Minimizing the Symbol-Error-Rate for Amplify and ... - IEEE Xplore

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TCOMM.2014.2375255, IEEE Transactions on Communications

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Minimizing the Symbol-Error-Rate for Amplify and Forward Relaying Systems using Evolutionary Algorithms Qasim Zeeshan Ahmed, Sajid Ahmed, Mohamed-Slim Alouini, and Sonia A¨ıssa

Abstract—In this paper, a new detector is proposed for amplifyand-forward (AF) relaying system. The detector is designed to minimize the symbol-error-rate (SER) of the system. The SER surface is non-linear and may have multiple minimas, therefore, designing a SER detector for cooperative communications becomes an optimization problem. Evolutionary based algorithms have the capability to find the global minima, therefore, evolutionary algorithms such as particle swarm optimization (PSO) and differential evolution (DE) are exploited to solve this optimization problem. The performance of proposed detectors is compared with the conventional detectors such as maximum likelihood (ML) and minimum mean square error (MMSE) detector. In the simulation results, it can be observed that the SER performance of the proposed detectors are less than 2 dB away from the ML detector. Significant improvement in SER performance is also observed when comparing with the MMSE detector. The computational complexity of the proposed detector is much less than the ML and MMSE algorithms. Moreover, in contrast to ML and MMSE detectors, the computational complexity of the proposed detectors increases linearly with respect to the number of relays. Index Terms—Cooperative networks, minimum mean square error (MMSE), bit error rate (BER), steepest descent (SD), particle swarm optimization (PSO), differential evolution (DE).

I. I NTRODUCTION Quality of service (QoS) has always been an important criterion for wireless systems [1–3]. Fading is a major problem that effects the desired QoS [1]. An easy approach to combat this fading is to transmit multiple copies of the desired signal, by exploiting spatial, time, frequency or code diversity [1, 2]. Cooperative communications assist in forming a distributed network where these communication devices are able to share their transmit antennas, enabling these devices to achieve spatial diversity at the mobile terminals [3, 4]. This spatial diversity can also be combined with other forms of diversities to further improve the QoS of the desired system [3, 5]. With this improved QoS, cooperative communications have found applications in LTE, LTE-A standards [6–8], and in vehicle safety [9] as well. Q. Z. Ahmed, S. Ahmed and M.-S. Alouini are with the Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, King Abdullah University of Science and Technology (KAUST), Thuwal, Makkah Province, Saudi Arabia; email: {qasim.ahmed,sajid.ahmed,slim.alouini}@kaust.edu.sa. S. A¨ıssa is with Institut National de la Recherche Scientifique (INRS), University of Quebec, Montreal, QC, Canada; email: [email protected]. Part of this work was presented in IEEE Vehicular Technology Conference (VTC-Spring), Yokohama, Japan, May 2012.

Low-complexity cooperative diversity protocols have been developed and analyzed for cooperative communications in different operating conditions and environments. According to [3], the family of fixed relaying arrangements have the lowest complexity as compared to all the other families. The family of fixed relaying consists of decode-and-forward (DF) and amplify-and-forward (AF) protocols. It has been proved that the AF protocol has the ability to achieve similar symbol error rate (SER) performance as compared to that of the DF protocol, while maintaining a lower complexity [3, 5]. Therefore, only the AF protocol is considered in our contribution. One of the key parameters to determine QoS in a wireless system is the SER performance. The SER function is nonlinear, multimodal and may have several local minima [10]. Maximum likelihood (ML) detection is the optimal scheme in terms of SER performance for equal likely symbols [11, 12]. However, due to the high computational complexity, it is not a preferred solutions [13]. Therefore, sub-optimal linear equalizers have been considered in [10, 14–16]. In suboptimal linear detectors, minimum mean square error (MMSE) detector minimizes the mean square error (MSE) between the transmitted and received signal and maximizes the SNR [17, 18]. In communication systems, it is the SER performance that needs to be minimized rather then the MSE of the system. In [15, 18–20], it has been shown that minimizing the MSE does not necessarily minimize the SER performance of the system. Therefore, a detector is required for a cooperative communication environment, which minimizes the SER. In this work the SER detector for cooperative communication is implemented with the help of steepest descent (SD) and evolutionary algorithms. There are three major problem with the SD based algorithm when applied to cooperative communication systems. Firstly, the SD based algorithms are usually slow converging and therefore, a large number of iterations are required to reach the global minimum of the system. Furthermore, as the number of relays increases the dimension (or size) of the weighting vector increases. The convergence speed of SD based algorithm is inversely proportional to the size of the weights, therefore, the convergence speed will be slow for large number of relays [21]. Secondly, as the SER surface may have several local minima, the SD based algorithm might get stuck in a local minima. In order to avoid this problem, a constraint on the SD based algorithm is imposed [19]. Therefore, in this contribution evolutionary algorithms have been invoked for the implementation of SER

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detector. The major advantages of using evolutionary algorithm are as follow • On expectation the global minima is guaranteed and reached with less number of iterations, thereby, improving the spectral efficiency of the system and making them implementable for real time systems [22–26]. • The performance of proposed algorithms do not degrade with the increase in number of relays [27]. • The proposed algorithms do not require the derivative of the probability of error, which reduces the computational complexity of the algorithm. In this contribution, particle swarm optimization (PSO) and differential evolution (DE) are applied to find the weights of the detector. The reasons for choosing them are: firstly, both of these algorithms require minimal tuning parameters, thereby, can be implemented in real time applications. Secondly, they can be implemented adaptively, thereby, decreasing the complexity of the system to the minimal [24, 28]. Our simulation results show that these evolutionary based algorithms outperform the SD approach in terms of the achieved SER. The convergence speed of these evolutionary based algorithms is faster than that of the SD based algorithm. These detectors are less than a dB away from a ML detector which have complete channel state information (CSI). Furthermore, in terms of rate these detectors perform very close to the rate of the ML detector and a significant gain can be observed when compared to the SD based algorithm. The main contributions of this paper are summarized as follows: 1) SER for cooperative communication system is calculated; 2) As SER for cooperative communication system does not have a closed form expression weights for the receiver needs to be determined iteratively. Two different approaches to achieve these weights are derived and presented in this paper; and 3) The computational complexity of all these algorithms are calculated and compared. The remainder of this paper is organized as follows. In Section II, a detailed explanation of the system model and the basic assumptions are elaborated. Section III investigates the conventional relay-assisted MMSE and SER detectors for a cooperative communication environment. Section IV, is devoted to describing the proposed detection scheme with the assistance of SD, PSO and DE based algorithms. Complexities of the SER detectors is calculated in Section V. In Section VI, simulation results of the proposed detectors are compared with the MMSE and ML detector. Finally, the paper is concluded in Section VII . II. U PLINK C OMMUNICATION M ODEL The basic cooperative communication system considered in this paper is shown in Fig. 1. It can be observed from Fig. 1 that the source S transmits data to the destination D with the support of L relays. The direct link between S and D, is ignored because of the large path loss between the S and D. The channel gains for the source to the lth relay and the lth relay to destination are respectively, denoted by hSRl and hRl D . Channel gains are assumed to be mutually independent. The data transmission takes place in two phases as shown in Fig. 1. Source S transmits data to the relays in phase-I, while

the data is amplified and forwarded to D through the relays in phase II.

