IEICE TRANS. COMMUN., VOL.E93–B, NO.10 OCTOBER 20102725

PAPER

Genetic Algorithm Based Equalizer for Ultra-Wideband WirelessCommunication Systems

Nazmat SURAJUDEEN-BAKINDE†, Xu ZHU†a), Jingbo GAO†, Asoke K. NANDI†, Nonmembers,and Hai LIN††, Member

SUMMARY In this paper, we propose a genetic algorithm (GA) basedequalization approach for direct sequence ultra-wideband (DS-UWB) wire-less communication systems, where the GA is combined with a RAKE re-ceiver to combat the inter-symbol interference (ISI) due to the frequencyselective nature of UWB channels for high data rate transmission. Theproposed GA based equalizer outperforms significantly the RAKE and theRAKE-minimum mean square error (MMSE) receivers according to resultsobtained from intensive simulation work. The RAKE-GA receiver alsoprovides bit-error-rate (BER) performance very close to that of the optimalRAKE-maximum likelihood detection (MLD) approach, while offering amuch lower computational complexity.key words: genetic algorithm, ultra-wideband, maximum likelihood detec-tion, minimum mean square error equalizer, RAKE receivers

1. Introduction

Ultra-wideband (UWB) systems operate in the spectrum al-lowed by the Federal Communications Commission (FCC)on an unlicensed basis. The ultrawide bandwidth and ul-tralow transmission power density for indoor applicationsmake UWB technology attractive for high-speed, short-range (e.g., indoor) wireless communications [1]. UWB sig-nal generations for the high-speed, short-range networkingis in support of a variety of potential low-cost, low-powermultimedia transport applications in home and enterpriseenvironments. Typical scenario is provisioning wireless dataconnectivity between desktop PC and associated peripheralslike keyboard, mouse, printer, etc. Additional driver appli-cations relates to streaming of digital media content betweenconsumer electronics appliances such as TV sets, VCRs, au-dio CD/DVD and MP3 players [2].

In an impulse-based DS-UWB system, the transmit-ted data bit is spread over multiple consecutive pulses ofvery low power density and ultra-short duration. This intro-duces resolvable multipath components having differentialdelays in the order of nanoseconds. Thus, the performanceof a DS-UWB system is significantly degraded by the inter-chip interference (ICI) and inter-symbol interference (ISI)due to multipath propagation [3]. In a frequency-selectivefading channel, a RAKE receiver can be used to exploit

Manuscript received July 14, 2009.Manuscript revised March 29, 2010.†The authors are with the Department of Electrical Engineer-

ing and Electronics, University of Liverpool, UK.††The author is with the Department of Electrical and infor-

mation Systems, Osaka Prefecture University, Sakai-shi, 599-8531Japan.

a) E-mail: xuzhu@liverpool.ac.ukDOI: 10.1587/transcom.E93.B.2725

multipath diversity by combining constructively the mono-cycles received from the resolvable paths. Maximum ratiocombining (MRC)-RAKE is optimum when the disturbanceto the desired signal is sourced only from additive whiteGaussian noise (AWGN), therefore it has low computationalcomplexity. However, the presence of multipath fading, ISI,and/or narrowband interference (NBI) degrades the systemperformance severely [4]. The maximum likelihood detec-tion (MLD) is optimal in such a frequency selective channelenvironment as UWB channel but its computational com-plexity grows exponentially with the constellation size andthe number of RAKE fingers.

The high computational complexity of MLD motivatesresearch for suboptimal receivers with reduced complexitysuch as linear and non-linear equalizers. In [5], performanceof non-linear frequency domain equalization schemes viz.decision feedback equalization (DFE) and iterative DFE forDS-UWB systems were studied. Eslami et al. in [6] pre-sented the performance of joint RAKE and minimum meansquare error (MMSE) equalizer receiver for UWB commu-nication systems. Parihar et al. in [7] and [8], gave thoroughanalysis of linear and non-linear equalizers for DS-UWBsystems considering two different modulation techniques,binary phase shift keying (BPSK) and 4-ary bi-orthogonalkeying (4BOK).

Known channel state information (CSI) has been as-sumed in previous work but practically this is not feasi-ble, because the wireless environment is always chang-ing. Channel estimation is of particular importance infuture broadband wireless networks since high data-ratetransmissions lead to severe frequency-selective channelfading, which necessitates the use of channel estima-tion/equalization techniques to combat the significant ISI[9].

Lots of research have been done on channel estima-tion techniques using both the training based and blind ap-proaches. In [4], [10] and [11], the pilot-aided channel es-timation were carried out. Sato and Ohtsuki in [4] useddata-aided approach based on using known pilot symbolsto estimate the channel (CIR) impulse response. The slid-ing window (SW) and successive cancelation (SC) algo-rithms were proposed in [10]. Chu et al. also proposeda pilot-channel-assisted log-likelihood-ratio selective com-bining (PCA-LLR-SC) scheme for UWB systems in [11].In [12], Lottici et al. proposed data-aided (DA) and non-dataaided (NDA) channel estimation scenarios based on the ML

Copyright c© 2010 The Institute of Electronics, Information and Communication Engineers

2726IEICE TRANS. COMMUN., VOL.E93–B, NO.10 OCTOBER 2010

criterion. Frequency domain channel estimation were re-ported in [13], where an iterative frequency domain chan-nel estimation technique was proposed for multiple-inputmultiple-output (MIMO)-UWB communication systems.

