Optimal Windowing and Decision Feedback Equalization for Space ...

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Optimal Windowing and Decision Feedback Equalization for Space–Frequency Alamouti-Coded OFDM in Doubly Selective Channels Ahmed Attia Abotabl, Amr El-Keyi, Yahya Mohasseb, and Fan Bai

Abstract—Space–frequency block coding with orthogonal frequency-division multiplexing (SFBC-OFDM) suffers from the effect of intercarrier interference (ICI) in doubly selective channels. In this paper, a scheme is proposed in which windowing is applied to the received signal to reduce the effect of ICI to a limited number of neighboring subcarriers. The subcarriers holding the SFBC components of each codeword are separated by a number of subcarriers larger than the ICI range, and hence, they do not interfere with each other. To preserve the structure of the SFBC, the separation between the codeword components is also selected within the coherence bandwidth of the channel. As a result, the diversity gain of the SFBC is preserved. By proper selection of the pilot locations, each OFDM symbol can be divided into subsymbols that can be decoded independently. We show that the proposed windowing technique allows the use of decision feedback equalization to estimate the data transmitted in each subsymbol with low complexity. Simulation results are presented showing the ability of the proposed scheme to significantly improve the performance of SFBC-OFDM and preserve its diversity gain. Index Terms—Alamouti and Doppler shift, orthogonal frequency-division multiplexing (OFDM), SFBC, vehicle-tovehicle.

I. I NTRODUCTION

V

EHICULAR communication systems are characterized by their challenging channel that is doubly selective in both time and frequency [1]. Due to the presence of many scatterers at different locations, the received signal is composed of multiple versions of the transmitted signal with different phases and amplitudes arriving at distinct delays, and hence, frequency Manuscript received April 27, 2013; revised September 20, 2013; accepted October 17, 2013. Date of publication November 20, 2013; date of current version June 12, 2014. This work was supported by a grant from General Motors Corporation, Warren, MI, USA. This paper was presented in part at the 2012 IEEE Vehicular Technology Conference, Quebec City, QC, Canada, September 2012. The review of this paper was coordinated by Prof. S.-H. Leung. A. A. Abotabl is with the University of Texas at Dallas, Richardson, TX 75080 USA (e-mail: [email protected]). A. El-Keyi is with the Wireless Intelligent Networks Center, Nile University, Giza 12677, Egypt (e-mail: [email protected]). Y. Mohasseb was with the Wireless Intelligent Networks Center, Nile University, Giza 12677, Egypt. He is now with the Department of Communications, The Military Technical College, Cairo 11787, Egypt (e-mail: [email protected]). F. Bai is with the Electrical and Control Integration Laboratory, Research and Development and Planning, General Motors Corporation, Warren, MI 480909055 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2013.2291872

selectivity arises. On the other hand, the temporal selectivity arises from the movement of the transmitter, receiver, and/or the scatterers, which causes fast variations in the impulse response of the channel. Several measurement campaigns for vehicular channels have been reported in the literature. An overview of some existing vehicle-to vehicle channel measurement campaigns in a variety of important settings and the channel characteristics such as delay and Doppler spreads can be found in [2]. In [3], the authors utilized a channel characterization platform to study the largescale path-loss models at 5.9 GHz. It is found that the fading statistics change from near Rician to Rayleigh as the vehicle separation increases. Furthermore, Cheng et al. [4] provided analysis of Doppler spread and coherence time and their dependence on the vehicular environment. For example, it was found that, for a highway environment, the coherence bandwidth and the coherence time can be on the order of 400 kHz and 0.3 ms, respectively. Orthogonal frequency-division multiplexing (OFDM) [5], [6] has been selected as the modulation scheme in the 802.11p protocol for wireless access in vehicular environments (WAVE) due to its ability to handle frequency-selective channels [7]. In OFDM, the number of subcarriers N is selected such that the frequency-selective channel is decomposed into a set of parallel noninterfering frequency flat channels. Furthermore, in order for OFDM-based systems to operate properly, the channel impulse response has to be constant over the OFDM symbol duration. In fact, in time-selective channels that are not quasi-static over the OFDM symbol duration, intercarrier interference (ICI) arises, and the orthogonality between the OFDM subcarriers is lost. Due to the doubly selective characteristics of vehicular channels, several modifications are needed for the 802.11p protocol to be able to increase the throughput and communication reliability. For example, it was shown in [7] that the original time-scaled IEEE 802.11a waveforms being proposed for the IEEE 802.11p WAVE standard for operation in the 20-MHz bandwidth would not be suitable due to inadequacy of the guard interval. On the other hand, if the same packet length is preserved, a 5-MHz packet would take longer transmission time than the coherence bandwidth of the channel. To overcome the temporal selectivity of the channel in OFDM systems, ICI cancellation is required. Complete removal of ICI in OFDM systems requires the inversion of an N × N channel matrix. This might be prohibitive, particularly if the number of subcarriers is large. To combat this problem, Lu et al.

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[8] proposed a finite-impulse response minimum mean square error (MMSE) equalizer with a few (typically three) taps per subcarrier. In addition, a low-complexity equalizer for OFDM signals was proposed in [9] by applying a window that maximizes the signal-to-interference (due to ICI)-plus-noise ratio. Reliability is an important requirement for vehicular communication, particularly for safety applications. Employing multiple antennas at the transmitting and/or receiving vehicle allows the use of spatial diversity techniques [10]. Space–time block coding with OFDM has been proposed to provide spatial diversity, e.g., [11]. However, it requires the channel to be constant over more than one OFDM symbol duration [12]. In contrast, space–frequency block coding (SFBC) maps the components of each codeword across antennas and different subcarriers within the same OFDM symbol [13]. Hence, it requires the channel to be constant during one OFDM symbol only. However, when the channel varies during the OFDM symbol duration, the resulting ICI destroys the structure of the SFBC scheme, and hence, the diversity gain of SFBC is lost [14]. Lu et al. [15] proposed separating the subcarriers holding the codeword components within the coherence bandwidth to reduce the effect of ICI. Nevertheless, in vehicular channels with high mobility and small coherence bandwidth, the ICI would still have a significant effect on the diversity gain. Another scheme has been proposed in [16] to mitigate the effect of high Doppler on SFBC-OFDM by repeating the codeword components with different polarity and adding them at the receiver to cancel the ICI. Although this approach achieves higher performance than [15], it sacrifices half the throughput in the repetition process. In this paper, we propose an SFBC-OFDM design technique for doubly selective channels that are often encountered in vehicular communication systems. The proposed scheme is a generalization of the windowing technique developed for the single-input–single-output (SISO) case in [9] to the multiple antenna case where windowing is used to limit the ICI power to a small number of subcarriers. However, the proposed windowing scheme is used not only to achieve a lower complexity detection as in [9] but also to achieve the orthogonality between the space–time codeword components. The window is designed to minimize the ICI power outside a certain adjustable range of neighboring subcarriers while preserving the total energy of the received signal. As a result, a small separation between the codeword components is enough to reduce the interference from these components on each other, where the separation needs to be only larger than the range of ICI. The separation is also selected smaller than the coherence bandwidth of the channel to guarantee that the SFBC codeword components are subjected to the same channel. As a result, the proposed scheme provides higher immunity against fading channels with severe temporal and frequency selectivity. Due to the design of the window, the data symbol can be divided into a number of subsymbols, where each subsymbol is equalized/decoded independently. As a result, a low-complexity equalizer can be used for each subsymbol. We design an MMSE-based decision feedback equalizer (DFE) to decode the subsymbols that takes into account the coloring effect of the window on the white noise. Simulation results are presented showing that the pro-