hSR

hR D

hSR

hR D

1

1

2

2

hR D

hSR

L

L

Figure 1. Schematic block diagram of a cooperative communication system assisted with L-relays.

A. Phase-I: Transmission from Source For simplicity, it is assumed that the source transmits independent and identically distributed (i.i.d) quadrature phaseshift keying (QPSK) symbol, s ∈ {±1 ± j}. In the first time-slot, the transmitted data symbol is forwarded to all the relays, R1 , R2 , · · · RL . The received signals at the relays can be represented as yRl = hSRl s + nRl ,

l = 1, 2, · · · , L,

(1)

where nRl is the additive white Gaussian noise (AWGN) with 2 mean zero and variance σR /2 per dimension. The channel is l assumed to follow the Rayleigh fading distribution and the probability density function (PDF) of the channel is given by [2] ! h2SRl hSRl exp − 2 , hSRl ≥ 0. (2) p(hSRl ) = 2 σhSR 2σhSR l

l

B. Phase-II: Transmission from Relays to Destination In this phase, after receiving signal yRl , the respective relay, i.e., p the lth terminal, normalizes this signal by a factor of E[yRl |2 ], where E[.] denotes the expectation operator. After this normalization, the resulting signal is transmitted to the destination. This operation is performed at all relays. As such, the signals received at the destination can be expressed as follows y Rl y l = h Rl D p + nDl , l = 1, 2, · · · , L, (3) E[|yRl |2 ] where hRl D denotes the complex fading coefficient of the link between relay l and destination D, with distribution as shown in (2). Substituting (1) in (3), we obtain yl

h n h h pRl D SRl s + p Rl D Rl + nDl 2 E[|yRl | ] E[|yRl |2 ] = hl s + nl , l = 1, 2, · · · , L,

=

(4)

where hR D hSRl hl = p l E[|yRl |2 ]


(5)


3

where zR is the real part and zI is the imaginary part of z, and are given by

and h R D n Rl nl = p l + nDl . E[|yRl |2 ]

(6)

In the above, hl and nl respectively represent the noise free term and noise part of yl . If the channel knowledge is available, nl can be approximated as a Gaussian noise with zero mean and variance per dimension given by σl2 =

2 |hRl D |2 σR l E[|yRl |2 ]

2 + σD , l

zR

=

zI

=

w H h s) + ℜ(w w H n ), ℜ(z) = ℜ(w w H h s) + ℑ(w w H n ). ℑ(z) = ℑ(w

(16) (17)

The estimate of the desired symbol s is expressed as sˆ = sˆR + jˆ sI = sgn(zR ) + jsgn(zI ),

(18)

where sgn(z) is the sign function. The PDF of zR and zI can be represented as 2 ! zR − ℜ w H h s 1 C. Receiver Structure ,(19) exp − pzR |s (zR |s) = √ w H Λw 2w w H Λw w 2πw In order to detect the transmitted symbol s, L copies of the 2 ! transmitted signal arriving at the receiver through L relays are zI − ℑ w H h s 1 exp − .(20) collected. The received signal at the destination can finally be pzI |s (zI |s) = √ w H Λw 2w w H Λw w 2πw represented as y

l = 1, 2, · · · , L.

= hs + n,

(7)

(8)

A. Relay-assisted MMSE Detector

(9)

Now we are considering the basic MMSE detector. The classical Wiener filter design is based on minimizing the MSE criterion [21]

where T y = [y1 , y2 , · · · , yL ] ,

"

hR D hSR1 hR D hSRL h= p1 ,··· , p L E[|yR1 |2 ] E[|yRL |2 ]

and n

=

"

#T

J(w) ,

h R D n RL h R D n R1 p 1 + nD1 · · · , p L + nDL 2 E[|yR1 | ] E[|yRL |2 ]

(10)

#T

.

(11)

n is an AWGN with mean zero and co-variance matrix Λ , which can be expressed as 2 Λ = diag[σ12 , σ22 , · · · , σL ].

(12)

In the following section, we will discuss the conventional detection methods and will propose a new method for detection of the desired signal s. III. D ETECTION FOR C OOPERATIVE C OMMUNICATION S YSTEMS Linear detectors are preferred over the optimal and other sub-optimal detectors due to their lower complexity [10, 16]. The receiver consists of a linear filter characterized by z

= w Hy = w H hs + w H n,

(13)

(14)

and wl is the l-th tap complex valued filter coefficient. As our transmitted symbol s is QPSK-modulated, the output of the receiver can be written as z = zR + jzI ,

The optimal weights can be derived by taking the derivative of (21) with respect to w and then setting the result to zero. The optimal weights in a relay assisted MMSE detector can be easily determined as [21] w

= R −1ρ ,

(22)

where ρ is the cross-correlation between y and s, and R is the auto-correlation matrix of y : ρ R

= E[yy s∗ ] = h hh H ] + 2Λ Λ. = E[yyy H ] = E[h

(23) (24)

In wireless communication systems, the performance is measured in terms of SER instead of MSE. MMSE detector minimizes the MSE, which may not translate into the lowest SER performance of the system [14, 20]. Accordingly, a detector that minimizes the SER performance of the system needs to be designed for a cooperative communication environment. B. Relay Assisted SER Detector

where w = [w0 , w1 , · · · , wL ]T ,

= E{|s − sˆ|2 }, w = E{ss∗ } − w H E{yy s} − E{s∗y H }w H H w y y w + E{y }w . (21)

(15)

The probability of symbol error (PE ) for complex modulation system is calculated as w) = PE (w =

P rob{s 6= sˆ}, (25) w) w )PEI (w w ) − PER (w w ) + PEI (w PER (w

where w ) = P rob{sR 6= sˆR }, PER (w w ) = P rob{sI 6= sˆI }. PEI (w


(26) (27)


