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(IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, o. 5, May 2011 Minimum Bit Error Rate Beamforming Combined with Space-Time Block Coding using Double Antenna Array Group Said Elnoubi Waleed Abdallah Mohamed M. M. Omar Tech. and App. Sc. Program Elect. & Comm. Eng. Electrical of Engineering Al-Quds Open University, AAST, Abukir Alexandria University Jerusalem, Palestine Alexandria, Egypt Alexandria, Egypt wsalos@qou.edu mohammad_yosef@hotmail.com saidelnoubi@hotmail.com Abstract— In this paper, we propose a Minimum Bit Error Rate maximizing SNR and minimizing the mean square error (MBER) beamforming combined with Space-Time Block Coding (MMSE) between the desired output and actual array output. (STBC) according to the number of antenna array. A class of This principle has its roots in the traditional beamforming adaptive beamforming algorithm has been proposed based on employed in sonar and radar systems. minimizing the BER cost function directly. Consequently, MBER For a communication system, it is the achievable BER, not the beamforming is capable of providing significant performance gains in terms of a reduced BER. The beamforming weights of MSE performance that really matters. Ideally, the system the combined system are optimized in such a way that the virtual design should be based directly on minimizing the BER, rather channel coefficients corresponding to STBC-encoded data than the MSE. For applications to single-user channel streams, seen at the receiver, are guaranteed to be uncorrelated. equalization and multi-user detection, it has been shown that Therefore the promised achievable diversity order by the MMSE solution can in certain situations be distinctly conventional system with STBC can be obtained completely. inferior in comparison to the MBER solution, and several Combined MBER beamforming with STBC single array adaptive implementations of the MBER solution have been performance measured by BER is compared under the condition studied in the literature [3]. This contribution derives a novel of direction of arrival (DOA) and signal-to-noise ratio (S R). The adaptive beamforming technique based on directly minimizing numerical simulation results of the proposed technique show that this minimum BER (MBER) approach utilizes the antenna array the system’s BER rather than the MSE. In [3], an adaptive elements more intelligently and have a performance dependent of implementation of the MBER beamforming technique is DOA and angular spread (AS). investigated. STBC and beamforming techniques are two emerging Keywords-MBER beamforming; STBC; DOA; angular spread; technologies that can be employed at base station with adaptive antenna array multiple antennas to provide transmit diversity and beamforming gain to increase SNR of the downlink. In [1] and I. INTRODUCTION [2], the idea of the combination of two schemes to get the full The growing demand for wireless high-speed data diversity order as well as beamforming gain is proposed. transmission in applications such as wireless web browsing, There, the beamforming gain is achieved by maximizing file downloading, wireless multimedia transmission,…, etc., received SNR at the receiver. It has shown real promise for will increase requirements for downlink throughput and increasing capacity and coverage and for mitigating multipath quality of service (QoS) significantly. But multipath fading is propagation of mobile radio communication systems. one of the major impairments limiting wireless In this paper, the MBER beamforming combined with STBC communication