A Two-Stage Memetic Algorithm for Blind Equalization in DS/CDMA Systems

Two-stage memetic algorithm for blind equalization in direct-sequence/code-division multiple-access Systems Luis M. San-Jos´ e-Revueltaa,∗, Pablo Casaseca-de-la-Higueraa,b aDepartment of Signal Theory and Communications, University of Valladolid, Paseo de Bel´en 15, 47011, Valladolid, Spain. bSchool of Computing, Engineering and Physical Sciences, University of the West of Scotland, High Street, Paisley, PA1 2BE, Scotland. Abstract This paper proposes a novel memetic algorithm (MA) for the blind equalization of digital multiuser channels with Direct-Sequence / Code-Division Multiple-Access (DS/CDMA) sharing scheme. Equalization involves two different tasks, the estimation of: (1) channel response and (2) transmitted data. The corresponding channel model is first analyzed and then the MA is developed for this specific communication system. Convergence, population diversity and near-far resistance have been analyzed. Numerical experiments include comparative results with traditional multiuser detectors as well as with other nature-inspired approaches. Proposed receiver is proved to allow higher transmission rates over existing channels, while supporting stronger interferences as well as fading and time-variant effects. Required computation requisites are kept moderate in most cases. Proposed MA saves approximately 80% of computation time with respect to a standard genetic algorithm and about 15% with respect to a similar two-stage memetic algorithm, while keeping a statistically significant higher performance. Besides, complexity increases only by a factor of 5, when the number of active users doubles, instead of 32×found for the optimum maximum likelihood algorithm. The proposed method also exhibits high near-far resistance and achieves accurate channel response estimates, becoming an interesting and viable alternative to so far proposed methods. 1. Introduction The use of wireless communications and applications has experienced a huge growth since the 90s. At the same time, transmission media (coaxial cable, optic fiber, etc) have also improved their technology and capacity. Users demand higher storage and transmission capacity since both terminals and applications become more complex every year. Consequently, techniques such as Direct-Sequence /Code-Division Multiple- Access (DS/CDMA) that admit several users in a single RF channel bandwidth, have This is the final manuscript (post-print) accepted and published in IET Communications, Oct. 2020, vol. 14, Issue 17, pp. 3039-3046. ISSN: 1751-8628. DOI: 10.1049/iet-com.2019.0692. (c) The Institution of Engineering and Technology. *Corresponding author: [email protected] been widely investigated. This multi-code system enables telecommunication operators to offer high data rates using available (limited) bandwidth [1, 2, 3, 4]. Its improvements in soft hand-offs, capacity, low probability of interception, interference rejection, low power spectral density, privacy and security makes of DS/CDMA an interesting scenario for testing novel algorithms [1]. CDMA is one of the most studied and implemented multi-access protocols. It was widely used in the second and third (2G and 3G) generations of cellular communications. In 5G, although it was initially one of the handled promising alternatives until a few months ago [4, 5] —specifically Low Density Signature (LDS) CDMA [3, 6, 7]–, in the last available specification 5G-NR Release 16, 3GPP opted for OFDM-derived schemes [8, 9]. However, countless applications today use CDMA, which is still being considered in many areas of research. For instance, CDMA continues to be investigated and implemented in numerous Internet of Things (IoT) related applications [12, 11, 10], in submarine communications [14, 13, 16, 15], in high-performance fiber optic communications [18, 17], or satellite communications in low orbit systems (LEO) [19]. In modern systems where security is a key design aspect, DS/CDMA has been proposed combined with both chaotic spreading sequences [25, 22, 20, 24, 13, 23, 21] and with MIMO techniques [26] to decrease the level of MAI, improving, this way, previous TDMA, SDMA and conventional CDMA schemes. Modern systems require very high transmission rates. At these rates, multi-access interference (MAI) and near-far effects are the two main critical issues affecting DS/CDMA cellular networks [1, 27]. Intersymbol and multi-access interferences (ISI and MAI) must be taken into account and controlled so that performance does not degrade [1]. Both ISI and MAI can be controlled from many points of view. Conventional multiuser detectors (MUDs) make use of filters matched to the codeword of the user of interest. However, this is only optimum if all received codewords are independent. In real applications this situation rarely occurs and performance notably reduces, especially if near-far degradations are present. In 1986, S. Verd´ u studied this issue and found that the joint extraction of users transmitted sequences could mitigate this problem [2]. However, complexity of the optimum detector relying on the ML criterion grows exponentially with the number of transmitters, turning