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For QPSK system, the probability of error for equally likely real signal sR = {±1}, can be calculated as 1 Z 0 w) = PER (w p(zR |sR = +1)dzR −∞ 2 ! Z 0 zR − ℜ w H h 1 √ = exp − dzR w H Λw w 2w w H Λw w −∞ 2πw ! ℜ wHh , (28) =Q √ w H Λw where Q(·) is the standard Gaussian Q-function: 2 Z ∞ 1 t Q(t) = √ dt. (29) exp − 2 2π t Similarly for equally likely imaginary data, the probability of error can be calculated as Z 0 w) = p(zI |sI = +1)dzI PEI (w −∞ 2 ! Z 0 zI − ℑ w H h 1 √ = dzI exp − w H Λw w 2w w H Λw w −∞ 2πw ! ℑ w Hh . (30) =Q √ w H Λw Substituting (28) and (30) in (25), we get ! ! ℜ w Hh ℑ wHh w) = Q √ PE (w +Q √ w H Λw w H Λw ! ! ℑ w Hh ℜ w Hh Q √ . (31) − Q √ w H Λw w H Λw From (31), it can be observed that the SER detector does not have a closed form like the MMSE detector in (22). Therefore, the weights of the detectors needs to be determined iteratively. As mentioned before, the SER function is nonlinear and there may exist more than one minimum [10] [19]. Therefore, an efficient detector is required that is capable of reaching the global minima with the least number of iterations. The complexity of the detector is required to be very low. In the next section two different methods for implementing the SER detector are proposed. IV. D ESIGNING SER D ETECTOR In this section, two different approaches for designing the SER detector are presented. The first approach is based on the SD based algorithm, where the first derivative of the cost 1 For higher modulation the probability of error is calculated based on decision boundaries.

w) ∇PE (w

= +

function as mentioned in (31) is required. The optimal weights are then calculated with the help of SD approach. While, the second approach is based on the evolutionary algorithms, which do not require the derivative of the cost function. Here, the weights of the filter are found directly using (31). A. Steepest Descent (SD) Based Algorithm SD based algorithm depends upon the initial choice of the weight vectors and if the function has more than one minimas the algorithm might get stuck in a local minima [19]. In order to reach global minima, constraint on the algorithm is placed where the weights must have unit norm, w H w = 1 [19]. The SD based algorithm involves five steps. Step 1. Initialize the weights of the filter randomly such that w H w = 1. Step 2. Determine a suitable step-size µ. A larger µ will lead to a faster convergence but with higher BER value. While, a smaller µ will lead to a slower convergence but lower BER value. Step 3. Once the weights are chosen, determine the gradient of w) the probability of error based on (31). The gradient of PER (w can be represented as H h ) 1 ℜ w H h w H Λ − 2 w H Λw (h w) = √ ∇PER (w 3 H 2π w Λw ) 2 (w 2 ! H ℜ w h , (32) × exp − w H Λw 2w w ) can be represented as and the gradient of PEI (w H h ) 1 ℑ w H h w H Λ + 2j w H Λw (h w) = √ ∇PEI (w 3 H w Λw ) 2 2π (w 2 ! H ℑ w h × exp − , (33) w H Λw 2w The details of determining the gradient can be found in the w ) can be represented appendix. Similarly, the gradient of PE (w as mentioned in (34). Step 4. Now the weight vector of the SD based algorithm is updated as w ), w (iter + 1) = w (iter) − µ∇PE (w

(35)

where iter represents the number of iteration. The weights are p w (iter + 1) to satisfy the constraint divided by w H (iter + 1)w w (iter + 1) = 1. w H (iter + 1)w Step 5. After the completion of total number of iterations Niter, the final weights wp (Niter + 1) are obtained. These w (Niter + 1) to w H (Niter + 1)w weights are divided by H w (Niter + 1) = 1 and to satisfy the constraint w (Niter + 1)w

H !! 2 ! h ) ℑ wHh ℜ wHh 1 ℜ w H h w H Λ − 2 w H Λw (h √ 1−Q √ exp − 3 w H Λw 2w 2π w H Λw ) 2 (w w H Λw ! !! 2 hH ) ℑ wHh ℜ wHh 1 ℑ w H h w H Λ + 2j w H Λw (h √ exp − 1−Q √ 3 w H Λw 2w w H Λw ) 2 2π (w w H Λw


(34)


5

obtain the final weights. The above steps of SD based algorithm are summarized in Table I. Table I S TEEPEST D ESCENT A LGORITHM

1. Initialize weights w with random values such that w H w = 1. 2. Find an appropriate step size µ. for iter = 1 : Niter. w ) using (34). 3. Evaluate ∇PE (w 4. Update the weights w (iter) using (35). end 5. The weights w (Niter + 1) is obtained. The final weights are w (Niter+1) . obtained by √ H w

Table II PARTICLE S WARM O PTIMISATION A LGORITHM

w (Niter+1) (Niter+1)w

B. Evolutionary Based Algorithms 1) Particle Swarm Optimisation (PSO) Based Algorithm: Particle swarm optimisation (PSO) is an heuristic algorithm and it guaranties the global solution [29]. The details of the PSO can be found in [25, 29] and the references therein. PSO algorithm is becoming popular because of its simple implementation, quick convergence to the desired solution and robustness against local minima [25, 30]. PSO is a stochastic optimization technique inspired by social behaviour of fish schooling or bird flocking [29]. The population of individuals, called particles, is randomly initialized within the search space. The coordinates of a particle, which represent the solution to the problem are called position of the particle. In PSO at each iteration, trajectory of each particle is adjusted towards the best location and toward the best particle of the swarm. For this problem L coordinates of the particle needs to be optimized, therefore the particle used for this problem is an L dimensional vector. In PSO based algorithm six steps are involved. Step 1. Initialize the particles w 1 (0), w 2 (0), · · · , w p (0) with Gaussian random numbers. Each particle w i (0), will be of dimension L. Step 2. Initialize, the velocity of i-th particle, v i , with uniform random variable, each velocity will also be a L-dimensional vector. Boundaries for particles and their velocities are defined and kept within the range throughout the algorithm. Step 3. For each particle’s position the value of the costfunction (fitting) is evaluated and the particle, which best fits the cost-function is found. This particle is denoted by g best and is the global best particle. Step 4. In iteration, iter the velocity v i and position w i of ith particle is updated as v i (iter + 1) = v i (iter) + c1 rand(L) ⊙ w ibest (iter) − w icurrent (iter) + c2 rand(L) ⊙ (gg best

− w icurrent (iter)), w i (iter + 1) = w i (iter) + v i (iter + 1),

considered equal to the w icurrent (0) for i = 1, 2, . . . , P . This step is repeated for each particle. Step 5. Once the value of the ith particle is updated its fitness is evaluated. If the updated fitness of the particle is less then the previous best-fitness of the particle then w ibest (iter) = w icurrent (iter), similarly the best-fitness of the ith particle is considered equal to its current-fitness. Step 6. The best-particle, g best , whose fitness is the best fit of the cost-function is found. The steps in the PSO are summarised in the Table II.