systems in performance and capacity. Lots of is proposed using single antenna array. This new technique is new technologies such as smart antenna and transmit diversity compared with the maximum SNR beamforming combined have been proposed [1]. Those two technologies have the with STBC in array gain versus DOA center and BER versus same features in the view of requiring the multiple antenna DOA center and SNR performances. The simulation results elements, but have the contradictive requirement for antenna show that the system's BER performance of the proposed element spacing. algorithm is better than that investigated in [1], [2]. Adaptive beamforming can separate signals transmitted in the This paper is organized as follows. First, the combined same carrier frequency, provided that they are separated in the beamforming with STBC single array is illustrated in Section II. Then the MBER beamforming algorithm is introduced in spatial domain. A beamformer combines the signal received Section III. The combined MBER beamforming with STBC by the different element of an antenna array to form a single double array is presented in Section IV. In Section V, output. This has been achieved by many criteria such as simulation results are conducted to evaluate the performance of Identify applicable sponsor/s here. (sponsors) 1 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, o. 5, May 2011 the proposed scheme, the combined MBER beamforming with B. Detection STBC single and double arrays, and compared with the In order to get maximal SNR, [1] tried to maximize (7) subject performance of the combined maximum SNR with STBC to (8) based on conventional STBC detection single and double arrays followed by the conclusion in Section VI. H 2 H 2 E w1 ⋅ H + w2 ⋅ H (7) II. COMBINED BEMNFORMING WITH SPACE TIME BLOCK H w1H ⋅ w1 + w2 ⋅ w2 = 1 (8) CODE SINGLE ARRAY H The downlink channel covariance matrix (DCCM) E[ H H ] A. System Model is well analyzed in [4] for TDD and FDD system. Fig. 1 shows the system employing STBC to combine with For simplicity set L=2, then equations (5) and (6) can be beamforming technique using single array [1-2]. The signal to rewritten as be transmitted, s (n) , 1 ≤ n ≤ is first coded using a STBC r1 = ( w1H ⋅ s1 + w2 .s2 ).[h1 ⋅ a(θ1 ) + h2 .a(θ 2 )] + η1 H (9) encoder, yielding two branch outputs as s1 (n) and s 2 (n) , r2 = [( w1 ⋅ (− s2 ) + w2 .( s1 ).][h1 ⋅ a (θ1 ) + h2 .a (θ 2 )] + η 2 H * H * where is the number of transmitted bit sequences. They are (10) then passed into two transmit beamformers w1 and w2 , In [2], at receiver the Alamouti STBC (2Tx, 1Rx) [5] detection respectively. At different time, they are simply added and is used transmitted as ~ = h* ⋅ r + h ⋅ r * s1 (11) 1 1 2 2 H H x1 = w1 ⋅ s1 + w2 ⋅ s2 (1) and the beamforming weight vectors w1 and w2 are set to be H * H * x2 = w1 ⋅ (− s2 ) + w2 ⋅ s1 (2) 1 1 w1 = ⋅ a (θ1 ) , w2 = .a (θ 2 ) (12) where wi is the weight vector of the ith beamformer and (.)H 2M 2M is the Hermitian. which are maximizing the receiving SNR at the receiver. The transmit beamforming weight are optimized by x11 maximizing the cost function, but increasing the computing s1 (h1 ,θ1 ) x12 complexity [2]. w1 y s III. MBER BEAMFORMING WITH STBC SOLUTION s2 x1M (h2 ,θ 2 ) w2 It is assumed that the system supports L users, each user transmits signal on the same carrier frequency. The linear antenna array considered consists of M uniformly spaced Figure 1. Combined beamforming with STBC using single array. elements and the signal received by the M-element antenna array are given by Suppose the physical channel consists of