posed scheme can provide high diversity gain even in channels with very high Doppler shift. Simulation results show that the proposed scheme achieves a significant improvement in the biterror-rate (BER) performance without severely sacrificing the throughput as in [16]. A version of this paper was presented at the 2012 IEEE Vehicular Technology Conference [17]. In the conference paper, we presented the idea of mitigating ICI and preserving orthogonality between the codeword components, supporting our contribution with positive simulations results. Here, we present the contribution in more detail in addition to providing a mathematical analysis for the structure of the matrices that are used in the DFE. The analysis provides guidelines on the design of the optimal window and the effect of the window width and proves the suitability of implementing DFE to decode the transmitted signal after windowing. In addition, the simulation results are extended to show the effect of different window configurations and the optimum value for the width of the window. The contributions of this paper are given here. 1) A windowing technique is proposed for Alamouti SFBCOFDM that provides more immunity against ICI similar to [9]. In addition, the proposed technique maintains orthogonality between the components of the codeword. 2) A low-complexity MMSE-based DFE is proposed that divides the OFDM symbol into a number of subsymbols, where each subsymbol is processed independently. 3) We show the ability of the proposed windowing technique and equalizer to maintain the same diversity order of Alamouti SFBC even in the presence of severe temporal selectivity of the channel. The remainder of this paper is organized as follows. In Section II, the SFBC-OFDM system model is described. Section III contains the proposed design approach for the window operator. In Section IV, we present a low-complexity DFE that can be used to decode the transmitted SFBC symbols. Simulation results are presented in Section V, and finally, this paper is concluded in Section VI. II. S YSTEM M ODEL We consider the SFBC-OFDM system shown in Fig. 1 with two transmit antennas and a single receive antenna. Let the N × 1 vector d = [d0 , d1 , . . . , dN −1 ]T denote the baseband modulated data symbols, where N is the number of subcarriers per OFDM symbol, and (·)T and (·)H denote the transpose and Hermitian transpose operators, respectively. The baseband modulated symbols d are Alamouti-coded across the two antennas using the OFDM subcarriers instead of time slots. The two components of the Alamouti codeword are separated by L subcarriers, as shown in Fig. 2. For example, the components of the first codeword [d0 d1 ]T and [−d∗1 d∗0 ]T are transmitted on subcarriers 0 and L, respectively, where (·)∗ denotes the complex conjugate operator. The separation should be selected to be smaller than the coherence bandwidth of the channel to guarantee that the channel is almost constant across the codeword components [15].

ABOTABL et al.: OPTIMAL WINDOWING AND DFE IN DOUBLY SELECTIVE CHANNELS

Fig. 1.

OFDM-SFBC transmitter and receiver (2 × 1).

Fig. 2.

Structure of Alamouti SFBC with separation across OFDM subcarriers.

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The output of the SFBC encoder is the two N × 1 vectors X 1 and X 2 that represent the frequency-domain OFDM symbols transmitted from each antenna. They are given by

length of the channel impulse response to prevent intersymbol interference. The received symbol after removing the cyclic prefix is given by

¯ 1 d∗ X 1 = P 1d − P

(1)

y = H (1) x1 + H (2) x2 + u

¯ 2 d∗ X 2 = P 2d + P

(2)

where H (i) is the ith time-domain channel matrix between the ith transmit antenna and the receiver, and u is the time-domain noise vector. The noise is white circular normal with zero mean and covariance σ 2 I N . In the conventional OFDM receiver, the received timedomain vector y is converted to the frequency-domain vector Y using an N -point FFT operation to obtain

¯ 1 , P 2 , and P ¯ 2 are given by where the N × N matrices P 1 , P   V P1 =I N ⊗ (3) 2L 0aL×2L   0L×2L ¯ P1 =I N ⊗ (4) 2L V¯   V¯ (5) P2 =I N ⊗ 2L 0L×2L   0L×2L ¯ P2 =I N ⊗ . (6) 2L V I K denotes the K × K identity matrix, ⊗ denotes the Kronecker product, 0m×n denotes an all-zero matrix of size m × n, and V and V¯ are the L × 2L matrices containing the odd and even rows of the matrix I 2L , respectively, i.e., V (i, j) = δ(2i − 1 − j)

(7)

V¯ (i, j) = δ(2i − j)

(8)

where X(m, n) is the element in the mth row and nth column of the matrix X, and δ(x) is the Kronecker delta function. Note that the two OFDM symbols X 1 and X 2 contain N /2 Alamouti codewords, as shown in Fig. 2. The two symbols are then converted to the time-domain symbols x1 and x2 using an N -point inverse fast Fourier transform operation. The cyclic prefix is then added with length equal to or larger than the

(2) Y = G(1) c X 1 + Gc X 2 + U c

(9)

(10)

where G(i) c is the ith frequency-domain channel matrix, i.e., = F H (i) F H ; the N × N matrix F is the unitary discrete G(i) c Fourier transform matrix; and U c is the frequency-domain noise vector, i.e., U c = F u. In quasi-static channels where the channel is constant over the OFDM symbol duration, the matrix H (i) is a circulant matrix, and hence, the frequency-domain channel matrix G(i) c is a diagonal matrix. In this case, because there is no ICI, the Alamouti codeword components are orthogonal, yielding the maximum diversity gain. In addition, the decoding is simple is diagonal. However, when temporal selectivity since G(i) c arises, the channel matrix H (i) is not circulant, and hence, F H (i) F H is not diagonal. Since the ICI is strongest for immediately neighboring subcarriers, the codeword components should be separated to reduce mutual ICI as in [15]. However, in doubly selective channels with high temporal and frequency selectivity, the required separation to eliminate the ICI may exceed the value of the coherence bandwidth. Increasing the separation between the codeword components beyond the coherence bandwidth destroys the structure of the space–frequency code as each codeword component experiences a different channel

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the shaded entries can be considered the “desired signal” components. Similar to the SISO case in [9], the window is designed to maximize the signal-to-interference-plus-noise ratio (SINR), which is defined as the ratio between the power contained in the desired signal components Es and that contained in the interference components plus the noise energy EIN . The noise component is taken into consideration to prevent its enhancement due to applying the window. The signal energy can be expressed in terms of the window as

Fig. 3. Banded structure of the equivalent channel matrices G after applying the window.