unfeasible in real scenarios [1, 2]. Therefore, many authors have paid attention to the development of suboptimal schemes that can be used on real systems. Several techniques based on Natural Computation and Artificial Intelligence have been proposed to address multiuser detection (see next Section). This paper deals with the development of a novel two-stage memetic algorithm (MA) and its application to blind joint channel estimation and symbol detection in DS/CDMA systems. Explicit estimation of channel coefficients allows posterior processing tasks such as MIMO signal separation, compensation of distortions and computation of certain channel parameters that can be fed back to the receiver for transmission fine-tuning. Proposed MA efficiently solves the CDMA equalization problem, while overcoming the drawbacks found in other approaches. For instance, conventional evolutionary algorithms (EAs) can only estimate the optimum search space area within a cost-effective time and present great problems in fine-tuning solutions [28, 29, 32, 31, 30]. These disadvantages can be overwhelmed by applying exploitative search to optimize the final population of solutions estimated by the EAs [33, 34]. Both effectiveness and solutions’ quality are enhanced using this two-step approach. This big family of optimization methods, which have elements from metaheuristic and evolutionary algo- 2 rithms, and also include local learning or improvement procedures are generally known as memetic algorithms (MAs) [34]. These have a number of advantages, such as simple implementation and capability to deal with different functional problem representations [33, 34]. In our case, a two-stage algorithm is used. First, a genetic algorithm with a specific method for adjusting diversity is used to find the optimal search area within a tolerable time. Secondly, a procedure making use of the k-opt heuristic local search algorithm is used to improve the solution estimated during first stage, and thus extract the global optimum solution with low computational expense [35, 36]. The main novelties of our proposal are: (i) the first stage uses both mutation and crossover (the latter with a very low probability), as opposed to [33], where mutation was only used, (ii) population diversity is monitored and controlled using the fitness entropy, (iii) probabilities of mutation and cross over are on-line adjusted using the fitness entropy, (iv) an elitism strategy is introduced in the first stage. Besides, mutation is applied to part of this elite, (v) a simple to implement termination criterion, and (vi) high bandwidth efficiency since it does not requiere training sequences. These improvements allow to work with smaller population sizes and less iterations, while convergence and near-far resistance are improved. The remainder of this paper is structured as follows: literature review is shown in section 2, whilst section 3 explains equalization –joint symbol and channel estimation– in DS/CDMA systems. Basic concepts and notation are here presented, along with the proposed fitness function to be used in the MA. Section 4 describes the proposed MA and shows how population diversity is monitored and controlled using the population fitness entropy. Next, section 5 shows the numerical results with emphasis on the comparison with other multiuser detectors, both traditional and nature-inspired. Finally, conclusions are presented in section 6. 2. Literature review Many different techniques based on Natural Computation and Artificial Intelligence have been proposed to address multiuser detection. Initial approaches were based on single-step evolutionary algorithms (EAs), mainly Genetic Algorithms (GAs). The work in [37] proposed a synchronous DS/CDMA MUD based on a GA. It is based on AWGN channel and does not use diversity techniques. Its main drawback is the requirement of good estimates of the first transmitted symbols. Later, in 2004, Yen studied the asynchronous case in [38], where the effect of the surrounding symbols from other system users is taken into account. This algorithm also estimates those symbols that are adjacent to those from the user of interest. Another variant of the GA, whose performance is close to the optimal by introducing a local search algorithm before the GA, was proposed in [39]. This idea of adding modules to the standard GA was used also in [40]. In that case a multistage detector is integrated into the GA in order to speed convergence up. Some remarkable recent works using GAs have tried to estimate the channel response, most of them are focused on selective Rayleigh channels [41, 42]. On the other hand, some approaches have studied both bit-error-rate (BER) and near-far effect performances. It is worth mentioning recent approaches using GAs such as [44, 43, 32, 28, 29, 30]. Earlier references can be found in [45]. 