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Minimum Bit Error Rate Beamforming Combined with Space-Time Block Coding using Double Antenna Array Group

VIEWS: 361 PAGES: 6

									                                                              (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
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                                                                                                   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




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                                                                                                                                  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.




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                                                                                                                                                                   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




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                                                                                                                                                                                                                         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).




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                                                                                                                                                                                                                           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.
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                                                                                                                                                                         ISSN 1947-5500

								
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