(1)

and G

(2)

Es =

F

i=1

frequency response. As a result, the orthogonality between the codeword components is lost, which reduces the diversity gain of the code.

Es =

In this paper, we focus on mitigating/exploiting the double selectivity of the channel as in [9] and do not consider the channel estimation problem. We assume that the receiver has an accurate estimate of the channel state, and hence, the matrices H (1) and H (2) are known. We propose the use of windowing to reduce the range of interference of each subcarrier as in [9]. As a result, a smaller separation between the codeword components is sufficient to limit the ICI, and hence, the proposed scheme can accommodate communication channels with high temporal and frequency selectivity. Windowing is performed by multiplying the time-domain received signal vector y by the N × N diagonal matrix W , as shown in Fig. 1. As a result, the received frequency-domain vector becomes (11)

where the equivalent frequency-domain channel matrix G(i) is given by G(i) = F W H (i) F H , and the N × 1 vector U represents the equivalent frequency-domain noise vector, i.e., U = F W u. The applied window is designed to modify the conventional frequency-domain channel matrices to have a structure, as shown in Fig. 3. In this figure, the entries in the unshaded region have insignificant values, and the parameter t controls the size of the shaded region. We require that L > 2(t − 1); however, typically, the parameter t should be chosen to be much smaller than L in order not to sacrifice too much throughput, as we will show in Section IV. Nevertheless, the smaller the value of t, the harder it becomes to force the entries in the unshaded region to zero using the applied window. Low interference between the codeword components is then achieved by separating them in the OFDM symbol by a number of subcarriers larger than the range of the shaded region t and smaller than the coherence bandwidth. Therefore, the elements of G(i) that lie within the unshaded region in Fig. 3 are considered nondesired “interference” components, whereas

(12)

where  · F denotes the Frobenius norm of a matrix, and the operator M{·} is a mask operator that selects the desired signal components that are present in the shaded region of the matrix in Fig. 3. The mask operator can be expressed in matrix notation as in [9] as

III. M AXIMUM S IGNAL - TO -I NTERFERENCE P LUS -N OISE -R ATIO W INDOW D ESIGN

Y = G(1) X 1 + G(2) X 2 + U

2   2    M F W F H F H (i) F H 

2  2    P F W F H D (i)  i=1

F

(13)

where D (i) is a rearrangement of G(i) c defined by D (i) (m, n) = G(i) c ([m + n − 2]N , n) .

(14)

[·]N denotes the modulo-N operator, and the N × N matrix P is given by ⎤ ⎡ 0 It 0 (15) 0 ⎦. P =⎣ 0 0 0 0 I t−1 Note that we have defined the matrices D (i) to rearrange the elements on the diagonals of the matrices G(i) c on the rows of D (i) . Since multiplying a matrix by the matrix P from the left keeps only the elements on the first t and the last t − 1 rows, we can write the desired signal power as given by (13). Now, using the identity X2F = tr{XX H }, where tr{X} is the trace of the matrix X and noting that P P H = P , we can write Es as 2

H   H (i) H (i) FWF D Es = tr P F W F D .

(16)

i=1

Note that multiplying a matrix from the left by the matrix P defined in (15) sets all the elements of the resulting matrix to zero, except the first t and last t − 1 rows. The value of the parameter t should be chosen according to the temporal and frequency selectivity of the channel. Note that as t increases, it becomes easier to limit the interference outside the shaded region of the matrix shown in Fig. 3. However, this puts more constraints on the system in terms of the amount of pilots required and the coherence bandwidth of the channel. Since the trace of a matrix is the sum of its diagonal elements, after some mathematical manipulations, we can write (16) as Es = w H R s w

(17)

ABOTABL et al.: OPTIMAL WINDOWING AND DFE IN DOUBLY SELECTIVE CHANNELS

where the N × 1 vector w contains the diagonal elements of W , and the N × N matrix Rs is given by RTs =

2  

 H

  diag{f j } F H D (i) F H D (i) diag f ∗j

i=1 j∈St

(18) where f k is the kth column of F , and diag{x} is a diagonal matrix with the vector x on its main diagonal. The inner summation is performed over values of j that belong to the set St = {j}t1 ∪ {j}N N −t+2 , i.e., the inner summation contains 2t − 1 terms. Next, we express the interference-plus-noise energy EIN in terms of the diagonal elements of the window. From the definition of the interference-plus-noise energy, it can be written as EIN = ET − Es

(19)

where ET represents the total energy of the desired signal terms and the interference terms in addition to the noise energy. The total energy is given by the sum of the squares of the Frobenius norms of the two matrices G(1) and G(2) plus the noise energy, i.e., ET =

2      H (20) tr W H (i) H (i) W H + E F W u2

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Note that both the numerator and the denominator of the cost function are nonnegative. Since the function f (x) = x/(1 − x) is monotonically increasing for 0 ≤ x < 1, the solution to the aforementioned problem is the unit-norm vector that maximizes the numerator of the objective function, i.e., the eigenvector associated with the maximum eigenvalue of the matrix −(1/2) −(1/2) RS RT . Hence, the vector containing the diagonal RT elements of the window is given by   −1 −1 −1 (26) w = RT 2 ν RT 2 RS RT 2 where ν{X} denotes the eigenvector associated with the maximum eigenvalue of the matrix X. −(1/2) Since the matrix RT is diagonal, evaluating RT −(1/2) RS RT requires only O(N 2 ) operations. In addition, the computational complexity of finding the maximum eigenvector of an N × N matrix is of O(N 2 ). Therefore, the computational complexity of finding the window is of O(N 2 ). Note that this computational complexity is much less than the complexity of the optimum MMSE equalizer that requires the inversion of a full N × N matrix. These computational savings are important for applications with strict latency requirements such as safety applications in vehicular networks. IV. D ECISION F EEDBACK E QUALIZER

i=1

where E{·} denotes the statistical expectation operator. Due to the diagonal structure of the matrix W , ET can be expressed in terms of the vector w that contains the diagonal elements of W as ET = wH RT w