The genetic algorithm (GA) works on the Darwinianprinciple of natural selection called “survival of the fittest.”GA possesses an intrinsic flexibility and freedom to choosedesirable optima according to design specifications. GApresumes that the potential solution of any problem is anindividual and can be represented by a set of parameters re-garded as the genes of a chromosome and can be structuredby a string of values in binary form [14]. GA is a well stud-ied and effective search technique used in lots of work inCDMA communication systems as can be found in [15],[16] and [17]. In [15], a hybrid approach that employs aGA and multistage detector for the multiuser detection inCDMA system was proposed. Yen and Hanzo in [16], ap-plied GA as a joint channel estimation and multiuser sym-bol detection in synchronous CDMA systems. A micro GAwas developed in [17], as a multiuser detection technique inCDMA system.

GA has also been applied to UWB communication sys-tems in [18], [19] and [20]. In [18], GA was used to opti-mally select RAKE fingers different from the conventionalmethods, i.e., a GA-based iterative finger selection scheme,which depends on the direct evaluation of the objective func-tion, was proposed. T. Wang et al. [19], effectively used theGA to find the optimal UWB system parameters to reducethe multi-band jam interference power, i.e., an optimizationproblem is formulated, aiming to reduce multiband jam in-terference power on UWB THSS IR system with 2-PPM,which belongs to the class of nonlinear combinational opti-mization. A flexible UWB pulse waveform design method,based on an approximation with B-spline basis was carriedout in [20], using the GA optimization. However, to the bestof our knowledge, no work has been done, using GA forchannel equalization in UWB communication systems.

In this paper, we propose a GA based equalizationapproach for DS-UWB wireless communication systems,where GA is combined with a RAKE receiver to combatthe ISI due to the frequency selective nature of UWB chan-nels for high data rate transmission. Our work is differentfrom all the aforementioned, in that this is the first workto employ GA for channel equalization in UWB systems.We also compare our proposed RAKE-GA equalization ap-proach with the MMSE based linear equalization approachand the optimal MLD approach to demonstrate a trade-offbetween performance and computational complexity. More-over, we employ a data aided approach to estimate the chan-nel amplitudes and delays using a sliding window method,which has lower complexity than ML based channel estima-tion methods.

Simulation results show that the proposed GA basedstructure significantly outperforms the RAKE and RAKE-MMSE receivers. It also provides bit error rate (BER) per-formance very close to the optimal RAKE-MLD approach,while offering a much lower computational complexity. The

impact of the number of RAKE fingers and the populationsize on the BER performance of the RAKE-GA algorithmand the speed of convergence in terms of the BER againstthe number of generations are investigated by simulation.The number of training overhead, that is the percentage ofpilot symbols size compared to the number of transmitteddata, is also presented with a plot of BER against the num-ber of training symbols.

Section 2 is the system model. We propose a RAKE-GA equalization approach and the algorithm description ofthe proposed RAKE-GA are all in Sect. 3. The data-aidedchannel estimation for all the receivers are presented inSect. 4. Section 5 presents the computational complexity ofthe RAKE-GA receiver in comparison to the other receivers.The simulation set-up, results and performance evaluationare presented in Sect. 6. Section 7 draws the conclusion.

2. System Model

2.1 Transmit Signal

The transmit signal for the DS-UWB can be expressed as

x (t) =√

Ec

∞∑k=−∞

dkvtr (t − kTs) (1)

where the transmit pulse vtr (t), is generated by using theTernary orthogonal spreading code sequence [4], [21], [22],due to its orthogonality. dk ∈ {±1} is the kth transmit sym-bol, Ec is the energy per transmitted pulse, Ts is the intervalof one symbol, each symbol is subdivided into Nc equallyspaced chips, Ts = NcTc, Es = NcEc is the energy per sym-bol.

vtr (t) =Nc−1∑i=0

biw (t − iTc) (2)

where bi ∈ {−1, 0, 1} is the ith component of the spreadingcode, Tc is the chip duration, w (t) represents the transmit-ted monocycle waveform which is normalized to have unitenergy and Nc, is the length of the spreading code sequence.

2.2 Channel Model

According to [23], a reliable channel model, which cap-tures the important characteristics of the channel, is a vi-tal prerequisite for system design. Towards this end, theIEEE 802.15.3a task group has evaluated a number of pop-ular indoor channel models to determine which model bestfits the important characteristics from realistic channel mea-surements using UWB waveforms. The goal of the channelmodel is to capture the multipath characteristics of typicalenvironments where IEEE 802.15.3a devices are expectedto operate. The model should be relatively simple to usein order to allow (PHY) proposers to use the model and, ina timely manner, evaluate the performance of their PHY intypical operational environments [23].