L spatially separated s1 (n) paths, whose fading coefficients and DOAs are denoted as (hl , θ l ) for l = 1...L . If the maximum time delay relative to x(n) = [a (θ1 ), a (θ 2 ),...., a (θ L )] s 2 (n) (13) the first arrived path is smaller than the symbol interval, a flat : fading channel is observed and the instantaneous channel s L (n) response can be expressed as L L where si is the signal to be transmitted for ith user. s1 (n) is H= ∑ h ⋅ a(θ ) = ∑α exp(φ ) ⋅a(θ ) l =1 l l l =1 l l l (3) assumed to be the desired user and the rest of the sources are the interfering users. To determine the MBER beamforming where α l and φl are the fading amplitude and phase. For M- weight vector w , we start by forming its BER cost function element uniform linear array (ULA) with spacing d, the [6]. The conditional probability density function (pdf) given downlink steering vector can be expressed as by a (θ l ) = [1, e j 2π sin(θ l ) d / λ ...e j 2π ( M −1) sin(θ l ) d / λ ]T (4) ( y − sgn( s (n)) y (n)) 2 ∑ exp − 1 (14) P( y s ) = s 1 R So the received signal at the receiver is given by 2πσ η2 2σ η2 n =1 r1 = r (t ) = w1 ⋅ H ⋅ s1 + w2 ⋅ H ⋅ s2 + η1 H H (5) is the best indicator of a beamformer's BER performance, ∗ r2 = r (t + T ) = w1 ⋅ H ⋅ (− s2 ) + w2 ⋅ H ⋅ ( s1 ) + η 2 H * H (6) where where T is the symbol duration, r1 and r2 are the received y ( n) = w H x ( n) (15) signals at time t and t + T , η1 and η 2 are complex-valued white y s (n) = sgn( s1 (n)) y R (n) (16) Gaussian noise having a zero mean and a variance of 2σ η . 2 sgn(.) denotes the sign function, y R (n) = Re{ y (n)} is the real part of the beamformer output y(n) and y s (n) is an error indicator for the binary decision, i.e., if it is positive, then we 2 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, o. 5, May 2011 have a correct decision, else if it is negative, then an error ∑ Q( g 1 ; occurred. PE ( w) = n ( w)) n =1 Hence, the error probability of the beamformer w , the BER sgn( s1 (n)) y R (n) cost function, is given by g n ( w) = ; ση ∑ Q( g 1 PE ( w) = n ( w)) (17) • Calculate the search direction from n =1 2 ∇PE ( w(i + 1)) where Q(.) is the Gaussian error function given by φi = 2 ; ∇PE ( w(i)) 1 ∞ − v2 2π ∫ Q (u ) = exp( )dv (18) D(i + 1) = φ i D(i ) − ∇PE ( w(i + 1)) ; u 2 • Increment the iteration number i = i +1 and • end of while loop sgn( s1 (n)) y R (n) g n ( w) = (19) ση Stop : w(i ) is the solution of the MBER weight vector. The MBER beamforming solution is then defined as To determine the MBER beamforming weight vector for another user, we can apply the algorithm stated in Table. I for wMBER = arg min PE ( w) (20) choosing s2 (n) as desired user and the remainder of the w sources are considered to be interfering sources. The gradient of PE (w) with respect to w can be shown to be As shown in [1], the equation denoted as array gain is given ∂PE ( w) ( y (n)) 2 by ∑ exp − 1 ∇PE ( w) = = R (21) ∂w 2σ η 2 2 2 2πσ η 2 ⋅ n =1 H w2 ⋅ w1 ⋅ sgn( s1 (n)( y R (n) w − x(n) ) ε= 2 (22) H The following simplified conjugate gradient algorithm [3] w2 ⋅ w2 provides an efficient means of finding a MBER solution. Fig.2 shows the array gain depends on DOA (center) and In this paper, we will demonstrate from the simulation results that the system's BER performance can be improved by angular spread (AS). At 10o AS case, as DOA (center) are applying the MBER solutions instead of the beamforming 0o and 60o , ε are equal to 0.378 and 0.799 for the maximum weight vectors given by (11) combined with STBC. SNR and are equal to 0.39 and 0.843 for the proposed The proposed MBER algorithm is summarized in Table I. We algorithm, respectively. It changes widely enough to affect the initialize the main algorithm parameters. The algorithm performance for two algorithms. consists of one main loop. This loop is repeated until the norm of the gradient vector is sufficiently small. 