(21)

where the N × N diagonal matrix RT contains the main  H diagonal of the matrix 2i=1 H (i) H (i) + σ 2 I N on its main diagonal. Using (17) and (21), the SINR can be written as SINR =

w H RS w . w H RT w − w H RS w

(22)

˜ = To maximize the SINR, we define the N × 1 vector w (1/2) RT w. Since RT is a diagonal full-rank matrix, we can −(1/2) ˜ in (22), which yields substitute with w = RT w −1

SINR =

−1

˜ ˜ H RT 2 RS RT 2 w w −1

−1

˜ ˜ 2−w ˜ H RT 2 RS RT 2 w w

max ˜ w

−1

˜ H RT 2 RS RT 2 w ˜ 1−w

˜ 2 = 1. s.t. w

(27)

¯ T ) selects the first (second) compowhere the matrix P T1 (P 1 nents of the codewords and rearranges them. By substituting from (1), (2), and (10) in (27), we can express Y˜ as a function of d and d∗ as follows: ˜ 2 d∗ + U ˜ ˜ 1d + G Y˜ = G

(23)

(28)



 ¯ T G(1)∗ P ˜ 1 =P T G(1) P 1 +G(2) P 2 − P ¯ 1 −G(2)∗ P ¯2 G 1 1



˜ 2 =P T G(2) P ¯T ¯ 2 −G(1) P ¯ 1 +P G 1 1

(29)  ∗ ∗ G(1) P 1 +G(2) P 2 (30)

−1

˜ H RT 2 RS RT 2 w ˜ w −1

¯TY ∗ Y˜ = P T1 Y + P 1

where .

Since the preceding expression for the SINR is invariant to ˜ by a scalar, we can set w ˜ 2=1 multiplying the vector w without any loss of generality. Hence, the window design problem can be formulated as −1

Conventional decoding of the Alamouti code is performed by applying the complex conjugate operator on the received signal corresponding to the second component of the codeword followed by maximal ratio combining. Hence, we first rearrange the frequency-domain received vector Y to make the two components of the same codeword adjacent (reversing the separation that was done at the transmitter) and apply the conjugate operation on the even entries of the rearranged vector. The resulting N × 1 vector Y˜ is given by

(24)

˜ is the noise vector, which is given by and the N × 1 vector U

(25)

˜ = PTFWu + P ¯ T F ∗ W ∗ u∗ U 1 1

(31)

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Fig. 4. Structure of the transmitted symbol d.

whose covariance matrix C is given by

 ¯ T F W W HF HP ¯1 C = σ 2 P T1 F W W H F H P 1 + P 1 (32) where we have used the fact that the expectation of uuT is zero due to the circularity of the noise vector u. Proposition 1: If the equivalent frequency-domain channel matrices G(1) and G(2) have the banded structure shown in Fig. 3, where the elements in the unshaded region are equal ˜ 2 in (30) can be written as to zero, then the matrix G   N ˜2 = G ˜ (1) , G ˜ (2) , . . . , G ˜ ( 2L ) G (33) 2 2 2 ˜ (k) where the matrix G 2

˜ (k) (i, j) 2L matrix with G 2

is an N × =0 for all 1 ≤ i ≤ N and for 2(t − 1) < j < 2L − 2(t − 1) + 1, where 0 < 2(t − 1) < L. Proof: See Appendix A. Proposition 1 states that, as a result of applying the window, ˜ 2 has few significant elements. In particular, the matrix G ˜ G2 can be considered a horizontal concatenation of N/(2L) submatrices each with dimensions N × 2L. The significant elements of each submatrix are located only in the first and last 2(t − 1) columns. To suppress the self-interference caused by the vector d∗ in (28), which leaks through the significant entries of the matrix ˜ 2 , we propose the use of the structure shown in Fig. 4 for G the OFDM data symbol d. According to this structure, the data symbol is divided into N/(2L) subsymbols. Each subsymbol contains 2L elements, where the first and last 2(t − 1) elements are pilots. Therefore, the total number of pilots within each OFDM symbol is given by 4(t − 1)N/(2L). Note that these pilots can be used, for example, for channel estimation and do not represent a waste of throughput as in [16], which requires retransmitting the data symbols twice. As a result of this structure, the number of subcarriers used for information transmission in each OFDM symbol is given by   2(t − 2) . (34) Ndata = N 1 − L From Proposition 1, the interference caused by the significant ˜ 2 arises from the first and last 2(t − 1) entries of the matrix G elements of each subsymbol only. Hence, using the channel state information and the pilots, the self-interference caused by the d∗ in (28) can be subtracted from the received symbol Y˜ . For the sake of simplicity, in the remainder of this paper, we will assume that the pilot symbols are guard tones, i.e., with zero value, and hence, we can write (28) as

Proposition 2: If the equivalent frequency-domain channel matrices G(1) and G(2) have the banded structure shown in Fig. 3 where the elements in the unshaded region are equal to ˜ 2 in (29) and (30) has a ˜ 1 and G zero, then each of the matrices G block diagonal structure, where each block is of size 2L × 2L. Proof: See Appendix B. As a result of Proposition 2, the block diagonal structure of ˜ 2 allows the detection of each subsymbol from the ˜ 1 and G G corresponding entries of the vector Y˜ only. Using the results of Propositions 1 and 2 and the symbol structure in Fig. 4, where the OFDM symbol d is composed of N/(2L) subsymbols, we can write the received signal due to the kth subsymbol of (35) as (k) ˜ (k) d(k) + U ˜ (k) =G Y˜ 1

(35)

N 2L

(36)

˜ (k) is the kth diagonal where d(k) is the kth subsymbol, G 1 ˜ 1 whose size is 2L × 2L, i.e., subblock of the matrix G ˜ 1 (m + 2L(k − 1), n + 2L(k − 1)) ˜ (k) (m, n) = G G 1

(37)

(k) ˜ (k) are the vectors conand the 2L × 1 vectors Y˜ and U taining 2L entries starting from the (1 + 2L(k − 1))th entry ˜ , respectively. The covariance matrix C (k) of the of Y˜ and U (k) ˜ is given by vector U

C (k) (m, n) = C (m + 2L(k − 1), n + 2L(k − 1)) .