SURAJUDEEN-BAKINDE et al.: GENETIC ALGORITHM BASED EQUALIZER2727

In this paper, the Saleh-Valenzuela model with a cou-ple of slight modifications is implemented. A log-normaldistribution rather than a Rayleigh distribution for the mul-tipath gain magnitude is recommended in this model, be-cause the log-normal distribution seems to better fit the mea-surement data. In addition independent fading is assumedfor each cluster as well as each ray within the cluster [24].The channel model recommended by the IEEE 802.15.3achannel modeling sub-committee is defined by the follow-ing channel impulse response (CIR):

h (t) =CL∑i=0

K∑k=0

αi,kδ(t − Ti − τi,k

)(3)

where αi,k = pi,kξi,k are the multipath gain coefficients,with pi,k ∈ {±1} denoting the random polarity (the possi-ble phases for real coefficients) with equal probability andthe fading amplitude ξi,k being log-normal-distributed. Ti isthe delay of the ith cluster and τi,k is the delay of the kth pathwithin the ith cluster relative to Ti. Ti and τi,k are describedwith a double-Poisson process and all of them are roundedto integer times of the delay resolution Tc [25]. CL and Kare the total numbers of observed clusters and the numberof multipath contribution within the ith cluster, respectively.

Thus, with τexc denoting the multipath delay spread,Ltot = τexc/Tc denotes the total number of paths. Let hl

denotes the sum of all αi,k at time index l, where l = �(Ti +

τi,k)/Tc�. Due to the clustering of multipath components, thechannel does not necessarily have multipath arrivals withineach delay bin. This is accounted for by setting hl = 0 forany lTc that has no path arrival [25]. Therefore, the CIR in(3) can be simplified to

h (t) =Ltot−1∑

l=0

hlδ (t − lTc) (4)

2.3 Receive Signal

The receive signal r (t), which is the convolution of thetransmit signal in (1) with the channel impulse responsesgiven in (4) and the addition of noise is shown in (5) as

r (t) = x (t) ∗ h (t) + n (t) (5)

=√

Ec

∞∑k=−∞

dkvtr

Ltot−1∑l=0

hl (t − kTs − lTc) + n (t) (6)

where n (t) is the additive white Gaussian noise (AWGN)with zero mean and a variance of σ2, ∗ denotes the convolu-tion operator.

3. RAKE-GA Based Equalization for DS-UWB Sys-tems

In this section, we present an equalization approach forDS-UWB systems by using GA. The block diagram ofthe GA based equalization approach is shown in Fig. 1,

Fig. 1 RAKE-GA for DS-UWB system.

where the blocks in the dashed boxing are the initializa-tion of the GA based equalization using RAKE demodu-lator. The GA is then employed to equalize the output sig-nals from the RAKE demodulator. Compared to the opti-mal MLD receiver, the proposed RAKE-GA receiver hasmuch lower computational complexity and negligible per-formance degradation. The iteration of GA is described insubsections in 3.2.1 to 3.2.5.

3.1 Initialization of RAKE-GA

It is well known that a good initial value is critical in GAbased algorithms. For DS-UWB systems, the performanceof GA only receiver without proper initialization is evenworse than RAKE receiver only, according to our initial re-sults, due to the frequency selective nature of UWB chan-nels. To this end we obtained our initial population for theGA optimization from the RAKE receiver output soft esti-mates, so as to improve the BER performance of our system.A typical RAKE receiver is composed of several correlatorsfollowed by a linear combiner, as shown in Fig. 1. The sig-nal received at the RAKE receiver of L fingers is correlatedwith delayed versions of the reference pulse, which is theTernary orthogonal spreading sequence, multiplied by thetap weights, the output signals are then combined linearly[26].

MRC-RAKE combiner, which uses the strongest esti-mated fingers to select the received signal at the delay times,τ f l (l = 0, ..., L − 1) [4], is employed in this work. Perfectchip synchronization between the transmitter and the re-ceiver is assumed. The lth correlator’s output, y f l

k of theRAKE receiver for the kth desired symbol is given by

yf lk =

∫ (k+1)Ts+τ f l

kT f+τ f l

r (t) vtr(t − kTs − τ f l

)dt (7)

Expression (7) in vector notation is expressed as shown in(8)

yk =√

Esdkh + ik + nk (8)

where nk =[nf0k , ..., n

fL−1

k ]T with nfL−1

k being the noisecomponent of the kth symbol for the lth correlator.

2728IEICE TRANS. COMMUN., VOL.E93–B, NO.10 OCTOBER 2010

ik =[i f0k , ..., i

fL−1

k ]T , with i fL−1

k denoting the ISI of thekth symbol for the lth correlator. h =[hf0 ..., hfL−1 ]

T ,yk =[y f0

k , ..., yfL−1

k ]T . The Selective RAKE receiver outputwith MRC technique is expressed as

dk = γT yk (9)

where γ = [γ0, ..., γL−1]T is the finger weights of the RAKEreceiver estimated from the channel taps, γl = h fl . h fl =

[h f0 , ..., h fL−1] are the channel estimates. The results obtainedin (9), which are soft estimates, are used as initialization ofthe GA optimization in the following section. The decisionfunction is used to determine the estimated received data forthe RAKE receiver only.

dk = sign(dk) =

{+1, dk ≥ 0−1, dk < 0

(10)

3.2 Algorithm Description of RAKE-GA

Despite the intuitive appeal and the symmetry of GAs, it iscrucial that we back these fuzzy feelings and speculationsabout GAs using cold, mathematical facts. The schematatheory will help us to do this. The schemata theory and theirnet effect of reproduction and genetic operators on buildingblocks contained within the population for the GA generally,and RAKE-GA in particular are discussed below [27].