(36) (37)

where rand is a uniformly distributed random number, w ibest is the best and w icurrent is the current position of the i-th particle. The letters c1 and c2 are constants and their values are kept close to 2 as explained in [29]. In the first iteration, w ibest is

1. Initialize P particles with random values w 1 (0), w 2 (0), . . . , w p (0). 2. Initialize the velocity of each particle v 1 (0), v 2 (0), . . . , v p (0). 3. Evaluate the fitness of each particle using (31). Find the global best particle, g best among all and its fitness. for iter = 1 : Niter. for i = 1 : P 4. Evaluate the velocity of the particle i using (36). Update the particle i using (37). Evaluate the fitness of the particle i, using (31). 5. if (particle-current-fitness < particle-best-fitness) particle-best-fitness = particle-current-fitness w ibest = w icurrent end 6. Find the global best-particle, g best end

2) Differential Evolution (DE) Algorithm: Like PSO, differential evolution (DE) is also a heuristic algorithm [26, 28]. This algorithm is based on the mechanics of biological evolution and provide efficient techniques for optimization and machine learning applications [26–28]. DEs are best used when the cost-function is discontinuous, nonlinear, stochastic or have undefined derivatives. In DE, generally three operations are performed [26–28]. 1) Mutation - change, to avoid similarity, 2) Crossover - recombination, 3) Natural Selection -variations improve survival. For this problem, a target vector of length L is required to be optimized. The DE algorithm involves following steps. Step 1. Similar to PSO, in DE first of all P target vector w 1 (0), w 2 (0), · · · , w P (0), are initialized where P is the population size. With each of these target vectors, the probability w i (0)), using (31) is evaluated, where i stands of error PE (w for the i-th target vector. Step 2. Mutation: Pick three random numbers p, q and r between 1 and P , to generate a donor vector d i with the help of mutation. w q (0) − w r (0)), d i = w p (0) + F (w

(38)

where F is a scaling factor and its value can be chosen between 0 and 2. Step 3. Crossover: After generating the donor vector d i for the i-th target vector, the trial vector t i is generated as di,l , rand ≤ CR ti,l = l = 1, 2 · · · , L, (39) wi,l , Otherwise



6

where CR is called a cross over ratio and its value can be chosen between 0 and 1. Step 4. Selection: After crossover, calculate the probability of error using trial vector t i , PE (tti ) using (31). Now compare w i (0)) and update the target vector with the PE (tt i ) with PE (w vector which yield the lower probability of error, PE , as w i (0)) t i , PE (tti ) ≤ PE (w w i (iter + 1) = . (40) w i (0), Otherwise Step 5. Repeat step-3 and step-4 for all the target vectors and find the global best target vector. The steps in the DE algorithm are summarised in the Table III. In the following section, the computational complexity of all Table III D IFFERENTIAL E VOLUTION A LGORITHM

1. Initialize P target vectors with random values w 1 (0), w 2 (0), · · · , w P (0). for iter = 1 : Niter for i = 1 : P 2. Generate 3 random numbers, p, q, and r between 1 and P to generate donor vector using (38). 3. Generate trial vector by comparing elements of d with randomly generated cross ratio (CR) using (39). 4. Evaluate PE with w i and t i using (31) and update w i with the vector which yields minimum PE . end 5. Find the global best chromosome end

the considered detectors is discussed. V. C OMPLEXITY C ALCULATIONS

AND

A NALYSIS

This section demonstrates the computational complexity of each detector in a cooperative communication system. The computational complexity is measured in terms of the number of additions and multiplications required to detect a bit. The complexity of ideal ML detector, ideal MMSE detector, SD, PSO and DE techniques is summarized in Table. IV. From Table IV, it can be observed that the complexity of SD, PSO and DE based BER detector is lower than the ideal ML and MMSE detector. In the table for ML detector, A represents the number of alphabets in the modulation scheme. It can be observed that the complexity of the proposed detectors increase linearly. Further analysis of the computational complexity will be carried out in the upcoming section. Table IV C OMPUTATIONAL COMPLEXITY.

VI. S IMULATION R ESULTS AND D ISCUSSION In this section, to validate the performance of our proposed algorithms SER performance is compared with the MMSE and ML detector. Initially, the convergence curve of the algorithm is plotted to choose an appropriate parameter for the algorithm. After this the SER performance versus SNR per bit is plotted for these algorithms. Finally, the rate of all these algorithms is compared with that of the ML and the MMSE detector. In our simulations, the channel gains were assumed to obey the time varying Rayleigh distribution according to Clarke’s model. The normalized Doppler frequency fD T is fixed to 1e − 05, where fD is the Doppler frequency and T is the inverse of the symbol rate. The communication is carried over L = 10 relays and the AF protocol is adopted by each relay. The MMSE algorithm is implemented with the help of least mean square approach. Furthermore, in order to minimize interference between the relays, orthogonality is assumed which can be achieved with the help of either frequency or time [31]. A. SD Based Algorithm: Fig. 2 shows the convergence behaviour of the SD algorithm for different step-sizes at SNR= 10 dB. The SER performance is averaged over 100, 000 independent realizations of the channel. The curves in the figure show that the step-size µ determines the convergence of the algorithm. With smaller step-size, the algorithm converges slowly as compared to bigger step-size but to a lower SER. It can also be observed that µ = 1.0 yields much faster convergence but higher SER values. On the other hand, µ = 0.15 yields slower convergence and a lower SER performance. Therefore, the step-size is fixed to µ = 0.15 in the sequel. Fig. 3 shows the SER performance of the cooperative communication system, as a function of the SNR per bit. In this simulation, different number of iterations were carried for detection of a bit. It can be observed from the Fig. 3 that the SER performance of the system improves as the number of iterations are increased. This improvement in SER performance is due to increased complexity and slower convergence of SD algorithm. From the Fig. 3, it can be observed that the MMSE detector at a typical SER of 2×10−2 is approximately 9.5 dB away from the ML detector. Furthermore, the SD based algorithm with even 10 iterations is 3 dB better than the MMSE detector at similar SER. Further gain in SER performance can be obtained with more iteration. The SER detector when implemented with the help of SD algorithm is just 4.5 dB away from the ML detector after 1000 iterations at a SER of 4 × 10−4 . B. PSO Based Algorithm:

Algorithm Ideal ML detector Ideal MMSE detector SD-based BER detector PSO-based BER detector DE-based BER detector

Number of operations per iteration Additions Multiplications AL AL L3 /6 + L2 + L L3 /6 + 2L2 + 2L 6L 18L + 7 7P L 7P L + 2P 5P L 4P L + 2P

Fig. 4 shows the learning curves of the PSO based algorithm with different number of agents. The SER performance is averaged over 100, 000 independent realizations of the channel. It can be observed from the Fig. 4 that all the algorithm converge to the same SER performance but require different number of iterations. By increasing the number of agents the algorithm converges faster. However, a tradeoff between the number of



7

0

−2

10

10

µ=1.0 µ=0.15 µ=0.01 µ=0.005 ML

−1

10

Agent = 50 Agent = 30 Agent = 10 Agent = 6 ML

−3

10

−2

SER

SER

10

−3

10

−4

10 −4

10

−5

−5

10

10

0

200

400

600

800

1000

0

100

Number of iterations

200

300

400

500


Figure 2. Learning curve of a cooperative communication system when communicating with respect to different step-size µ. The other parameters for the simulations were SNR= 10 dB and L = 10-relays.

Figure 4. Learning curve of a cooperative communication system when communicating with respect to different agents. The other parameters for the simulations were SNR= 10 dB and L = 10-relays.

0

0

10

10

−1

−1

10

10

−2

−2

10

SER

SER

10

−3

−3

10

−4

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−5

10 −10

10

MMSE SD, 10 iterations SD, 100 iterations SD, 1000 iterations ML −5

−4

10

−5

0

5

10

10 −10

SNR (dB)

MMSE PSO, 10 iterations PSO, 100 iterations PSO, 1000 iterations ML −5

0 SNR (dB)

5

10

Figure 3. SER performance of a cooperative communication system when communicating with the assistance of L = 10 relays. The step-size was fixed to µ = 0.15.

Figure 5. SER performance of a cooperative communication system when communicating with the assistance of L = 10 relays. The number of agents was fixed to 30.

agents and complexity of the algorithm exists. Usually, higher number of agents or particle require more complexity as more particles have to be initialized and more calculations have to be carried out. From the Fig. 4, it can also be observed that the convergence of population size of 30 and 50 is similar. Therefore, in the sequel, the number of agents is fixed to 30. The values of c1 = 1.2 and c2 = 1.2. Fig. 5 shows the effect of number of iteration on the SER performance of the cooperative communication system. It can be observed from the Fig. 5 that the improvement in SER performance is relatively negligible with the increase in number of iterations. The reason for this is faster convergence of PSO based algorithm as observed from Fig. 4. The algorithm has already converged for less than 10 iterations. Finally, it can be observed that the PSO-algorithm with 10 iterations is less than 2 dB away from the ML detector at a typical SER of 3×10−5. Furthermore, it can be observed that the proposed PSO based SER detector outperforms the MMSE detector, significantly.

converge to the same SER performance but with different number of iterations. It can be observed that a bigger population size converges faster as compared with a smaller population size. However, the complexity of the algorithm is directly proportional to the population size. Therefore, in the sequel, the population size is fixed to 50. The value of F = 0.6 and CR = 0.5. Fig. 7 shows the SER performance of the cooperative communication system, as a function of the SNR per bit for different number of iterations. From Fig. 6 it can be observed that the algorithm has already converged for less than 100 iterations, therefore, the improvement in terms of SER performance is negligible after 100 iterations. Therefore, the SER performance is similar when using 100 or 1000 iterations. However, the performance significantly improves from 10 to 100 iterations, as the algorithm has not completely converged. Finally, it can be observed that the DE based SER algorithm with 100 iterations is less than 1 dB away from the ML detector at a SER of 9 × 10−5 . Let us now compare the performance of all these detectors.

C. DE Based Algorithm: Fig. 6 shows the learning curves of the DE based algorithm with different number of population size. The average was taken over 100, 000 independent realizations of the channel. It can be observed from Fig. 6 that all the population size

D. Comparisons: Fig. 8 shows the learning curves of all the SER algorithms for the AF relaying system at 10 dB SNR. The average SER



8

−2

−1

10

10

PS = 150 PS = 100 PS = 50 PS = 24 ML

−3

SD, µ = 0.15 PSO, Agent = 50 DE, PS = 100 ML

−2

10

SER

SER

10

−3

10

−4

10

−4

10

−5

−5

10

10 0

100

200

300

400

500

0

200


400

600

800

1000


Figure 6. Learning curve of a cooperative communication system when communicating with respect to different population size. The other parameters for the simulations were SNR= 10 dB and L = 10-relays.

Figure 8. Learning curve of a cooperative communication system when communicating with respect to different BER detectors. The other parameters for the simulations were SNR= 10 dB and L = 10-relay.

0

0

10

10

−1

−1

10

10

−2

−2

10

SER

SER

10

−3

−3

10

−4

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−5

10 −10

10

MMSE DE, 10 iterations DE, 100 iterations DE, 1000 iterations ML −5

−4

10

−5

0 SNR (dB)

5

10 −10

10

performance is taken over 100, 000 independent realizations of the channel. It can be observed from Fig. 8 that the DE based SER algorithm converge to the lowest SER performance when using 100 iterations. The PSO algorithm has the fastest convergence but the difference between the PSO algorithm and DE algorithm is minimal. Therefore, if less number of iterations is required PSO based SER detector can be deployed. From the Fig. 8 it can be observed that the convergence of SD based SER algorithm is the slowest despite initializing the weight of the algorithm w with the assistance of PSO and deploying a step-size µ = 0.15. Fig. 9 shows the SER performance of all the algorithms for the cooperative communication system. The iterations for all the algorithms were fixed to 100. It can be observed that the PSO based and DE based algorithms are 1 dB away from the ML detector with complete CSI knowledge. However, the performance of the SD based algorithm is the worst among these SER detectors. The SER performance of the proposed detectors is much superior to the MMSE based detector. The maximum value of capacity is achieved when the input symbols are equally likely [2]. Therefore, the channel capacity can be calculated as = 2 (1 + [PE (i) log2 PE (i) + (1 − PE (i)) log2 (1 − PE (i))])

−5

0

5

10

SNR (dB)

Figure 7. SER performance of a cooperative communication system when communicating with the assistance of L = 10 relays. The population size was fixed to 100.