0 1) Use the abbreviation “Fig. 1”, even at the beginning of a sentence. -10 TABLE I. SUMMARY OF THE MBER ALGORITHM -20 Array gain (dB ) Initialization -30 w(0) = x(0) / x(0) , µ = .8, β = .01 ( typically, β can be set to the machine accuracy). The adaptive gain µ and a termination scalar β are the two algorithmic parameters that have to be set -40 appropriately to ensure a fast convergence rate and small steady- state BER. AS=10o MinBER (1 iter.) • Calculate variance of noise. -50 AS=50o MinBER (1 iter.) • Calculate the gradient vector form (21). AS=10o close-form Max-SNR [1] • Complexity of (21) is O (M) for one bit [6]. AS=50o close-form Max-SNR [1] • Initialize the search direction , D = −∇PE , i=1; ∇PE -60 -60 -40 -20 0 20 40 60 DOA (Center) while ( ∇PE < β ) • Update the beamformer weight w(i + 1) = w(i ) + µD Figure 2. Array gain. • Normalize the solution w(i + 1) = w(i + 1) / w(i + 1) • Calculate the cost function BER and the gradient vector IV. COMBINED BEAMFORMING WITH SPACE TIME BLOCK ∂ PE ( w ) ( y ( n )) 2 CODE DOUBLE ARRAY ∑ 1 ∇ PE ( w ) = = exp − R ⋅ ∂w 2σ η2 2 2 πσ 2 η n =1 For array gain will strongly affect the system detection sgn( s 1 ( n ) ( y R ( n ) w − x ( n ) ) Complexity is O (M) for one bit [6]. performance, we find another scheme to minimize the disadvantage. 3 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, o. 5, May 2011 Fig.3 shows the double array (Combined beamforming with space time block code double array) model. Unlike combined -1 Performance Comparison : BER vs.DOA ( CB-STBC-S, As=10o ) 10 beamforming with space time block code single array model, 5dB after being put into the two beamformers, two data streams are sent by two dependent antenna arrays. The element number for one array is M. All parameters of equations shown in Fig.3 are 10 -2 same as those in section II. Bit Error Rate (BPSK) S1 (h1 , θ1 ) -3 10 w1 S y 10dB S2 w2 (h2 ,θ 2 ) 10 -4 15dB Figure 3. Combined beamforming with STBC using double array. SNR (5 10 15) dB Single-array MinBER (1 iter.) -5 SNR (5 10 15 dB Single-array [1] 10 The received signals at the mobile terminal can be expressed -60 -40 -20 0 20 40 60 as: DoA (Center ) r1 = w1H ⋅ h1 ⋅ a (θ1 ) ⋅ s1 + w2 ⋅ h2 ⋅ a (θ 2 ).s 2 + η1 H (23) Figure 5. Performance comparison : BER vs. DOA (Combined beamforming with STBC using single array, As=10o). r2 = w1H ⋅ h1 ⋅ a (θ1 ) ⋅ (− s1 ) + * H w2 ⋅ h2 ⋅ a(θ 2 ).s1 * + η2 (24) And the detection for s1 is It can be seen for large angular spread the BER performance ~ = h* ⋅ r + h ⋅ r * does not affected by DOA but is seriously affected for small s1 1 1 2 2 (25) angular spread case, especially with bigger SNR. Fig.6 and Fig.7 illustrate the average BER performance of the CB-STBC single array using maximum SNR and MBER V. SIMULATION RESULTS schemes versus SNR. Also, the same two cases are considered In our numerical simulations, we consider the same example in each Figure to represent the cases with small and large AS. investigated in [1] to make comparisons. A 6-element uniform For this example, the superior performance of the MBER linear array (ULA) antenna is assumed in the base station with scheme over the MSNR scheme becomes evident. element spacing of λ / 2 , while the mobile terminal has single Performance Comparison ( AS=50o) BER vs. SNR antenna. We simulate the BER supposing the desired user 