A schema is a similarity template describing a sub-set of strings with similarities at certain string positions.A schema is motivated by appending a * or don’t caresymbol to the binary alphabet of genes. A schema (plu-ral, schemata), matches a particular string, if at every lo-cation in the schema, a 1 matches a 1 in the string, a 0matches a 0, or a * matches either. As an example, aschema, H = {∗101∗} describes a subset with four members,{01010, 01011, 11010, 11011}. The idea of schema gives apowerful and compact way to talk about all the well-definedsimilarities among finite length strings over a finite alpha-bet. The don’t care symbol, *, is only a metasymbol (a sym-bol about other symbols), it is never explicitly processed bythe GA. It is simply a notational device that allows descrip-tion of all possible similarities among strings of a particularlength and alphabet. In general, a particular string contains2l schemata, and a population with size, n contains some-where between 2l and n2l schemata, depending upon thepopulation diversity. l is the length of the binary string andl = 5 in the example illustrated above.

3.2.1 Fitness Function Evaluation

A fitness value is used to reflect the degree of goodness ofthe chromosome for the problem which would be highly re-lated with its objective value [14]. The fitness values of indi-viduals within the population of size P, for our GA is evalu-ated before implementing the GA operations. The GA refinethe specified population which consists of the chromosomes,through the reproduction, selection, crossover and mutationoperations. The initial population obtained from the RAKE

receiver outputs is used in the GA optimization. The GAminimizes the fitness function in terms of the distance mea-sure criteria according to the cost function below:

J =M∑

k=1

|γT ek| (11)

where ek = yk − hdk, dk is a given candidate solution and his an estimate of the channel.

3.2.2 Reproduction

Proportional fitness scaling is used to convert the raw fit-ness score returned by the objective function to values in arange that is suitable for the selection function. This repro-duction method makes the expectation proportional to theraw fitness scores. This is advantageous when the raw scoresare in good range. When the objective values vary a little,all individuals have approximately the same chance of re-production.

Stochastic selection now chooses parents for the nextgeneration based on their scaled values from the fitness scal-ing function. It lays out a line in which each parent corre-sponds to a section of the line of length proportional to itsscaled value. There is a movement along the line in stepsof equal size. At each step, a parent is allocated from thesection it lands on. The first step is a uniform random num-ber less than the step size. A certain elites are now chosenwhich are guaranteed to survive to the next generation.

The effect of reproduction on a particular schema iseasy to determine; since more highly fit strings have higherprobabilities of selection, on average an ever increasingnumber of samples are given to the observed best similar-ity patterns, however, reproduction alone samples no newpoints in the search space. Suppose we have m examplesof schema H contained within the population A(t), wherewe write m = m(H, t) (there are possibly different quanti-ties of different schemata H at different times t). Duringreproduction, a string is copied according to its fitness, ormore precisely, a string Ai gets selected with probabilitypi = fi/

∑f j, where fi is the fitness value of the string

schema and∑

f j is the total fitness values of all stringschemata. After picking a non-overlapping population ofsize n, with replacement from the population A(t), we ex-pect to have m = m(H, t + 1) representatives of the schemaH in the population at time t + 1 as given by

m (H, t + 1) = m (H, t) nfi∑n

j=1 f j(12)

where fi is the average fitness of the strings representingschema H at time t and recognizing that the average fitnessof the entire population may be written as f =

∑nj=1 f j/n

then (12) may be rewritten as the reproductive schemagrowth equation as

m (H, t + 1) = m (H, t)fif

(13)

SURAJUDEEN-BAKINDE et al.: GENETIC ALGORITHM BASED EQUALIZER2729

Expression (13) means schemata with fitness values abovethe population average fitness values will receive an in-creasing number of samples in the next generation, whileschemata with fitness values below the population averagewill receive a decreasing number of samples.

The RAKE-GA can be explained using the reproduc-tive schema growth equation in (13), if we have a schemathat represents the parent strings in our simulation, the par-ent strings has ten genes which is M = 10, that means fi rep-resents the fitness values of the schema that we have. The∑n

j=1 f j is the sum of all the parent strings that can be ob-tained from the already defined schema. The m = m(H, t)represents the number of parent strings that can be obtainedfrom the schema at a generation. We can therefore evaluatehow many parent strings will progress to the next genera-tion.

3.2.3 Crossover

Scattered crossover combines two parents to form a childfor the next generation. It creates a random binary vector,rv, then selects the genes where the vector is a 1 from thefirst parent, and the genes where the vector is a 0 from thesecond parent, and combines the genes to form the child.