C

MMSE SD PSO DE ML

(41)

Figure 9. SER performance of a cooperative communication system when communicating with the assistance of L = 10. The number of iterations was fixed to 100 for all the BER detectors.

Note from (41) that the channel capacity is determined by the transition probability, which depends on the SER of the detector as calculated in (31). The rate of all the algorithms is plotted in Fig. 10. As L = 10 relays are used to transmit a bit the maximum rate which can be achieved is 0.1 bps/Hz. It can be observed from Fig. 10 that the ML detector is able to achieve this rate at SNR of 4 dB. A similar rate can be achieved with the help of PSO or DE based algorithms. From Fig. 10 it can be observed that the SD based algorithm will be able to achieve the rate of 0.2 bps/Hz after 10 dB. However, a higher SNR will be required by the MMSE detector to achieve this rate. It can also be observed that the rate achieved by proposed SER detectors is much superior to that of the MMSE detector. Fig. 11 shows the performance of the SER detector for higher modulation. As PSO and DE based algorithms are better than SD-based and MMSE algorithm only performance of PSO and DE based algorithm are shown. From the figure it is observed that the SER performance of all these algorithms are equivalent. The number of iterations are fixed to 100 for QPSK, 350 for 16-QAM, and 500 for 64-QAM modulation, respectively. The number of agents and population size were kept the same as mentioned in the previous results. It can be observed from the figure that the performance of these



9

be observed that the performance of both these algorithms is close to the ML detector with channel knowledge.

0.20 0.18

0.14

5000

0.12

4500

0.10

4000

0.08 0.06 MMSE SD PSO DE ML with CSI

0.04 0.02 0 -10

-8

-6

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-2

0

2

4

6

8

10

SNR (dB)

Number of Multiplications

Rate (bps/Hz)

0.16

SD DE PSO MMSE ML

3500 3000 2500 2000 1500 1000 500

Figure 10. Rate of a cooperative communication system when communicating with the assistance of L = 10 relays.

0

5

10

15

20

25

30

Number of Relays 0

ML PSO DE

10

Figure 13. Number of multiplications versus the selected size L.

-1

SER

10

64−QAM

-2

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-3

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-10

16−QAM

QPSK

-4

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-5

0

5

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30

SNR (dB)

Figure 11. SER performance of a cooperative communication system when communicating with the assistance of L = 10 relays.

algorithms is very close to the ML detector. The SER performance of these algorithms is less than 2 dB away from the ML detector which has complete channel knowledge. 0

10

ML PSO DEO

−1

10

L =5

−2

SER

10

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L =20

−4

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10 −10

−5

0

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20

SNR (dB)

Figure 12. SER performance of a cooperative communication system when communicating with the assistance of L = 5 and L = 20 relays, respectively.

From Fig. 12, it can be observed that the SER performance of all the algorithms using PSO and DE are equivalent despite using L = 5 and L = 20 number of relays. The number of iterations were fixed to 100, while the number of agents for PSO algorithm was fixed to 50, while the population size was fixed to 100 for DE algorithm. From the figure it can

In Fig. 13, the number of multiplications is plotted with respect to the number of relays L, as multiplications is more complex as compared to addition. It can be observed that, as L increases, more operations are required to detect a bit. The complexity of the ideal ML is more than all the detectors. The complexity of MMSE-based scheme increases quadratically. In order to compare the complexity of PSO and DE algorithms, the number of agents for PSO and target vectors for DE are fixed to 20. From the figure it can be observed that the complexity of the PSO- and DE-based schemes increases linearly where PSO-based scheme is little higher than the DEbased scheme. Finally, it can be concluded that the SD-based scheme has the lowest amount of complexity. VII. C ONCLUSION In this paper, we have proposed a new detector for AF relaying systems. This detector has the capability of improving the SER performance when communicating over Rayleigh fading channels. Furthermore, three different algorithms for SER detectors are proposed, SD, PSO and DE. The SD based detector outperform the MMSE detector in terms of SER and rate. However, we need to determine the derivative of the probability of error and the convergence speed of the algorithm is slow. The evolutionary based algorithms, the PSO and the DE, outperform the SD based algorithm due to their faster convergence. Furthermore, these detectors do not require to evaluate the derivative of the probability of error. From the simulation, it can be observed that the PSO and DE based algorithms are much closer to the ML detector in terms of SER and rate but have a higher complexity as compared to the SD based SER detector. ACKNOWLEDGMENT This work is supported by a KAUST Global Cooperative Research (GCR) fund. The work of M. -S. Alouini was supported by the Qatar National Research Fund (a member of Qatar Foundation) under NPRP Grant NPRP 5-250-2-087. The statements made herein are solely the responsibility of the authors



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APPENDIX A

R EFERENCES

From (28) and definition of Q(·) as mentioned in (29) the w ) can be written as probability of error PER (w 2 Z ∞ 1 −t w) = √ PER (w dt. (42) exp wHh) ℜ(w 2 2π √