3 Apart from GAs, several other nature-inspired methods have also been applied to multiuser detection. During last decade it deserves special attention those bio-inspired methods based on swarm and evolutionary computation. These methods include the use of ant-colony algorithms (ACO) [46, 27, 47, 48] and particle swarm optimization (PSO) [49, 50, 51, 52, 53, 31] , among others. [49] combines a PSO algorithm with the conventional detector, which is initially used to initialize the position of a particle, showing, this way, better capability against bit error tan conventional detector. In [54] a binary PSO is applied for CDMA multiuser detection, while [51] proposed the use of the decorrelating detector and the linear minimum mean square error (MMSE) detector to initialize the PSO multiuser detector. Recently, [52] proposed a completely binary PSO algorithm which is reported to resist higher noise levels and to converge in a very short time. [53] compares performance of a PSO-based detector for CDMA with another receiver that uses the Spider monkey optimization (SMO) scheme, showing better results for the later. [55] includes an interesting list of references in this area. This paper proposes the use of a memetic algorithm to solve the equalization problem in DS/CDMA, i.e. the joint symbol detection and channel estimation tasks in a multiuser communication system. To the best of our knowledge, no work has been dedicated to the joint estimation of fading coefficients and users’ data symbols using a MA. 3. Channel estimation and symbol detection in DS/CDMA 3.1. DS/CDMA channel model The multiuser communication environment and the channel model used in this work is next described. This channel is simultaneously shared by Uactive users transmitting binary symbol sequences. Each user operates with a confidential normalized signature (or codeword) from set {si(t)}U i=1. Channel response is considered to be completely represented by both a set of flat-fading coefficients, and an additive zero-mean white Gaussian noise (AWGN) component. All signals are supposed to be synchronously transmitted. This assumption is considered for simplicity as it captures most of the effects of asynchronous systems with a low delay spread [56]. User itransmits an F-length sequence xi(n)of statistically-independent symbols. Each of them modulates a codeword, si(t), which is obtained as si(t)= N−1 X `=0 si,`γ(t−`Tc)(1) where si=(si,0, ..., si,N−1)Tstands for the signature of user i,Tc=T/Nis the chip period (Nis known as processing gain), Tdenotes the symbol period and γ(t)represents a chip waveform whose energy has been normalized. As a consequence, the frequency content is spread by a factor Nand the original narrowband signal is de-sensitized to some potential channel degradation and interference [1]. This way, the ith user transmits the following signal yi(t)= F−1 X n=0 xi(n)si(t−nT)(2) 4 where xi(n)are the data symbols transmitted by the ith user. The signal at the receiver input is r(t)=PU i=1ri(t)+g(t) 0 ≤t≤TF(3) where g(t)denotes a complex AWGN component, which is not correlated with the users’ transmitted symbols xi(n),TFrepresents the frame duration, and ri(t)is ri(t)=pEi F−1 X n=0 bi(n)xi(n)si(t−nT)(4) Eidenotes the energy per bit of the ith user, and bi(n)the flat-fading coefficient of this user. In this work, a non-stationary channel is considered, with a time variation model defined in [57], where fading coefficients bi(n)change with time as a function of a Doppler frequency, fd, as bi(n+1) =α·bi(n)+ϕ(5) with α=exp(−2πfdT)and ϕrepresents a zero-mean AWGN signal. The joint task of channel response estimation and detection of transmitted symbols can be seen in Eq. (4), where both data symbols xi(n)and fading coefficients bi(n)need to be estimated. An schematic representation of this multiuser communication system is shown in Fig. 1. The first block in the proposed receiver consists of a set of Nfilters distributed in parallel, each of them matched to a different user signature, just after sampling the received signal at 1/Trate. The aim of this bank of filters is to capture signal energy only from the user of interest. Figure 1: Representation of the multiuser channel model where Uusers transmit simultaneously using a DS/CDMA sharing strategy. Ei: bit energy of user i,xi(n): symbol sequence transmitted by user i,si(t): codeword of user i,ˆxi(n): estimate of nth symbol transmitted by user i. In order to estimate the transmitted symbols’ vector x(n)=[x1(n),...,xU(n)]T, we have followed ideas in [57], where estimation is presented as a maximization issue, and the output of the matched filters’ bank, z(n), is obtained as z(n)=[z1(n),...,zU(n)]T=RB(n)Ex(n)+g(6) 5 with Rbeing the cross-correlation matrix of users’ codewords, B(n)=diag(b1(n),...,bU(n)), E=diag(√E1,..., √EU),x(n)=[x1(n),...,xU(n)]Tand g=[g1(n),...,gU(n)]T. In [58] it is demonstrated that, given vector z, the log-likelihood conditional pdf given both the fading coefficients’ matrix and the transmitted symbols’ vector, can be obtained as L(B(n),x(n))=2<nx(n)TE[B(n)]∗z(n)o −x(n)TEB(n)R[B(n)]∗Ex(n)(7) with “<” and “*” stand for the real part of a complex magnitude, and the complex conjugate operator, respectively. Hence, both the fading coefficients’ matrix and the users’ transmitted symbols are estimated as (d B(n),d x(n)) =arg max B(n),x(n){L(B(n),x(n))}(8) Finally notice that fading coefficients are supposed to vary slowly enough so that this fading is assumed to be constant within each symbol interval. Besides, fadings from users iand j,i,j, are considered to be