(38)

Proposition 3: If the equivalent frequency-domain channel matrices G(1) and G(2) have the banded structure shown in Fig. 3, where the elements in the unshaded region are equal ˜ (k) are to zero, then the elements of each diagonal subblock G 1 equal to zero, except those on the upper and lower first 2t − 1 diagonals. Furthermore, the even elements of the 2t − 1th upper and lower diagonals are equal to zero, i.e., ˜ (k) (m, m + 2t − 1) = 0 for G 1 (k) ˜ G1 (m + 2t − 1, m) = 0 for

m = 2, 4, . . . 2L − 2t (39) m = 2, 4, . . . 2L − 2t. (40)

Proof: See Appendix C. ˜ (k) according to Fig. 5 shows the structure of the matrix G 1 Proposition 3, where the matrix contains significant elements on the first upper and lower 2t − 1 diagonals. Next, we will consider the decoding/equalization of the data symbols within the kth subsymbol. Since the first and last 2(t − 1) elements of each subsymbol are guard elements, we can write1 (k) ¯ (k) + U ¯ (k) d ˜ (k) =G Y˜ 1 1 Equation

˜. ˜ 1d + U Y˜ = G

∀k = 1, . . . ,

(41)

(41) can be easily modified in the case of using pilots instead of

guard elements by subtracting their effect from Y˜

(k)

.

ABOTABL et al.: OPTIMAL WINDOWING AND DFE IN DOUBLY SELECTIVE CHANNELS

˜ (k) and the matrix G ¯ (k) obtained Structure of the 2L × 2L matrix G 1 1 (k) ˜ . by removing the first and last 2(t − 1) columns of G

Fig. 5.

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Fig. 6. SINR versus Doppler for different windows.

1

(k)

¯ where d is a 2L − 4(t − 1) × 1 vector containing the unknown data elements in the subsymbol d(k) , and the matrix ¯ (k) is a 2L × (2L − 4(t − 1)) matrix that is obtained from G ˜ (k) by deleting the first and last 2(t − 1) columns, the matrix G 1 as shown in Fig. 5. From Proposition 3, we can see that the ¯ (k) has the structure shown in Fig. 5. This structure matrix G lends itself readily to the use of DFE to remove the interference caused by the Alamouti codewords on each other. Using the channel state information, the decoding of the kth subsymbol starts by MMSE estimation of the last codeword in the subsymbol as

−1 (k) H ˆ (k) = E (1) G ¯ (k) G ¯ (k) + C (k) ¯ (k) G (42) Y˜ (1) d (1) (1) (1) (1) (1) ¯ (k) is the 2(t+1)×2(t+1) matrix composed of the last where G (1) ¯ (k) , Y˜ (k) is a 2(t+1)×1 vector 2(t+1) rows and columns in G (1) (k) ˆ (k) is the containing the last 2(t+1) entries in the vector Y˜ , d (1)

(k)

¯ , E (1) = estimated value of the data in the last codeword in d (k) [0(2,2t) , I 2 ], and the 2(t + 1) × 2(t + 1) matrix C (1) is the co˜ (k) that contribute variance matrix of the last 2(t + 1) entries in U (k) to Y˜ and is given by the last 2(t + 1) rows and columns of (1)

¯ (k) , the decision C (k) . After estimating the last codeword in d (k) using on this codeword is used to cancel its contribution to Y˜ (k) ¯ the last two columns of G . The rest of the codewords could be estimated using the same procedure. V. S IMULATION R ESULTS We consider an OFDM system with N = 1024 subcarriers and 10-MHz bandwidth employing Alamouti SFBC. The data bits are modulated using QPSK modulation. We consider an urban channel with a TU-06 delay profile defined by the COST 207 project, where each discrete channel tap is

generated as an independent complex Gaussian random variable with time correlation based on Jakes’ model [18], [19]. First, we investigate the effect of the designed window on the SINR. Fig. 6 shows the SINR with and without windowing versus the normalized Doppler (the ratio between the Doppler shift in hertz and the subcarrier spacing) for different choices of the parameter t. We can see from this figure that, for t = 1, i.e., the elements on the main diagonal only of the channel matrices are considered as the desired ones, windowing does not yield significant improvement in the SINR. This can be attributed to the small number of dimensions that are used by the window to focus the desired signal energy in. In contrast, when we set t = 2, the elements of the channel matrices that are located on the main and first upper and lower diagonals are considered as desired signal components, and hence, the SINR without windowing increases compared with the case of t = 1. Furthermore, using windowing, significant gain in the SINR can be achieved, where the SINR after windowing is almost equal to that observed in the case when there is no Doppler and the channel matrices are diagonal. However, when t = 3, the gain in the SINR after windowing is negligible compared with that obtained after windowing when t = 2. Hence, for this channel, t = 2 is the best value for t to be used to achieve a good tradeoff between throughput and performance. In the rest of the simulation section, we set the separation between the codeword components as L = 16, and simulations are done for different values of the desired signal region width: t = 1, where there is no loss in throughput; t = 2, where the loss in throughput is 6.25%; and t = 3, where the loss in throughput is 12.5%. Next, we compare the performance of the proposed algorithm with that of the conventional SFBC and the SFBC-OFDM with separation and three-tap MMSE equalizer proposed in [15]. The channel is time varying with normalized Doppler shift equal to 0.25, and perfect channel knowledge is assumed for all algorithms. As a lower bound on the BER, we also consider a conventional SFBC-OFDM system operating in a static channel (without Doppler).

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Fig. 7. BER curve for the proposed SFBC-OFDM.

Fig. 7 shows the BER versus the signal-to-noise ratio (SNR) for different systems. Note that we do not use any error correction coding in order not to mask the diversity gain of the Alamouti code by the gain of the error correction code [20]. We can see in Fig. 7 that conventional SFBC fails completely due to the Doppler. We can also see that separating the codeword components is not sufficient to overcome the ICI for this high value of Doppler shift. In accordance with the results shown in Fig. 6, we can see that the proposed system with t = 1 does not yield significant improvement in the BER of the system as the SINR gain due to windowing is very low. In contrast, the proposed scheme with t = 2 and t = 3 preserves the diversity gain that is evident from the slope of the BER curve at high SNR, which is similar to the slope of the conventional SFBCOFDM in the absence of Doppler. We can also see in Fig. 7 that using t = 3 yields an SNR gain of around 1 dB over t = 2. However, this comes at the expense of a decrease in throughput as mentioned earlier. Fig. 8 shows the performance of different schemes versus the normalized Doppler at SNR equal to 20 dB, where we show three different choices for the parameter t. We can see from this figure that, in contrast with earlier approaches, the proposed scheme can combat high values of the Doppler shift and that the BER does not rise catastrophically as the Doppler increases. In addition, we can also see that, at the same value for the separation L = 16, a higher value for t is better at high Doppler, whereas a lower value of t is better in low values of Doppler. The reason behind this is that, for low values of Doppler, such as 0.1, the significant elements are already on the main diagonal; thus, using t = 1 works well. On the other hand, for higher values of Doppler, such as 0.3, the significant elements are around the main diagonal by around three diagonals, and hence, window of width t = 3 works better.