[1] A. Sendonaris, E. Erkip and B. Aazhang, “User cooperative diversity: Parts I and II,” IEEE Transactions on Communications, vol. 51, no. 11, pp. 1927–1948, Nov. 2003. [2] J. G. Proakis and M. Salehi, Digital Communications. McGraw-Hill, 4th ed., 2008. [3] J. N. Laneman, D. N. C. Tse and G. W. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,”IEEE Transactions on Information Theory, vol. 50, no. 12, pp. 3062–3080, Dec. 2004. [4] Y. Cao and B. Vojcic, “MMSE multiuser detection for cooperative diversity CDMA system,” in Proc. IEEE Wireless Communications and Networking Conference (WCNC’04), Atlanta, GA, USA, pp. 42–47, Sep. 2004. [5] Y. Zhao, R. Adve and T. J. Lim, “Improving amplify-and-forward relay networks: Optimal power allocation versus selection,” IEEE Transcations on Wireless Communications, vol. 6, no. 8, pp. 3114–3122, Aug. 2007. [6] O. N. Gharehshiran, A. Attar, and, V. Krishnamurthy, “Collaborative subchannel allocation in cognitive LTE femto-cells: a cooperative gametheoretic approach,” IEEE Transactions on Communications, vol. 61, no. 1, pp. 325-334, Jan. 2013. [7] W. Saad, Z. Han, T. Basar, M. Debbah, and, A. Hjorungnes, “Network formation games among relay stations in next generation wireless networks,” IEEE Transactions on Communications, vol. 59, no. 9, pp. 2528–2542, Sept. 2011. [8] J. W. Huang and V. Krishnamurthy, “Cognitive base stations in LTE/3GPP femtocells: a correlated equilibrium game-theoretic approach,” IEEE Transactions on Communications, vol. 59, no. 12, pp. 3485–3493, Dec. 2011. [9] A. Vinel, “3GPP LTE versus IEEE 802.11p/WAVE: which technology is able to support cooperative vehicular safety applications? ,”IEEE Wireless Communications Letters, vol. 1, no. 2, pp. 125-128, Feb. 2012. [10] S. Verdu, Multiuser Detection. Cambridge University Press, 1998. [11] Y. Ding, J.-K. Zhang, and K. M. Wong, “The amplify-and-forward half-duplex cooperative system: Pairwise error probability and precoder design,” IEEE Transactions on Signal Processing, vol. 55, no. 2, pp. 605– 617, Feb. 2007. [12] K. Yen, and L. Hanzo, “Antenna-diversity-assisted genetic-algorithmbased multiuser detection schemes for synchronous CDMA systems,” IEEE Transactions on Communications, vol. 51, no. 3 pp. 366–370, Mar. 2003. [13] F. Gao, T. Cui, and A. Nallanathan, “On channel estimation and optimal training design for amplify and forward relay networks,” IEEE Transactions on Wireless Communications, vol. 7, no. 5, pp. 1907–1916, May 2008. [14] Q. Z. Ahmed, M.-S. Alouini, and S. A¨ıssa, “Bit error-rate minimizing detector for amplify and forward relaying systems using generalized Gaussian kernel,” IEEE Signal Processing Letters, vol. 20, no. 1, pp. 55-58, Jan. 2013. [15] Q. Z. Ahmed, K.-H. Park, M.-S. Alouini, and S. A¨ıssa, “Linear transceiver design for nonorthogonal amplify-and-forward protocol using a bit error rate criterion,” IEEE Transactions on Wireless Communications, vol. 13, no. 4, pp. 1844–1853, Apr. 2014. [16] A. Hedayat, and A. Nosratinia, “Outage and diversity of linear receivers in flat-fading MIMO channels,” IEEE Transactions on Signal Processing, vol. 55, no. 12, pp. 5868-5873, Dec. 2007. [17] Q. Z. Ahmed, K.-H. Park, M.-S. Alouini, and S. A¨ıssa, “Compression and combining based on channel shortening and rank reduction techniques for cooperative wireless sensor networks,” IEEE Transactions on Vehicular Technology, vol. 63, no. 1, pp. 72-81, Jan. 2014. [18] K. S. Gomadam and S. A. Jafar, “Optimal relay functionality for SNR maximization in memoryless relay networks,” IEEE Journal on selected areas in Communications, vol. 25, no. 2, pp. 390–401, Feb. 2007. [19] S. Chen, S. Tan, L. Xu, and L. Hanzo, “Adaptive minimum error-rate filtering design: A Review,” Elsevier Signal Processing, vol. 88, no. 7, pp. 1671–1679, 2008. [20] A. I. Abuzaid, Q. Z. Ahmed, and M.-S. Alouini, “Joint preprocesserbased detector for cooperative networks with hardware constraint,” IEEE Signal Processing Letter, vol. 22, no. 2, pp. 216–219, Feb. 2015. [21] S. Haykin, Adaptive Filter Theory. Prentice Hall, 4th ed., 2002. [22] A. Talari, and N. Rahnavard,“Distributed unequal error protection rateless codes over erasure channels: a two-source scenario,” IEEE Transactions on Communications, vol. 60, no. 8 pp. 2084–2090, Aug. 2012.

w H Λw

Taking the derivative w , and applying Leibnitz’s rule, we get 2 ! w H h) − ℜ(w w) dPER (w 1 √ , (43) = − √ A exp w dw 2π 2 w H Λw where, A is given as wH h) ℜ(w d √ w H Λw A = dw √ w d√w H Λw wHh) H w − ℜ(w h ) w H Λw ℜ(wdw w w dw = √ 2 w H Λw √ H w H h ) √w HΛ w H Λw h H − ℜ(w 2 w Λw = H H w Λw H H H w h) w Λ 2 w Λw h − ℜ(w = . (44) 3 w H Λw ) 2 2 (w Substituting (44) in (43), gives us (32).

APPENDIX B From (30) and definition of Q(·) as mentioned in (29) the w ) can be written as probability of error PEI (w 2 Z ∞ 1 −t w) = √ PEI (w exp dt. (45) wH h) ℑ(w 2 2π √ w H Λw

Taking the derivative w , and applying Leibnitz’s rule, we get 2 ! wHh) − ℑ(w w) dPEI (w 1 √ , (46) = − √ B exp w dw 2π 2 w H Λw where, B is given as wHh) ℑ(w d √ w H Λw B = dw √ w d√w H Λw wH h) H w − ℑ(w h ) w H Λw ℑ(wdw w w dw = 2 √ w H Λw √ H hH ) − ℑ(w w H h ) √w HΛ w H Λw (−jh 2 w Λw = H H w Λw H H H w h) w Λ 2j w Λw h + ℑ(w = − . (47) 3 w H Λw ) 2 2 (w Substituting (47) in (46), gives us (33).