Crossover is a structured yet randomized informationexchange between strings. Crossover creates new struc-tures with minimum disruption to the allocation strategydictated by reproduction alone. Crossover leaves a schemaunscathed if it does not cut the schema, but it may dis-rupt a schema when it does. Schemata of short defininglength, δ, are left alone by crossover and reproduced at agood sampling rate by reproduction operator. A schemasurvives when the crossover site falls outside the defininglength, δ, the survival probability under simple crossover isps (H) = 1 − σ(H)

l−1 , since the schema is likely to be disruptedwhenever a site within the defining length, δ is selected fromthe (l − 1) possible sites. If crossover is itself performed byrandom choice, say with probability pc at a particular mat-ing, the survival probability may be given by the expression

ps (H) ≥ 1 − pcσ (H)l − 1

(14)

where σ(H) is the defining length of the schema H, definedas the distance between the outermost fixed string positionsand l is the length of the binary string.

In scattered crossover, as is implemented in RAKE-GA, it can be concluded that the number of possiblecrossover sites will have uniform distribution, and it is morelikely to generate crossover strings that are half 0’s and half1’s after many simulation runs and for more than one gen-erations. The probability of crossover, pc = 0.85 and thedefining length, δ, will be the distance between the first andthe last fixed position in our schema. It can be possible tofind the probability of survival using (14), but with the as-sumption that the (l − 1) in (14) becomes (l − 5), since ourcrossover sites will be 5, with l being M in our simulation.Schemata strings with, defining length, δ < 5 will survive

the crossover operation and will progress from one genera-tion to the other generation, with a probability of crossover,pc = 0.85.

3.2.4 Mutation

Gaussian mutation is used to provide genetic diversity, en-able the GA to search a broader space and prevent conver-gence to local minimum, by making small random changesin the individuals in the population. It adds a random num-ber from a Gaussian distribution with mean zero to eachvector entry of an individual. The variance of this distribu-tion is determined by the parameters scale and shrink. Thescale parameter determines the variance at the first genera-tion, that is, it controls the standard deviation of the mutationand it is given by standard deviation = scale × (v(2) − v(1)),where scale = 0–10. The initial range is a 2-by-1 vec-tor, v = [0, 1]T . The shrink parameter controls how thevariance shrinks as generations go by. That is, it con-trols the rate at which the average amount of mutationdecreases. The variance at the generation G is given byvark = vark−1

(1 − shrink × k

G

), where shrink = −1–3. If

the shrink parameter is 0, the variance is constant, if theshrink is 1, the variance shrinks to 0 linearly as the lastgeneration is reached and a negative value of shrink causesthe variance to grow [28].

Mutation is the random alteration of a single positionwith probability pm. Mutation at normal, low rates does notdisrupt a particular schema very frequently. In order fora schema H to survive, all of the specified positions mustthemselves survive. Therefore, since a single allele surviveswith probability (1 − pm), and since each of the mutationsis statistically independent, Schema H survives when eachof the o(H) fixed positions within the schema survives. Theprobability of a schema surviving mutation is

ps (H) = (1 − pm)o(H) (15)

For small values of pm (pm 1), the schema survival prob-ability can be approximated by:

ps (H) ≈ 1 − o (H) pm (16)

The probability o f mutation, pm = 0.15 and the order,o(H), of schema will be the number of fixed positions in theschema. We can then use this information to calculate theprobability of survival after mutation using (16). Schematastrings with low-order will survive mutation and will be ableto progress from one generation to the other. The algorithmis terminated after a fixed number of generations G.

3.2.5 Schemata Growth Equation

Combining the effect of reproduction, crossover and muta-tion, it can thus be concluded that a particular schema, Hreceives an expected number of copies in the next genera-tion, as given by the following expression:

m (H, t + 1)

2730IEICE TRANS. COMMUN., VOL.E93–B, NO.10 OCTOBER 2010

≥ m (H, t)fif

[1 − pc

σ (H)l − 1

− o (H) pm

](17)

Based on (17), it can be concluded that short defining length,low-order and above-average schemata receive exponen-tially increasing trials in subsequent generations [27].

Schemata theory when related to RAKE-GA meansthat parent strings, with above-average fitness values whencompared to the average fitness values of all the parentstrings in the search space and with short distance betweenthe first and the last position and with low number of fixedgenes, will have a higher probability of making it to the nextgenerations, than parent strings with below-average fitness,long defining length and high order.

3.3 RAKE-GA vs. RAKE-MLD

The RAKE-GA receiver is proposed to reduce the high com-putational complexity of the RAKE-MLD receiver which isan optimum receiver in a frequency selective channel likeUWB. In the MLD scheme, where the whole search spaceof possible solutions are utilized, the soft estimate output,of the RAKE receiver is also used as the input to the MLDreceiver. The MLD detector searches through all the possi-ble solutions of data bits, 2M , and the one close in distanceto the transmitted data based on the distance measure crite-ria is chosen. The cost function for the RAKE-MLD is alsopresented in expression (11) thereby making the MLD tospend longer simulation time and consequently to be morecomputationally complex.

It is worth noting that the proposed RAKE-GA equal-izer is also applicable to a system with higher order mod-ulation because GA has been successfully used to detectcomplex-valued signals such as QPSK signals in narrowband systems [29].