independent. As a consequence, the optimization problem to solve consists in the joint estimation of B(n)and x(n), which is repeated at every symbol period T. 4. Design methodology The proposed algorithm involves two stages: first, it uses a GA with a diversity control procedure, and afterwards, an heuristic k-opt exploitative search algorithm to fine-tune the output from the first stage. It is well known that one of the main advantages of GAs is that, considering a specific application, they require very few a priori assumptions to achieve a near optimum estimate [40, 37, 38]. This GA constitutes the first stage. Next, the local search method fine-tunes the fittest GA output so as to efficiently provide a quasi-optimum solution. Notice that this procedure is run assuming that the first stage (GA) has reached a near-optimum solution estimate. 4.1. Genetic algorithm (Step 1) 4.1.1. Basic concepts In a GA, possible solution estimates are encoded in a binary vector usually known as chromosome (or individual) and, during the GA cycle, genetic operators are applied to a subgroup of the fittest chromosomes with the aim of preserving crucial knowledge. The selection process relies on the principle of survival of the fittest individuals: those ones with highest fitness will have more chances to be selected for reproduction. This description of the standard GA is quite generic, however, implementation of many aspects can be particularized to each specific problem, for instance: initial generation of individuals and their encoding, definition of the operators (selection, crossover and mutation) and many other implementation tasks. Some of these design issues are next described. 6 4.1.2. Coding, selection and fitness evaluation First, the initial population is randomly created with npbinary-encoded individuals, and each one is evaluated according to its fitness. In the proposed equalization problem, Eq. (7) is used for evaluating the fitness of every member of the population, since both transmitted symbols and fading coefficients are encoded into chromosome CHRi(n,k) as: CHRi(n,k)=[Bi(n,k),xi(n,k)] =[(bi,1(n,k),bi,2(n,k),...,bi,U(n,k)), . . . . . . (xi,1(n,k),xi,2(n,k),...,xi,U(n,k))] 1≤k≤ng,1≤i≤np,0≤n≤F−1(9) where n,k,iand Ustand for the nth symbol period, the kth GA generation, the ith population individual, and the amount of active transmitters, respectively. On the right part of CHRi(n,k), vector xi(n,k)represents the estimates of the Utransmitted symbols. On the left, fading coefficients bi(n,k)are encoded. Since these coefficients are usually complex values, their real and imaginary parts are, each one, binary encoded, using 10+1 (sign) bits. A 22-bit long string is this way obtained. Due to the assumption of synchronous transmission, one GA is executed in each symbol interval (every Tseconds). Therefore, fading coefficients estimates obtained when the GA finishes, are kept as initialization values for next symbol period, where a new GA will start. This agrees with the hypothesis of low time variation of the channel fading, involving that fading coefficients slightly change within each period T. In contrast to the MA proposed in [33], our proposed genetic algorithm implements two different genetic operators: crossover and mutation, with the former used with a very low probability. Selection of chromosomes for mutation and crossover is based on a stochastic rule, where the fittest chromosomes can be selected with a higher probability than the weakest ones. Therefore, the ith chromosome CHRi(k)will be selected at iteration kwith probability Φi(k)/Pnp j=1Φj(k), where Φirepresents the fitness of individual igiven by Eq. (7). This scheme is readily implemented using a selection method known as roulette wheel, where the size of each circular sector is proportional to the aptitude of each chromosome [59]. 4.1.3. Genetic operators Two genetic operators are applied: mutation and crossover. Mutation modifies chromosomes with probability Pm, modifying the value of certain positions. Both the specific position within CHRiand its new value, are randomly obtained. This operator increases the explorative search of the solutions’ space. A low probability Pmprevents any part in CHRifrom remaining fixed, while a high value results in a random search. Therefore, Pmshould be correctly adjusted. For instance, in our application, and in accordance to [60], a nice trade-off solution is achieved with an initial value Pm(0) ∈[0.02 −0.05]. Mutation operator is invoked following the scheme proposed in [33], i.e., descendant chromosome comes given by NEW CHRi,k=sign(CHRi,k+Nk(0, σ)),k=1,2,...,K(10) 7 where NEW CHRi,kand CHRi,krepresent the k-th component of the i-th offspring and parent individuals, respectively, Nk(η, σ)is a Gaussian random variable with mean η and standard deviation σ. A new random value is obtained for each k. Notice that σ allows to control how closely the offspring is relative to its corresponding parents. Meanwhile, crossover operator obtains two new chromosomes (descendants) by merging two parents at specific points. The crossover operator is applied with probability Pc1. Since progenitors are selected from highest fitness chromosomes, the small modifications performed over these data structures are supposed to generate good individuals, as well. Crossover is applied with probability Pc=0.01. We get next generation by selecting the npfittest individuals from the parents and descendants sets considered together. 