Fig. 8.

BER curves versus Doppler shift.

We have proposed an optimal windowing technique at the receiver that limits the ICI to a limited number of neighboring subcarriers. As a result, the codeword components can be separated within the coherence bandwidth of the channel, where the separation is larger than the range of ICI. The SFBC-OFDM symbol is divided into several subsymbols, where each subsymbol can be decoded independently. We have also proposed a reduced complexity MMSE-based DFE that significantly reduces the equalization complexity. Simulation results have been presented that illustrate the improved performance of the proposed scheme even in doubly selective channels with very high Doppler. A PPENDIX A P ROOF OF P ROPOSITION 1 For the sake of simplicity, we will consider the case of N = 2L, where we can write the matrices G(1) and G(2) as2   (i) (i) G1,1 G1,2 (i) G = (43) (i) (i) G2,1 G2,2 where i = 1, 2, and each submatrix is of dimension L × L. Due to the banded structure of G(1) and G(2) in Fig. 3, we have (i)

G1,2 (m, n)  (i) = α1,2 (m, n) 0

if

m = 1, . . . , t − 1 n = N2 − t + 1 + m, . . . , N2 else

(44)

n = 1, . . . , t − 1 m = N2 − t + 1 + m, . . . , N2 else

(45)

(i)

G2,1 (m, n)  (i) = α2,1 (m, n) 0

if

VI. C ONCLUSION High mobility degrades the performance of SFBC-OFDM due to ICI that destroys the orthogonality between subcarriers.

2 Proposition 1 can be proved for the more general case of N > 2L using the same techniques applied in the proof of Proposition 2. For space considerations, we will omit the general proof Proposition 1.

ABOTABL et al.: OPTIMAL WINDOWING AND DFE IN DOUBLY SELECTIVE CHANNELS

(i)

(i)

where |α1,2 (m, n)| ≥ 0 and |α2,1 (m, n)| ≥ 0. Substituting ˜ 2 as with (3)–(6) in (30), we can write the matrix G

  ∗ ∗ ˜ 2 = V T G(2) V − G(1) V¯ + V¯ T G(1) V + G(2) V¯ . G 2,1 2,1 1,2 1,2 (46) Using (44) and (45) to include only the nonzero entries of (i) (i) the matrices G1,2 and G2,1 in the preceding equation, and substituting with (7) and (8), we can write the (i, j)th element ˜ 2 as of G ˜ 2 (i, j) G =

t−1 

L 

2) The upper diagonal group, (i) (N/2L) {Gm,[m+1](N/2L) }m=1 , where

−

L 

(1) α1,2 (m, n)δ(2m−1−i)δ(2n

− j)



+

L 

(1)∗

α2,1 (m, n)δ(2m − i)δ(2n − 1 − j)

n=1 m=L−t+1+m

+

t−1 

L 

(2)∗

α2,1 (m, n)δ(2m−i)δ(2n−j). (47)

n=1 m=L−t+1+m

The preceding equation consists of four terms each containing a summation of t(t − 1)/2 terms. We will consider each of these four terms when 2(t − 1) < j < 2L − 2(t − 1) + 1. The (m, n)th term of the first and third terms in (47) will be nonzero when j = 2n − 1, and hence, for 2(t − 1) < j < 2L − 2(t − 1) + 1, we have t − 1/2 < n < L − t + 2. Since the values of n in the summations of the first and third terms are outside this interval, then the first and third terms in (47) are equal to zero. Similarly, for the (m, n)th term in the second and fourth terms to be nonzero, we must have j = 2n, and hence, for 2(t − 1) < j < 2L − 2(t − 1) + 1, we have t − 1/2 < n < L − t + 3/2, which are also outside the range of values of n in the summation. Therefore, the second and fourth ˜ 2 (i, j) = 0 for terms in (47) will also vanish. As a result, G 2(t − 1) < j < 2L − 2(t − 1) + 1, which proves Proposition 1 for the case of N = 2L.

matrices

2L

(i)

αm,[m+1] N (k, l)

=

2L

0

l = 1, . . . , t − 1 k = 2L − t + 1 + l, . . . , 2L . else (48) if

3) The lower diagonal group, (i) (N/2L) {G[m+1](N/2L) ,m }m=1 , where G[m+1] N

i.e.,

the

matrices

,m (k, l)

2L

 =

(i)

α[m+1] N 0

,m (k, l)

2L

m=1 n=L−t+1+m t−1 

the

(i)

(i)

(2)

α1,2 (m, n)δ(2m−1−i)δ(2n − 1 − j)

i.e.,

Gm,[m+1] N (k, l)

m=1 n=L−t+1+m t−1 

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k = 1, . . . , t − 1 l = 2L − t + 1 + k, . . . , 2L . else (49) if

¯ 1 , P 2 , and P ¯ 2 in (3)–(6) are block Since the matrices P 1 , P ˜ 1 as diagonal, we can write the (m, n)th block of G        V V¯ (2) ˜ 1 = V T , 02L×L G(1) +G G m,n m,n m,n 0 0  L×2L   L×2L    ∗ ∗ 0 0L×2L T L×2L − 02L×L , V¯ G(1) . −G(2) m,n m,n V V¯ (50) (2) Note that the submatrices G(1) m,n and Gm,n are equal to zero, except those in the main, upper, and lower diagonals, and hence, we need only to investigate whether the upper and ˜ 1 are equal to zero. Let us lower diagonal subblocks of G ˜ 1 . From (48), we consider the upper diagonal subblocks of G (1) (2) can see that the matrices Gm,[m+1](N/2L) and Gm,[m+1](N/2L) are lower triangular where the nonzero entries of these matrices are located on the lower 2L − t + 2 to 2L diagonals, where t < L, and hence, by substituting in (50), we get

˜1 = 02L×2L . G m,[m+1] N

(51)

2L

(1)

Similarly, from (49), we can see that the matrices G[m+1](N/2L) ,m (2)

A PPENDIX B P ROOF OF P ROPOSITION 2 ˜ 1 . The same We will prove Proposition 2 for the matrix G ˜ 2 . First, we procedure can be applied to prove it for the matrix G ¯ ¯ note that the matrices P 1 , P 1 , P 2 , and P 2 in (3)–(6) are block diagonal, where all the diagonal blocks are identical and given by the second argument of the Kronecker product operator in (3)–(6). Let us divide the matrices {G(i) }2i=1 into blocks each of size 2L × 2L. We denote the (m, n)th block of the matrix G(i) by G(i) m,n . Due to the banded structure of the two matrices, and since we require that L > 2(t − 1), only 3N/2L blocks will be nonzero. These blocks can be divided into three groups. (N/2L) 1) The main diagonal group, i.e., the matrices {G(i) m,m}m=1 , where the nonzero elements of each matrix are located on its main diagonal and the upper and lower t − 1 diagonals.

and G[m+1](N/2L) ,m are upper triangular where the nonzero entries of these matrices are located on the upper 2L − t + 2 to 2L diagonals, where t < L, and hence, by substituting in (50), we get ˜1 G [m+1] N

,m

= 02L×2L .