4. Channel Estimation

In this work, a data-aided approach used in [12] is alsoimplemented in estimating the channel impulse responses.The sliding window correlator method [30] and [10] is usedin estimating the channel gains and delays so as to reducethe high computational complexity of the ML approach. Adata-aided approach for channel estimation is employed inthis work and this implies that the transmitted signal, x(t),is known to the receiver. The ML channel estimation hasa very good performance but it is too complicated to beimplemented in UWB systems which usually require lowcomplexity receivers [26]. B known pilot symbols are sentfor the training, i.e. dt

k, (k = 1, 2..., B) in order to estimatethe channel. The RAKE receiver gave an output during thetraining and is presented as in [4].

yLest

k =

∫ (k+1)Ts+τ f l

kTs+τ f l

rt (t) vtr(t − kTs − τ f l

)dt (18)

where yLest

k =[y1

k , y2k , ..., y

Lest

k

]T, rt(t) is the received training

signal for the kth pilot symbol, Lest is the number of paths

to be estimated and it is assumed that the receiver knows theoptimal value of Lest (i.e.Lest = Ltot) (3), [4]. All other termsare as already defined in the previous section. The estimated

path gains of the channel vector, h =[h1, h2, ..., hLest

]T, can

be expressed as follows using the cross-correlation method,where Es is the energy per symbol [4].

h =1

B√

Es

B∑k=1

dtky

Lest

k . (19)

5. Computational Complexity

We provide a complexity analysis of the proposed RAKE-GA in terms of complex valued floating point multipli-cation, in comparison with the RAKE, RAKE-MMSEand RAKE-MLD receivers. We assume all the receiversuse the same channel estimation as presented in Sect. 4.Therefore, the complexity of channel estimation is notconsidered here. The order of complexity, O (Lest M) isfor the RAKE receiver. The RAKE-MMSE is of theorder of O

([L3

c + L2c M + Lest M

]). The RAKE-GA has

an order of complexity O([

GP(Lest M + logP

)]+ Lest M2

).

The RAKE-MLD has a complexity of the order ofO([

M2M (Lest M + log2)])

. Lest is the number of paths tobe estimated during the channel estimation process, M isthe number of symbols per block, Nc is the length of theternary orthogonal code sequence. G is the number of gen-erations and P is the population size for the RAKE-GA. Thecomputational complexities of the receivers depend on thederivation of the finger weights, the fitness function evalua-tion and the demodulation of the signal.

Table 1 shows the complexities of the RAKE, RAKE-MMSE, RAKE-GA and RAKE-MLD at Lest = 1024. TheRAKE-MMSE, RAKE-GA and RAKE-MLD are normal-ized to the RAKE receiver, being the least complex receiverbut with the worst BER performance. The RAKE-MMSEis five times more complex than the RAKE receiver, but hascorresponding improved performance. The RAKE-GA ismore complex than the other two receivers but obviouslywith much better BER performance with no error floor asencountered in the other receivers. The RAKE-MLD is themost complex of the four receivers but with the best BERperformance. The BER of the RAKE-GA is very close tothe RAKE-MLD with a huge reduction in the complexity ofthe RAKE-GA when compared to the RAKE-MLD.

Table 1 Computational complexity (Lest = 1024).

Receiver Parameters NormalizedRAKE [4] M=100 1

RAKE-MMSE [6] M=100, Lc=5 5RAKE-GA M=10, P=100, G=10 103

RAKE-MLD M=10 1025

SURAJUDEEN-BAKINDE et al.: GENETIC ALGORITHM BASED EQUALIZER2731

6. Simulation Results

6.1 Simulation Setup

We evaluate the performance of the proposed RAKE-GAreceiver, in comparison with RAKE [4], RAKE-MMSE [6],and RAKE-MLD receivers by simulation. All systems useBPSK modulation, with Ternary orthogonal spreading codesequence of length Nc = 24, to spread the transmit symboland a chip duration of Tc = 0.167 ns [4]. This results in asymbol duration of Ts = NcTc = 4 ns. Invariably, the trans-mission rate is Rs = 1/Ts = 250 Mbps [4]. The simulatedIEEE 802.15.3a UWB multipath channel model with data-aided channel estimation using pilot symbols of B = 10–100for a single user scenario is employed for the simulation.The channel model 3 (CM3) [24], which is a non-line-of-sight (NLOS) environment, with a distance of 4–10 m, meanexcess delay of 15.9 ns and root mean square (RMS) delayspread of 15 ns is considered in this work.

The number of RAKE fingers used are L = 5, 10, 15,20, to verify how RAKE finger size affect the convergencespeed of our algorithm in terms of BER vs. SNR and BERvs. number of generations. The equalizer taps of Lc = 5is used for the RAKE-MMSE. The GA simulation set-upis based on results obtained, after trying with different pa-rameters combination, to reduce the simulation time. Forthe proposed GA approach, the population size is P = 50and 100 while the number of generations is G = 1–20. Theproportional scaling is employed for the scaling of the fit-ness values before selection. The probability of crossoveris pc = 0.85 and the probability of Gaussian mutation ispm = 0.15, with values of shrink = 1.0 and scale = 0.75.We use 1000 channel realizations in our simulations and thechannel is assumed to be constant over 100 symbols. Thus,a total of 100000 symbols are simulated to guarantee theaccuracy of the results.