4.1.4. Elitism, termination criteria and convergence Elitism is implemented in our GA. This means that individuals with the highest fitness are directly selected and inserted into next generation. In our experiments mutation is applied to half of the elite with probability Pm,e=0.2Pm, while crossover is not implemented. Successive iterations of the GA are performed until a termination criterion is verified; in our real-time DS/CDMA application, the algorithm is iterated until a predetermined number of fitness evaluations is reached. Once the last iteration has been run, the GA output is given by the chromosome whose fitness is the highest, GA OUTPUT =CHRi best(ng,k)= =[Bi best(ng,k),xi best(ng,k)] (11) An schematic flowchart of the GA structure is shown in Fig. 2. Once the GA has finished, the exploitative searching method of Step-2 is invoked to improve the solution estimate in Eq. (11). 4.1.5. Diversity control GA convergence is greatly improved with the introduction of procedures that optimize population diversity. Classic GAs tend to converge to non-optimal solutions, mainly as a result of a selection that greatly relies on fitness [61]. This implies that population will be formed mainly by the fittest individuals, resulting in low diversity and low quality solutions. On the other hand, GAs suffer from excessive computational load, in part due to the load of the genetic operators in addition to fitness evaluations. Common population sizes (np) can be a huge number of several hundreds (300-2000) for equalization involving both users’ data and channel coefficients estimation. The GA here proposed works with less chromosomes (60 to 400 individuals) due to the use of a population diversity control scheme, where genetic operators rely on the Shannon entropy of the population fitness, which is obtained as H(P[k]) =− np X i=1 Φ∗ ilog Φ∗ i(12) with Φ∗ i(k)being the normalized value of the fitness of the ith individual, i.e., Φ∗ i(k)= Φi(k) Pnp j=1Φj(k),1≤i≤np(13) 8 Evaluatefitnessof individualsin P[ ]k Fitness-basedselection G completed? eneration P[ +1]k Evaluate terminationcriterion. Finished? P[k+1] NO NO YES YES Crossover Mutation + Elitism Ek Eliteselection Mutation (probability Replaceindiv.with lowest withtheelite:Fi P P*[k+1]={ [k+1], }Ek (probability )Pc (probability )Pm Pm,e) Geneticoperators Generation of Initial Population Report Final Solution Figure 2: Simplified flowchart of the proposed GA constituting the first stage of the memetic algorithm. Two genetic operators are implemented: crossover and mutation. Elitism is also implemented at the end of each iteration. The aim is to adapt the explorative/exploitative sense of the search depending on the population diversity estimated at each stage of the convergence cycle. When entropy His high, it means that population individuals are very similar. In this case, Pmis increased and Pcis decreased, in order to increase diversity by boosting explorative search. On the other hand, if His low, meaning that individuals are quite different, then Pmis decreased and Pcincreased. The thus designed GA is implemented in stage I of the proposed MA. It requires notably less computational load than the standard GA since dynamic operators allow to work with smaller population sizes, and, consequently, genetic operators and fitness evaluations are computed less frequently. 4.2. Local refinement using the k-opt algorithm (Step-2) Local search procedures focus their search in the neighborhood of the best solution estimate found so far until no improvement is found. The neighborhood of chromosome 9 8 16 32 40 48 24 10 10 10 10 10 10 10 -3 -5 -4 -6 -2 -1 0 E/N(dB) ProbabilityofError ofuser1(UOI) BER single-user 10 E/E=10dB, =2,...,U(decorrelator)k E/E=10dB, =2,...,U(MA LK)k - E/E=15dB, =2,...,U(M )kA k k k E/E=0dB, =2,...,U(M )kA E/E=10dB, =2,...,U(M )kA E/E=5dB, =2,...,U(M )kA k k k 1 1 1 1 1 1 Figure 6: BER performance for K=10 users with Ek/E1=0, 5, 10 and 15 dB for k=2,...,U. User 1: user of interest. even some Bayesian approaches, as well. Proposed MA is an efficient alternative when approaching this complex optimization problem, offering a remarkable performance, especially under unfavorable conditions (e.g. low signal-to-noise power ratio of the user of interest, considerable number of interferers, or existence of near-far effects). Whenever these degradations are not high, other two-stage nature-inspired algorithms show a performance similar to that of the MA detector and the optimum receiver. When ISI or MAI become stronger or the UOIs power is smaller, proposed MA achieves a better performance, in part as a result of its efficient search capabilities that adjust population diversity by in-service monitoring the population fitness entropy. This way, probabilities of crossover and mutation are fine-tuned using this information, thus adapting the exploitative/explorative sense of the search. 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