(52)

2L

˜ 1 is a block diagonal matrix, which Therefore, the matrix G proves Proposition 2 for this matrix. A PPENDIX C P ROOF OF P ROPOSITION 3 We will prove Proposition 3 for the case of N = 2L. In ˜ 1 . Using this case,3 there is only one subblock of the matrix G 3 The proof can be extended to the more general case, where N > 2L, by ˜ 1 , as shown in the proof of Proposition 2. decomposing the matrix G

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the decomposition of the matrices G(1) and G(2) in (43) and ˜ 1 as substituting with (3)–(6) in (29), we can write G 

 ∗ ∗ ˜ 1 = V T G(1) V + G(2) V¯ − V¯ T G(1) V¯ − G(2) V . G 2,2 2,2 1,1 1,1 (53) ˜ 1 can be written as The (i, j)th element of G ˜ 1 (i, j) G =

L L  

(1)

G1,1 (m, n)δ(2m − 1 − i)δ(2n − 1 − j)

values of G(i) v,v (m, n) included in the summations of (55) are equal to zero for k ≥ 2t. Similarly, we can prove then that the ˜ 1 that lie on the kth lower diagonal elements of the matrix G where k ≥ 2t are equal to zero. This proves the first part of Proposition 3. We will consider the proof of the second part of Proposition 3 for the 2t − 1th upper diagonal. Substituting in (54) with j = i + 2t − 1, we get  (2) ˜ 1 (i, i + 2t − 1) = G1,1 (m, n)δ(2m − 1 − i) G 2n−2m=2t−2

(57)

m=1 n=1

+

L 

L 

(2)

G1,1 (m, n)δ(2m − 1 − i)δ(2n − j)

m=1 n=1

−

L  L 

(1)∗

G2,2 (m, n)δ(2m − i)δ(2n − j)

m=1 n=1

+

L L  

(2)∗

G2,2 (m, n)δ(2m − i)δ(2n − 1 − j). (54)

m=1 n=1

R EFERENCES

To prove the first part of Proposition 3, we will examine the ˜ 1 that lie on the kth upper diagonal, elements of the matrix G where k ≥ 2t. Substituting in (54), we get ˜ 1 (i, i + k) G  =

(1)

G1,1 (m, n)δ(2m − 1 − i)δ(2n − 1 − i − k)

2n−2m=k

+



(2)

G1,1 (m, n)δ(2m − 1 − i)δ(2n − i − k)

2n−2m=k−1

−



(1)∗

G2,2 (m, n)δ(2m − i)δ(2n − i − k)

2n−2m=k

+

= 0 only if |2m − where we have used the ˜ 2n| ≤ 2t − 2. We can see from (57) that G1 (i, i + 2t − 1) is ˜ 1 (i, i + 2t − nonzero only for odd values of i, and hence, G 1) = 0 for i = 2, 4, . . . 2L − 2t, which proves the second part of Proposition 3 for the 2t − 1th upper diagonal. Similarly, we can prove the second part of Proposition 3 for the 2t − 1th lower diagonal. fact that G(i) v,v (m, n)



(2)∗

G2,2 (m, n)δ(2m − i)δ(2n − 1 − i − k)

2n−2m=k+1

(55) where all the preceding summations are over the values of m, n from 1 to L that satisfy the condition under the operator. Due to the banded structure of G(1) and G(2) shown in Fig. 3, we have G(i) v,v (m, n) ⎧ (i) ⎪ ⎪ ⎪ αv,v (m, n) ⎪ ⎪ ⎪ ⎨ (i) = αv,v (m, n) ⎪ ⎪ ⎪ (i) ⎪ ⎪ α (m, n) ⎪ ⎩ v,v 0

m = 1, . . . , t n = 1, . . . m + t − 1 m = t + 1, . . . , 2L − t if n = m − t + 1, . . . m + t − 1 m = 2L − t + 1, . . . , 2L if n = m + t − 1, . . . 2L else if

(i)

(56)

where v = 1, 2 and |αv,v (m, n)| ≥ 0. From (56), we can see that G(i) v,v (m, n) = 0 only if |m − n| ≤ t − 1, and hence, G(i) (m, n)

= 0 only if |2m − 2n| ≤ 2t − 2. Since the sumv,v mations in (55) are over values of 2n − 2m = k − 1, k, k + 1, where the minimum value of k is given by 2t, then all the