6.2 Performance Evaluation

The BER performance of RAKE, RAKE-MMSE, RAKE-GA and RAKE-MLD receivers at L = 10 with both knownCSI and pilot-aided channel estimation scenarios are pre-sented in Fig. 2. The four receivers perform better as ex-pected when the CSI is provided as the channel estimationerrors incurred will degrade the performances. The errorfloors encountered by both the RAKE and RAKE-MMSEreceivers are taken care of by the RAKE-GA and RAKE-MLD as explained thus:

• The RAKE receiver cannot capture a large signal en-ergy with few number of RAKE fingers and more soa RAKE with MRC weight estimation cannot removeISI. RAKE receiver also needs very high number of pi-lot symbols during the channel estimation as the chan-nel estimation error incurred using a few number ofpilot symbols resulted in the performance being de-graded.

Fig. 2 BER vs. SNR for all receivers.

• The RAKE-MMSE receiver achieves better BER thanRAKE receiver because the equalizer removes the ISIsymbol by symbol but the error floor is still encoun-tered since the RAKE receiver output with few RAKEfingers is the input to the equalizer, and so the RAKE-MMSE cannot capture a large signal energy.• The RAKE-GA receiver on the order hand has no er-

ror floor with the same number of RAKE fingers asthe other two receivers because it is able to remove theISI using the distance measure criteria. The soft esti-mates of the RAKE receiver is a very good initial pop-ulation choice for the GA and so is the reason for theimprovement in the BER performance. The RAKE-GA performs well even with moderate number of pilotsymbols.• The RAKE-MLD receiver has the best BER perfor-

mance, as is the optimal receiver which is able to re-move the ISI, and capture a large signal energy, usinga few RAKE fingers, and not very high pilot symbols,since the RAKE receiver output is also the input intothe RAKE-MLD receiver.

Figure 3 demonstrates the average, worst and bestBERs for the RAKE-GA receiver, for 1000 channel realiza-tions, with P = 100, G = 10, L = 10. As stated in Sect. 6.1,each channel is assumed to be constant over 100 symbols. Itis shown that different channel realizations result in BERperformance of the same slope. The performance of theworst channel is only 4 dB worse than the average perfor-mance, while the best channel leads to an SNR gain of 4 dBover the average performance.

The impact of the number of RAKE fingers on the per-formance of the scheme is shown in Fig. 4, where the BERis plotted against the SNR for the RAKE-GA receiver at P= 100, G = 10 at values of L = 5, 10, 15, 20. The averageBER performance improvement encountered in Fig. 4 is asa result of increase in the number of RAKE fingers. TheRAKE-GA at L = 5 is of higher BER, when compared towhen L = 10, 15, 20, where they are almost of the same

2732IEICE TRANS. COMMUN., VOL.E93–B, NO.10 OCTOBER 2010

Fig. 3 Worst, average and best BERs for RAKE-GA with differentchannel realizations.

Fig. 4 Effect of the number of RAKE fingers on the BER performanceof RAKE-GA.

BER at all SNR values.The speed of convergence of the algorithm is investi-

gated in Fig. 5, where the impact of the number of gener-ations on the average BER performance is demonstrated,where G = 1–20 for P = 100 and G = 2–20 for P = 50both at L = 10. The algorithm at G = 1–10 for P = 100 givesbetter BER generally, than at G = 2–20 for P = 50. It canthus be concluded that the GA with a relatively large popu-lation size achieves a lower steady state BER than the casewith only half the population size at a cost of slightly moregenerations.

In Fig. 6, we show how the average BER of the RAKE-GA receiver with channel estimation, decreases with in-crease in the number of pilot symbols giving us the numberof training overhead for the pilot-aided channel estimation.

The average BER performance improves as the RAKEfingers size increases from 2 to 10 with a step of 2, with afixed population size and same SNR value. This is demon-

Fig. 5 Impact of population size on convergence speed of RAKE-GA.

Fig. 6 Impact of Pilot size on convergence speed of RAKE-GA.

Fig. 7 Impact of the number of RAKE fingers on convergence speed ofRAKE-GA.

SURAJUDEEN-BAKINDE et al.: GENETIC ALGORITHM BASED EQUALIZER2733

strated in Fig. 7, where the impact of the number of RAKEfingers on the convergence speed of our RAKE-GA receiveris presented. It is shown that the performance of the RAKE-GA equalizer improves with the increase in the number ofRAKE fingers, due to enhanced initialization. The perfor-mance gap decreases with the increase in the number ofRAKE fingers. It is also observed that various RAKE fin-ger sizes all lead to the steady state of GA at approximately8 generations.

7. Conclusion

We have proposed a GA based channel equalization schemefor DS-UWB wireless communication and compared theresults obtained from intensive simulation work with theRAKE, RAKE-MMSE and RAKE-MLD for both knownCSI and pilot-aided channel estimation scenarios. Our sim-ulation results show that the proposed RAKE-GA receiversignificantly outperforms the RAKE and the RAKE-MMSEreceivers. The GA based scheme also gives BER perfor-mance very close to the optimal MLD approach at a muchlower computational complexity. Moreover, we have inves-tigated the effect of the number of RAKE fingers, the popu-lation size and the pilot overhead on the BER performance.RAKE-GA obtains a good performance with a moderatenumber of RAKE fingers and a further increase in the num-ber of RAKE fingers has little effect on the performance.GA with a relatively large population size achieves a lowersteady state BER than the case with only half the populationsize at the cost of slightly more generations.