11

[23] A. Talari, and N. Rahnavard,“On the intermediate symbol recovery rate of rateless codes,” IEEE Transactions on Communications, vol. 60, no. 5 pp. 1237–1242, May. 2012. [24] C. Sacchi, M. Donelli and F. G. B. D. Natale, “Genetic-algorithmassisted maximum-likelihood detection of OFDM symbols in the presence of nonlinear distortions,” IEEE Transactions on Communications, vol. 55, no. 5, pp. 854–859, May 2007. [25] H. Gao and W. Xu, “A new particle swarm algorithm and its globally convergent modifications,” IEEE Transactions on Systems, Man, Cybernetics, Part B, vol. 41, no. 5, pp. 1334–1351, Oct. 2011. [26] E. R. Hruschka, R. J. G. B. Campello, A. A. Freitas and A. C. P. L. F. de Carvalho, “A survey of evolutionary algorithms for clustering,”IEEE Transactions on Systems, Man, Cybernetics, Part C, vol. 39, no. 2, pp. 133–155, Mar. 2009. [27] S. Das, A. Abraham and A. Konar,“Particle swarm optimization and differential evolution algorithms: Technical analysis, applications and hybridization perspectives,” Studies in Computational Intelligence, vol. 116, pp. 1-38, 2008. [28] S. L. Cheng, “Optimal approximation of linear systems by a differential evolution algorithm ,”IEEE Transactions on Systems, Man, Cybernetics, Part A, vol. 31, no. 6, pp. 698–707, Nov. 2001. [29] M. Clerc and J. Kennedy, “The particle swarm-explosion, stability, and convergence in a multidimensional complex space,”IEEE Transactions on Evolutionary Computation, vol. 6, no. 1, pp. 58–73, Feb. 2002. [30] K. K. Soo, Y. M. Siu, W. S. Chan, L. Yang and R. S. Chen, “Particle-swarm-optimization-based multiuser detector for CDMA communications,”IEEE Transactions on Vehicular Technology, vol. 56, no. 5, pp. 3006-3013, Sept. 2007. [31] D. Chen and J. N. Laneman, “Modulation and demodulation for cooperative diversity in wireless systems,” IEEE Transactions on Wireless Communications, vol. 5, no. 7, pp. 1785–1794, Jul. 2006.

Qasim Zeeshan Ahmed received his B.Eng. degree in Electrical Engineering from the National University of Sciences and Technology (NUST), Rawalpindi, Pakistan in 2001, MSc degree from the University of Southern California (USC) LosAngeles, USA in 2005 and his Ph.D. degree from the University of Southampton, UK in 2009. He worked as an assistant professor at the National University of Computer and Emerging Sciences (NUCES-FAST) Islamabad, Pakistan. Since June 2011, he has been a postdoctoral fellow with Computer, Electrical and Mathematical Sciences and Engineering Division at King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia. His research interests include mainly ultrawide bandwidth systems, adaptive signal processing and cooperative-communications.

Sajid Ahmed (M’08-SM’12) received the B.S. degree in Electronics Engineering from Sir Syed University of Engineering and Technology Karachi, Pakistan, in 1998 and the M.Sc. degree in Communi cation Engineering from University of Manchester, Institute of Science and Technology, U.K., in 2002. He completed his Ph.D. degree in Digital Signal Processing at the King’s College London and Cardiff University, U.K., in 2005. He was a researcher at the Queen?s University Belfast, Northern Ireland and the University of Edinburgh, U.K. Presently, he is working as a research scientist with the King Abdullah University of Science and Technology (KAUST), Thuwal, Kingdom of Saudi Arabia. He is a recipient of contribution award from the defense, science, and technology laboratory (DSTL) of Ministry of Defense UK. Dr. Ahmed’s current research interests include the linear and non-linear optimisation techniques, low complexity parameter estimation for communication and radar systems, passive radar, and waveform design for MIMO radar.

Mohamed-Slim Alouini (S’94, M’98, SM’03, F’09) was born in Tunis, Tunisia. He received the Ph.D. degree in Electrical Engineering from the California Institute of Technology (Caltech), Pasadena, CA, USA, in 1998. He served as a faculty member in the University of Minnesota, Minneapolis, MN, USA, then in the Texas A&M University at Qatar, Education City, Doha, Qatar before joining King Abdullah University of Science and Technology (KAUST), Thuwal, Makkah Province, Saudi Arabia as a Professor of Electrical Engineering in 2009. His current research interests include the modeling, design, and performance analysis of wireless communication systems.

Sonia A¨ıssa (S’93-M’00-SM’03) received her Ph.D. degree in Electrical and Computer Engineering from McGill University, Montreal, QC, Canada, in 1998. Since then, she has been with the Institut National de la Recherche Scientifique-Energy, Materials and Telecommunications Center (INRS-EMT), University of Quebec, Montreal, QC, Canada, where she is a Full Professor. From 1996 to 1997, she was a Researcher with the Department of Electronics and Communications of Kyoto University, and with the Wireless Systems Laboratories of NTT, Japan. From 1998 to 2000, she was a Research Associate at INRS-EMT. In 2000-2002, while she was an Assistant Professor, she was a Principal Investigator in the major program of personal and mobile communications of the Canadian Institute for Telecommunications Research, leading research in radio resource management for wireless networks. From 2004 to 2007, she was an Adjunct Professor with Concordia University, Montreal. In 2006, she was Visiting Invited Professor with the Graduate School of Informatics, Kyoto University, Japan. Her research interests lie in the area of wireless and mobile communications, and include radio resource management, cross-layer design and optimization, design and analysis of multiple antenna (MIMO) systems, cognitive and cooperative transmission techniques, performance evaluation, and energy efficiency, with a focus on Cellular and Cognitive Radio networks. Dr. A¨ıssa is the Founding Chair of the IEEE Women in Engineering Affinity Group in Montreal, 2004-2007; acted or is currently acting as TPC Leading Chair or Cochair of the Wireless Communications Symposium at IEEE ICC in 2006, 2009, 2011 and 2012; PHY/MAC Program Cochair of the 2007 IEEE WCNC; TPC Cochair of the 2013 IEEE VTC-spring; and TPC Symposia Cochair of the 2014 IEEE Globecom. Her main editorial activities include: Editor, IEEE T RANSACTIONS ON W IRELESS C OMMUNICATIONS, 20042012; Associate Editor, IEEE C OMMUNICATIONS M AGAZINE, 2004–2009; Technical Editor, IEEE W IRELESS C OMMUNICATIONS M AGAZINE, 20062010; and Associate Editor, Wiley Security and Communication Networks Journal, 2007-2012. She currently serves as Area Editor for the IEEE T RANSACTIONS ON W IRELESS C OMMUNICATIONS, and Technical Editor for the IEEE C OMMUNICATIONS M AGAZINE. Awards to her credit include the NSERC University Faculty Award in 1999; the Quebec Government FQRNT Strategic Faculty Fellowship in 2001-2006; the INRS-EMT Performance Award multiple times since 2004, for outstanding achievements in research, teaching and service; and the Technical Community Service Award from the FQRNT Centre for Advanced Systems and Technologies in Communications in 2007. She is co-recipient of five IEEE Best Paper Awards and of the 2012 IEICE Best Paper Award; and recipient of NSERC Discovery Accelerator Supplement Award. She is a Distinguished Lecturer of the IEEE Communications Society (ComSoc) and an Elected Member of the ComSoc Board of Governors.


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