{1},x _{2},…,x _{ K })^{ T }, where x _{ i } ∈ {−1, + 1} and i = 1,2,…,K.
- (2)
Initialization. The initial state of each AF is selected randomly in the discrete space with 2^{ K } likely solutions.
- (3)
The distance between different states. In this case, the operator XOR is used to calculate this distance. For example, if X _{ i } = (1,1,–1,1,1) and X _{ j } = (1,–1,1,–1,1), then the distance d _{i,j} = X _{ i } XOR X _{ j } = 3.
- (4)
The food concentration or the fitness function for AFs is the criterion of OMD in Equation (10).
- (5)The operations in Equations (19), (22), and (23) are be modified as follows, respectively:$\begin{array}{l}{\mathbf{X}}_{\mathit{inext}}={\mathbf{X}}_{j},\\ {\mathbf{X}}_{\mathit{inext}}={\mathbf{X}}_{c},\\ {\mathbf{X}}_{\mathit{inext}}={\mathbf{X}}_{max}\text{.}\end{array}$(24)
4.2. The improved scheme for the selection of initial states and the simplification of solution space
Since AFSA is a kind of random-searching swarm-intelligence algorithms, its convergence speed and computational complexity mainly depend on its initial states and searching space. This suggests that, in order to enhance the speed of convergence and decrease the computational complexity of AFSA-MUD, the initial states should be selected with a priori knowledge, rather than selected randomly, and the K-dimensional solution space should be simplified.
- (1)
Initialization. Let the detection results of MMSE, DEC, and SIC detectors be the K-dimensional vectors X _{1}, X _{2}, and X _{3}. Thus, the number of AFs can be set as 3 and their initial states are assigned by X _{1}, X _{2}, and X _{3}, respectively. Notice that this initialization can be expanded to the situation with more than three sub-optimal detectors effortlessly.
- (2)The center of the simplified space. Here, the majority voting method is applied, which has widely been used to solve the conflict problem both in engineering and social fields, to the fixing of the center point:${X}_{0}=\text{sgn}\left(\frac{1}{3}\left({X}_{1}+{X}_{2}+{X}_{3}\right)\right)\text{.}$(25)
- (3)The radius of the simplified space. In this algorithm, the radius is determined by the maximum distance between the center and these initial states (or sub-optimal solutions):$\begin{array}{l}{d}_{\mathit{radius}}=max\left\{{d}_{0,1}\right({\mathbf{X}}_{0},{\mathbf{X}}_{1}),{d}_{0,2}({\mathbf{X}}_{0},{\mathbf{X}}_{2}),{d}_{0,3}({\mathbf{X}}_{0},{\mathbf{X}}_{3}\left)\right\}\\ \phantom{\rule{3.9em}{0ex}}=max\left\{\right({\mathbf{X}}_{0}\phantom{\rule{0.1em}{0ex}}\text{XOR}\phantom{\rule{0.1em}{0ex}}{\mathbf{X}}_{1}),({\mathbf{X}}_{0}\phantom{\rule{0.1em}{0ex}}\text{XOR}\phantom{\rule{0.1em}{0ex}}{\mathbf{X}}_{2}),({\mathbf{X}}_{0}\phantom{\rule{0.1em}{0ex}}\text{XOR}\phantom{\rule{0.1em}{0ex}}{\mathbf{X}}_{3}\left)\right\}\text{,}\end{array}$(26)
Considering the analysis above, when the case X_{1} = X_{2} = X_{3} occurs, the radius calculated by Equation (26) is zero, which means the solution space is null. In order to avoid this problem, the radius is set as 1, if X_{1} = X_{2} = X_{3} is satisfied.
- i.
none of these sub-optimal solutions equals to another (X _{1} ≠ X _{2} ≠ X _{3});
- ii.
two of these solutions are equal, but not three (X _{1} =X _{2} ≠ X _{3});
- iii.
all of these solutions are equal (X _{1} = X _{2} = X _{3}).
4.3. The proposed AFSA-MUD algorithm
- (1)
The output of a bank of single-user MF receivers is fed to sub-optimal detectors, such as SIC, DEC, and MMSE.
- (2)
The detection results of these sub-optimal detectors are used to construct a simplified solution space and initialize the states of AFs.
- (3)
The AFSA is executed in this space.