Acknowledgment

This work was supported by the Commonwealth Scholar-ship Commission, UK, the University of Liverpool, UK, andthe University of Ilorin, Nigeria.

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Nazmat Surajudeen-Bakinde received theB.Eng. and the Masters degrees in Communica-tion Engineering degree in Electrical Engineer-ing from the University of Ilorin, Nigeria, in1998 and 2004 respectively. She is presently un-dergoing her PhD in the University of Liverpooland her current research interests are MultipleInputs Multiple Outputs (MIMO) Communica-tions Systems, Ultra Wideband (UWB) Technol-ogy for Short Range and High Speed Commu-nications Systems, Spread Spectrum Communi-

cations Systems, Channel Equalization and Signal Detection in WirelessCommunications Systems and Genetic Algorithms as Optimization tech-nique for Wireless Communications Systems.

Xu Zhu received the B.Eng. degree (withfirst class honors) from Huazhong Universityof Science and Technology, Wuhan, China, in1999, and the Ph.D. degree from the Hong KongUniversity of Science and Technology, HongKong, in 2003, both in Electrical and ElectronicEngineering. Since May 2003, she has beenwith the Department of Electrical Engineeringand Electronics, the University of Liverpool,Liverpool, U.K., where she is currently a se-nior lecturer. Dr. Zhu was the vice chair of the

2006 and 2008 ICA Research Network International Workshops, held inLiverpool. She has served as a session chair and a technical programcommittee member for various conferences, such as IEEE GLOBECOM2009 and IEEE VTC Spring-2009. Her research interests include MIMO,OFDM, equalization, blind source separation, cooperative communicationsand cross-layer optimization, etc.

Jingbo Gao received the Ph.D. degree inElectronics and Information Engineering fromHuazhong University of Science and Technol-ogy, Wuhan, China, in 2006. He is currentlyworking as a post-doctorial research associatein the Department of Electrical Engineering andElectronics, the University of Liverpool, Liver-pool, U.K. His research interests include blindsource separation, MIMO, OFDM, frequencydomain processing, and the implementation ofbroadband wireless communication systems.

Asoke K. Nandi received the degree ofPh.D. in High Energy Physics from the Univer-sity of Cambridge (Trinity College), Cambridge,UK, in 1979. He held several research posi-tions in Rutherford Appleton Laboratory (UK),European Organisation for Nuclear Research(Switzerland), Department of Physics, QueenMary College (London, UK) and Departmentof Nuclear Physics (Oxford, UK). In 1987, hejoined the Imperial College, London, UK, as theSolartron Lecturer in the Signal Processing Sec-

tion of the Electrical Engineering Department. In 1991, he jointed the Sig-nal Processing Division of the Electronic and Electrical Engineering De-partment in the University of Strathclyde, Glasgow, UK, as a Senior Lec-turer; subsequently, he was appointed a Reader in 1995 and a Professorin 1998. In March 1999 he moved to the University of Liverpool, Liver-pool, UK, to take up his appointment to the David Jardine Chair of SignalProcessing in the Department of Electrical Engineering and Electronics.In 1983 he was a member of the UA1 team at CERN that discovered thethree fundamental particles known as W+, W− and Z◦, providing the ev-idence for the unification of the electromagnetic and weak forces, whichwas recognized by the Nobel Committee for Physics in 1984. Currently, heis the Head of the Signal Processing and Communications Research Groupwith interests in the areas of non-linear and non-Gaussian signal process-ing, communications and machine learning research. With his group hehas been carrying out research in communications signal processing, blindsource separation, development and applications of machine learning, ma-chine condition monitoring, and biomedical signal processing. He has au-thored or co-authored over 400 technical publications; these include twobooks, entitled “Automatic Modulation Recognition of CommunicationsSignals” (Boston, MA: Kluwer Academic, 1996) and “Blind EstimationUsing Higher-Order Statistics” (Boston, MA: Kluwer Academic, 1999),and over 160 journal papers. Professor Nandi was awarded the Mounbat-ten Premium, Division Award of the Electronics and Communications Di-vision, of the Institution of Electrical Engineers of the U.K. in 1998 andthe Water Arbitration Prize of the Institution of Mechanical Engineers ofthe U.K. in 1999. He is a Fellow of the Cambridge Philosophical Society,the Institution of Engineering and Technology, the Institute of Mathematicsand its applications, the Institute of Physics, the Royal Society for Arts, theInstitution of Mechanical Engineers, and the British Computer Society.

Hai Lin received the B.E. degree in electri-cal power engineering from Shanghai JiaoTongUniversity in 1993, with a second B.E. degree inapplied electronic engineering. He also receivedthe M.E. degree from University of the Ryukyusin 2000, and the Dr.Eng. degree from Osaka Pre-fecture University in 2005, both in electrical en-gineering. Since 2000, he was a research as-sociate in the Graduate School of Engineering,Osaka Prefecture University, where now he is anassistant professor. His current research inter-

ests include OFDM, UWB, mobile communications, cognitive radio, andcooperative communications.