[1] C. Mecklenbrauker, A. Molisch, J. Karedal, F. Tufvesson, A. Paier, L. Bernado, T. Zemen, O. Klemp, and N. Czink, “Vehicular channel characterization and its implications for wireless system design and performance,” Proc. IEEE, vol. 99, no. 7, pp. 1189–1212, Jul. 2011. [2] A. Molisch, F. Tufvesson, J. Karedal, and C. C. Mecklenbrauker, “A survey on vehicle-to-vehicle propagation channels,” IEEE Wireless Commun., vol. 16, pp. 12–22, Dec. 2009. [3] L. Cheng, B. E. Henty, D. D. Stancil, F. Bai, and P. Mudalige, “Mobile vehicle-to-vehicle narrow-band channel measurement and characterization of the 5.9 GHz dedicated short range communication (DSRC) frequency band,” IEEE J. Sel. Areas Commun., vol. 25, no. 8, pp. 1501–1516, Oct. 2007. [4] L. Cheng, B. E. Henty, R. Cooper, D. D. Standi, and F. Bai, “A measurement study of time-scaled 802.11a waveforms over the mobile-tomobile vehicular channel at 5.9 GHz,” IEEE Commun. Mag., vol. 46, no. 5, pp. 84–91, May 2008. [5] J. A. C. Bingham, “Multicarrier modulation for data transmission: An idea whose time has come,” IEEE Commun. Mag., vol. 28, pp. 5–14, May 1990. [6] J. L. J. Cimini, “Analysis and simulation of a digital mobile radio channel using orthogonal frequency division multiplexing,” IEEE Trans. Commun., vol. COM-33, no. 7, pp. 665–765, Jul. 1985. [7] D. Jiang and L. Delgrossi, “IEEE 802.11 p: Towards an international standard for wireless access in vehicular environments,” in Proc. IEEE VTC Spring, Singapore, May 2008, pp. 2036–2040. [8] S. Lu, R. Kalbasi, and N. Al-Dhahir, “OFDM interference mitigation algorithms for doubly-selective channels,” in Proc. IEEE VTC Fall, Montreal, QC, Canada, Sep. 2006, pp. 1–5. [9] P. Schniter and S. D’Silva, “Low-complexity detection of OFDM in doubly-dispersive channels,” in Conf. Rec. 36th Asilomar Conf. Signals, Syst., Comput., Pacific Grove, CA, USA, 2002, vol. 2, pp. 1799–1803. [10] S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Sel. Areas Commun., vol. 16, no. 8, pp. 1451–1458, Oct. 1998. [11] D. Agrawal, V. Tarokh, A. Naguib, and N. Seshadri, “Space–time coded OFDM for high data-rate wireless communication over wideband channels,” in Proc. IEEE VTC, Ottawa, ON, Canada, May 1998, vol. 3, pp. 2232–2236. [12] J. Wu and G. J. Saulnier, “Orthogonal space–time block code over timevarying flat-fading channels: Channel estimation, detection, and performance analysis,” IEEE Trans. Commun., vol. 55, no. 5, pp. 1077–1087, May 2007. [13] K. Lee and D. Williams, “A space–frequency transmitter diversity technique for OFDM systems,” in Proc. IEEE GLOBECOM, San Francisco, CA, USA, Nov. 2000, vol. 3, pp. 1473–1477. [14] M. Torabi, S. Aissa, and M. Soleymani, “On the BER performance of space–frequency block coded OFDM systems in fading MIMO channels,” IEEE Trans. Wireless Commun., vol. 6, no. 4, pp. 1366–1373, Apr. 2007.

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[15] S. Lu, B. Narasimhan, and N. Al-Dhahir, “A novel SFBC-OFDM scheme for doubly selective channels,” IEEE Trans. Veh. Technol., vol. 58, no. 5, pp. 2573–2578, Jun. 2009. [16] D. Li, K. Wu, H. Yang, and L. Cai, “A novel double-polarized SFBCOFDM scheme for ICI suppression,” in Proc. IEEE WCNC, Budapest, Hungary, Apr. 2009, pp. 1–4. [17] A. Abotabl, A. El-Keyi, Y. Mohasseb, and T. ElBatt, “Reducedcomplexity SFBC-OFDM for vehicular channels with high mobility,” in Proc. IEEE VTC Fall, Quebec City, QC, Canada, 2012, pp. 1–5. [18] S. Tomasin, A. Gorokhov, H. Yang, and J. P. Linnartz, “Iterative interference cancellation and channel estimation for mobile OFDM,” IEEE Trans. Wireless Commun., vol. 4, no. 1, pp. 238–245, Jan. 2005. [19] “Cost 207: Digital land mobile radio communications,” Commiss. Eur. Commun., Brussels, Belgium, Final Rep., 1989. [20] T.-W. Feng, B. Williams, P.-C. Wang, and S.-K. Jeng, “Window design for SISO and MIMO OFDM systems,” in Proc. 6th IEEE Consum. Commun. Netw. Conf., 2009, pp. 1–5.

Ahmed Attia Abotabl received the B.Sc. degree (with honors) in electrical engineering from Alexandria University, Alexandria, Egypt, in 2010 and the M.Sc. degree in electrical engineering from Nile University, Giza, Egypt, in 2012. He is currently working toward the Ph.D. degree with the University of Texas, Richardson, TX, USA. His research interests include information theory, coding theory estimation, and detection.

Amr El-Keyi received the B.Sc. (with highest honors) and M.Sc. degrees in electrical engineering from Alexandria University, Alexandria, Egypt, in 1999 and 2002, respectively, and the Ph.D. degree in electrical engineering from McMaster University, Hamilton, ON, Canada, in 2006. From November 2006 to April 2008, he was a Postdoctoral Research Fellow with the Department of Electrical and Computer Engineering, McGill University, Montreal, QC, Canada. From May 2008 to February 2009, he was an Assistant Professor with Alexandria University, where he taught several undergraduate courses. In April 2009, he joined Nile University, Giza, Egypt, as an Assistant Professor with the School of Communication and Information Technology. His research interests include array processing, cognitive radio, channel estimation, and interference management and cooperative relaying for wireless communication systems.

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Yahya Mohasseb received the B.Sc. (with highest honors) and M.S. degrees in electrical engineering from The Military Technical College, Cairo, Egypt, in 1991 and 1996, respectively. From 1991 to 1992, he was with the Egyptian Department of Defense. From 1992 to 1998, he was with the Department of Communications, The Military Technical College, where he was a Teaching and Research Assistant. He received a doctoral fellowship from the Egyptian government in 1998 when he joined the Department of Electrical Engineering, The Ohio State University, Columbus, OH, USA, as a doctoral student. In March 2002, he returned to the Department of Communications, The Military Technical College, as an Assistant Professor. His research interests include channel modeling, multiuser detection, satellite asynchronous transfer mode networks, orthogonal frequency-division multiplexing, and interference cancellation.

Fan Bai received the B.S. degree in automation engineering from Tsinghua University, Beijing, China, in 1999 and the M.S.E.E. and Ph.D. degrees in electrical engineering, from the University of Southern California, Los Angeles, CA, USA, in 2005. He has been a Senior Researcher with the Electrical and Control Integration Laboratory, Research and Development and Planning, General Motors Corporation, Warren, MI, USA, since September 2005. He has published about 40 book chapters and conference and journal papers. His current research is focused on the analysis and design of protocols/systems for next-generation vehicular ad hoc networks, safety, telematics, and infotainment applications. Dr. Bai served as a Technical Program Co-Chair for the 2007 IEEE International Symposium on Wireless Vehicular Communications and the 2008 IEEE International Workshop on Mobile Vehicular Networks. He is an Associate Editor of the IEEE T RANSACTIONS ON V EHICULAR T ECHNOLOGY and serves as a Guest Editor of IEEE Wireless Communication Magazine, IEEE Vehicular Technology Magazine, and Elsevier’s Ad Hoc Networks Journal. In 2006, he received the Charles L. McCuen Special Achievement Award from General Motors Corporation “in recognition of extraordinary accomplishment in area of vehicle-to vehicle communications for drive assistance and safety.”