5. Numerical results
Simulation parameters
System | DS-UWB |
---|---|
Modulation mode | BPSK |
Spreading codes (SC) | m sequences |
The length of SC | 31 |
Communication channel | AWGN or IEEE 802.15.3a |
(CM1–CM4) | |
The number of testing information bits | 50000 |
The width of UWB pulse | 0.7531 ns |
The pulse repetition period | ≈2 ns |
Visual | 2 |
Try _number | 5 |
The iterative times | 5 |
5.1. The BER performance versus E_{ b }/N_{0}comparison
It can be seen from Figure 6 that the BER performance of AFSA-MUD is superior to those of other sub-optimal detectors including MF, SIC, DEC, and MMSE, and it even coincides with that of OMD. The reason is that this proposed AFSA-MUD algorithm can make a search within a simplified solution space constructed by the solutions of these sub-optimal detectors, rather than a random search. Therefore, all these sub-optimal solutions are certainly contained in this searching space. Although all the performances of these algorithms are aggravated in the multipath environment (Figure 7), the BER performance of AFSA-MUD is still close to that of OMD, both of which are the best.
From the simulation results in Figure 8, we can see that, as the communication channel condition deteriorates from CM1 to CM4, the BER performance of AFSA-MUD also deteriorates. In detail, CM1, compared with CM2–CM4, is LOS and its transmission distance is the shortest, so that the power of its received signal is larger than others.
5.2. The BER performance versus K comparison
The BER performance curves of these detectors with different number of active users K are analyzed in this experiment, considering two cases: (i) the AWGN channel with the E_{ b }/N_{0} set as 5 dB for all detectors; (ii) the multipath CM2 channel with the E_{ b }/N_{0} set as 10 dB (to distinguish these curves clearly) for all detectors.
In addition, there are some conspicuous differences between these two figures. The performance of SIC is better than that of MF in Figure 9 but worse in Figure 10, which is because the interfering user’s bits estimated in AWGN environment are much more accurate than in multipath environment. That is, SIC cannot improve the BER performance of MF in low E_{ b }/N_{0} environment. Then, limited by its ability to amplify the interference of background noise, DEC cannot achieve the optimal performance, especially in Case two where its performance is the worst when K = 5, 10.
5.3. The NFE resistant capability comparison
The BER performance of these detectors with imperfect power control, called the NFE, is discussed in this simulation. Also we give two cases: (i) the AWGN channel with the number of users set as 10, when the transmitted energy per information bit of the first user E_{b 1} keeps the same with its E_{b 1}/N_{0} = 5 dB while that of other users E_{b 2–10}/N_{0} varies from 0 to 15 dB synchronously; (ii) the multipath CM2 channel with the number of users set as 10, when E_{b 1}/N_{0} = 10 dB (to separate these curves clearly) while that of other users E_{b 2–10}/N_{0} also varies from 0 to 15 dB synchronously. Notice that only the BER of the first user is analyzed and depicted.
5.4. The computational complexity comparison
The computational complexity comparison
MUD algorithms | Computational complexity |
---|---|
MMSE | K (From Equation 13) |
DEC | K (From Equation 14) |
SIC | K (From Equation 15) |
AFSA-MUD | $K+\left(K+1\right)\left\{\left(\begin{array}{l}K\\ \phantom{\rule{0.1em}{0ex}}0\end{array}\right)+\left(\begin{array}{l}K\\ \phantom{\rule{0.1em}{0ex}}1\end{array}\right)+\cdots +\left(\begin{array}{l}K\\ {L}_{i}\end{array}\right)\right\}$(From Appendix) |
OMD | 2^{ K }(K + 1) (From Equation 10) |
6. Conclusion
In this article, the focus has been on the MUD technology used in the DS-UWB system. In consideration of the high-computational complexity of OMD, and the low BER performance of sub-optimal multiuser detectors, a complexity-performance balanced MUD algorithm is proposed on the basis of AFSA, named AFSA-MUD. This method executes the different behaviors of AFs in a simplified Euclidean solution space, which is built by the detection results of sub-optimal detectors. Simulation results have indicated that the BER performance and the NFE resistant ability of this novel algorithm are quite close to those of OMD, and they are also superior to those of MF, SIC, DEC, and MMSE; furthermore, it takes much lower computational complexity to achieve this performance.
Appendix
The computational complexity of AFSA-MUD
and in consideration of the parallel execution of these detectors (from Figure 5), the number of calculating the K-vector inner products for this parallel execution is considered K here.
where the term $\left(\begin{array}{l}K\\ \phantom{\rule{0.1em}{0ex}}i\end{array}\right)$ (i = 0, 1, …, L_{ i }) means the number of all solutions that satisfies d(X_{0}, X) = i.
Declarations
Acknowledgements
This study was supported by “the National Natural Science Foundation of China” (Grant no. 61102084), “the Fundamental Research Funds for the Central Universities in China” (Grant no. HIT.NSRIF.2010092), and “the China Postdoctoral Science Foundation” (Grant no. 2011M500665). Besides, the authors would like to thank the anonymous reviewers for their invaluable comments.
Authors’ Affiliations
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