10 0 moves in a sector of 1200. The channel is assumed suffering Single-array MaxSNR from Rayleigh fading with various AS. -1 Single-array of MinBER (1 iter.) Fig.4 and Fig.5 illustrate the average BER performance of the 10 combined beamforming with space time block coding (CB- STBC) single array using maximum SNR and MBER schemes 10 -2 B it E rror Rate (B P S K ) versus DOA for two different cases, AS = 50° and 10°. Performance Comparison : BER vs.DOA ( CB-STBC-S, As=50o ) -1 -3 10 10 0 dB -4 10 0 dB -2 10 5 dB Bit Error Rate (BPSK) -5 10 5 dB -6 10 10dB 0 2 4 6 8 10 12 14 16 18 -3 SNR in dB 10 10 dB Figure 6: Performance Comparison : BER vs. SNR. SNR (0 5 10) dB Single-array MinBER (1 iter.) Combined beamforming with STBC using double array -4 SNR (0 5 10 dB Single-array [1] overcomes the disadvantages appeared on the single array 10 -60 -40 -20 0 20 40 60 model. Fig. 8 and 9 show us a stable performance which is not DoA (Center ) dependent on AS. Figure 4. Performance comparison: BER vs. DOA (Combined beamforming Fig.10 illustrates the average BER performance of the CB- with STBC using single array, As=50o). STBC double array using maximum SNR and MBER schemes 4 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, o. 5, May 2011 versus SNR. Also, the same two cases are considered in each -1 Performance Comparison : BER vs.DOA ( CB-STBC-D, As=50o ) Figure to represent the cases with small and large AS. 10 (0 5 10 ) dB MaxSNR Double-array (As=50o) (0 5 10) dB MinBER Double-array (As=50o) 0 Performance Comparison (AS=10o) BER vs. SNR 10 maxSNR at AS=100 MinBER(1 iter.)AS=10o -2 Bit Error Rate ( BPSK ) 10 -1 10 -2 10 Bit Error Rate (BPSK) -3 -3 10 10 -4 10 -5 -4 10 10 -60 -40 -20 0 20 40 60 DOA -6 10 0 2 4 6 8 10 12 14 16 18 Figure 9. Performance comparison: BER vs. DOA (combined beamforming SNR in dB with STBC double array, As=50o). Figure 7: Performance Comparison: BER vs. SNR. -1 Performance Comparison : (BER vs.SNR) 10 -1 Performance Comparison : BER vs.DOA ( CB-STBC-D, As=10o ) Double-array (As=10o for MaxSNR) 10 Double-array(As=50o) for MaxSNR Double-array (As=10o) for MinBER -2 10 Double-array(As=50o) for MinBER -2 Bit Error Rate (BPSK) 10 Bit Error Rate ( BPSK ) -3 10 -3 10 -4 10 -4 10 (0 5 10 ) dB MaxSNR Double-array (As=10o) -5 10 (0 5 10) dB MinBER Double-array (As=10o) 0 2 4 6 8 10 12 14 16 18 -5 10 SNR in dB -60 -40 -20 0 20 40 60 DOA Figure 10. Performance Comparison: BER vs. SNR with DOA(center)=0o. Figure 8. Performance comparison : BER vs. DOA (combined beamforming with STBC double array, As=10o). 0 single-array at SNR =0dB 0 single-array at SNR =5dB 10 10 A. Computational Complexity -1 10 The proposed MBER maintains the linearity in complexity; 10 -1 however, its performance is better than the maximum SNR Bit Error Rate (BPSK) Bit Error Rate (BPSK) -2 algorithm. Since addition is much easier than multiplication, 10 we focus on multiplication complexities. Table I, illustrates 10 -2 the number of multiplication required to complete a single 10 -3 iteration, i.e., detecting one bit. -3 10 B. Convergent Rate MinBER at AS=50o(11 iter.) 10 -4 MinBER at AS=50o(11 iter.) MinBER at AS=10o (11 iter.) MinBER at AS=10o (11 iter.) In this section, we run the algorithm of the MBER for 1000 samples and are limited to 1 and 11 iterations. The results are -4 10 shown in Fig. 11, where we can see that the proposed 0 5 10 0 5 10 iteration iteration algorithm converges very fast to the optimal solution (after Figure 11. Convergence rate vs. iteration of the MBER algorithm. one iteration only). 5 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, o. 5, May 2011 Furthermore, we can observe in Fig. 12, a significant [6] S. Zhou and G. B. Giannakis, “Optimal transmitter eigen-beamforming and space-time block coding based on channel mean feedback,” IEEE improvement over the maximum SNR algorithm by means of Trans. Signal Processing, vol. 50, no. 10, pp. 2599–2613, Oct. 2002. only one iteration. [7] Y-C. Liang and F. P. S. Chin, "Downlink channel covariance matrix 0 0 (DCCM) estimation and its applications in wireless DS-CDMA 10 10 MaxSNR AS=50o, MaxSNR AS=10o, systems", IEEE JSAC, Vol. 19, pp. 222-232, Feb. 2001. MinBER(1 iter.)AS=50o MinBER(1 iter.)AS=10o [8] M. Lin, M. Li, L. Yang and X. You, “Adaptive transmit beamforming -1 MinBER AS=50o (>=10 iter.) 10-1 MinBER AS=10o (>=10 iter.) with space-time coding for correlated MIMO fading channels,” in Proc. 10 IEEE ICC '07, June 2007. [9] S. M. Alamouti, “A simple transmit diversity technique for wireless Bit Error Rate (BPSK) Bit Error Rate (BPSK) -2 -2 communications,” IEEE JSAC, Vol. 16, No. 8, pp. 1451-1458, October 10 10 1998. [10] M. Lin, M. Li, L. Yang and X. You, “Adaptive transmit beamforming -3 -3 with space-time coding for correlated MIMO fading channels,” in Proc. 10 10 IEEE ICC '07, June 2007. [11] S. Chen, N. N. Ahmad, and L. Hanzo, "Adaptive Minimum Bit-Error -4 -4 Rate Beamforming", IEEE Transactions on Wireless Communications, 10 10 VOL. 4, NO. 2 MARCH 2005. [12] T. A. Samir, S. Elnoubi, and A. Elnashar, “Class of minimum bit error rate algorithms,” in Proc. 9th ICACT, Feb. 12–14, 2007, vol. 1, pp. 168– 0 5 10 15 0 5 10 15 173. SNR in dB SNR in dB [13] S. Chen, A. K. Samingan, B. Mulgrew, and L. Hanzo, “Adaptive Fig.12. : Convergence of the MinBER algorithm. minimum- BER linear multiuser detection for DS-CDMA signals in multipath channels,” IEEE Trans. Signal Process., vol. 49, no. 6, pp.1240–1247, Jun. 2001. VI. CONCLUSION In this paper, a downlink transmit diversity scheme is proposed to achieve both full diversity gain and optimized beamforming gain. It is obtained by combining MBER beamforming technique with STBC for multiple beamforming antenna systems (single and double array). An adaptive MBER beamforming technique has been developed. It has been shown that the MBER beamformer exploits the system’s resources more intelligently than the other standard beamformers and, consequently, can achieve a better performance in terms of a lower BER. The combined beamforming with STBC using single array are shown to be dependent on the DOA and angular spread. However combined beamforming with STBC using double array is shown to have a stable performance independent of DOA and angular spread. REFERENCES [1] Fan Zhu, Kyung Sik, Myoung Lim, "Combined beamforming with space-time block coding using double antenna array group", Electronics Letters, 2004, 40 (13):811-813. [2] Zhongding Lei, Chin F.P.S., Ying-Chang Liang, “Combined beamforming with space-time block coding for wireless downlink transmission,” Vehicular Technology Conference, 2002. Proceedings .VTC 2002-Fall. 2002 IEEE 56th, Vol. 4, pp. 24-28 Sept. 2002. [3] Frank B.Gross, PhD, "Smart Antennas For Wireless Communications with matlab",2005. [4] Said Elnoubi,Waleed Abdallah,Mohamed M. M. Omar, "Minimum Bit Error Rate Beamforming Combined with Space-time Block Coding", International Conference on Communications and Information Tech. ICCIT-2011,Aqaba-Jordan. [5] Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high data rate wireless communication: Performance criterion and code construction,” IEEE Trans. Inf. Theory, vol. 44, no. 2, pp. 744– 765,Mar.1998. 6 http://sites.google.com/site/ijcsis/ ISSN 1947-5500