95 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) ISSN (Print) 2313-4410, ISSN (Online) 2313-4402 Β© Global Society of Scientific Research and Researchers http://asrjetsjournal.org/ Synthesis of Antenna Arrays for Maximum Gain and Its Impact on BER Performance of MIMO Systems Nourhan M. Salema*, Amr H. Husseinb, Mohamed Nasrc a,b,cElectronics and Electrical Engineering Dept., Faculty of Engineering, Tanta University, Tanta 3111, Egypt aEmail: nouraa.magdy@gmail.com bEmail: amrvips@yahoo.com cEmail: menasr2001@yahoo.com Abstract Multiple-Input Multiple-Output (MIMO) is the most promising technology that improves the system capacity and data rate by using multiple antennas at transmitting and receiving sides of wireless communication systems. Many research efforts are introduced to enhance the bit error rate (BER) performance of MIMO systems. In this paper, detection algorithms based on antenna arrays synthesis have been proposed for bit error rate performance enhancement of MIMO systems. It is well known that the maximum number of data streams that can be supported by MIMO system using spatial multiplexing is given by 𝑁𝑁𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = π‘šπ‘šπ‘šπ‘šπ‘šπ‘š (𝑁𝑁𝑇𝑇 ,𝑁𝑁𝑅𝑅). Where 𝑁𝑁𝑇𝑇 is the number of transmitting antennas and 𝑁𝑁𝑅𝑅 is the number of receiving antennas. For a given (𝑁𝑁𝑇𝑇 Γ— 𝑁𝑁𝑅𝑅) MIMO system, the existing number of antenna elements at transmitting and receiving sides are individually used to synthesize larger size antenna arrays to provide higher antenna gains without using additional antenna elements or changing the number of transmitted data streams. The achieved array gain will enhance the signal to noise ratio of the system giving rise to lower bit error rate. The proposed system is tested for both Zero Forcing (ZF) and Minimum Mean Square Error (MMSE) detectors. The simulation results revealed that the proposed system outperforms the traditional ZF and MMSE detectors. Keywords: Multi Input- Multi Output (MIMO); Zero Forcing (ZF); Minimum Mean Square Error (MMSE); Bit Error Rate (BER). ------------------------------------------------------------------------ * Corresponding author. http://asrjetsjournal.org/ American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2018) Volume 49, No 1, pp 95-105 96 1. Introduction Multiple-input multiple-output (MIMO) systems exploit multipath propagation to achieve higher data rates, without the need for additional bandwidth [1-5]. For optimum detection, the Maximum Likelihood accomplishes the most elevated performance to the detriment of high computational complexity. In this context, great research efforts are exerted to introduce new detection algorithms of high performance close to the ML optimal performance. The sphere decoding (SD) algorithm can efficiently attain the optimal maximum-likelihood (ML) performance, although it has higher complexity at lower signal-to- noise ratio (SNR) [2,3]. The linear detectors, like the Minimum Mean Square Error (MMSE) based detectors, have much lower complexity, but there also exists significant performance degradation comparing with the SD algorithm. On the other hand, non-linear detectors provide better performance with higher complexity. The vertical Bell-laboratories layered space-time (V- BLAST) system, is based on the MMSE principle with the optimal successive interference cancellation (OSIC). The V-BLAST is one of the most well-known MIMO detection techniques [4]. A fast detector for MIMO system which utilizes the lattice reduction to improve the symbols detection was introduced in [5]. It employs the orthogonality defect factor to select the best available channel submatrix for conditional detection. After channel submatrix selection, the lattice reduction is applied to the first channel submatrix. Zero Forcing (ZF) as a linear detector is applied to estimate the first symbols subset. These estimated symbols are used in conditional detection for the second symbols subset applying the ML detection technique. The estimated second symbols subset are utilized again to enhance the estimation of the first symbols subset applying the ZF detector again. But, staring with ZF detector which has lower estimation accuracy than ML may affect the results of the second and third stages. In this paper, enhanced detection techniques based on synthesis of antenna arrays at both transmitting and receiving sides are introduced for BER performance enhancement of MIMO systems. Many research efforts for antennas arrays synthesis using reduced number of antenna elements are introduced in [6-10]. In [10], the efficient MOM/GA array synthesis technique was introduced for arbitrarily shaped patterns synthesis using reduced number of antenna elements. In this work, the reverse process is executed where the existing few number of antenna elements is used to synthesize larger size antenna arrays with higher gains. This synthesis is intended to reduce the BER by increasing the signal to noise ratio of the MIMO signal via increasing the array gain. 2. Problem Formulation Consider an 𝑁𝑁𝑇𝑇 Γ— 𝑁𝑁𝑅𝑅 MIMO model as shown in Figure (1) where 𝑁𝑁𝑇𝑇 and 𝑁𝑁𝑅𝑅 are the number of transmitting and receiving antennas respectively. The antenna elements of the transmitting and receiving arrays are aligned linearly with uniform spacing 𝑑𝑑 = πœ†πœ† 2⁄ . The received signal 𝑦𝑦 is given by [1]. 𝑦𝑦 = 𝐻𝐻𝐻𝐻 + 𝑣𝑣 (1) American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2018) Volume 49, No 1, pp 95-105 97 where 𝐻𝐻 is the 𝑁𝑁𝑇𝑇 Γ— 1 baseband signal vector transmitted during each symbol period formed by the antenna elements. 𝑦𝑦 denotes the received symbol vector with dimension 𝑁𝑁𝑅𝑅 Γ— 1 where 𝑁𝑁𝑇𝑇 ≀ 𝑁𝑁𝑅𝑅 . 𝑣𝑣 is a complex white Gaussian noise vector of dimensions 𝑁𝑁𝑅𝑅 Γ— 1 with zero mean and variance 𝜎𝜎2 . The channel matrix 𝐻𝐻 is a 𝑁𝑁𝑅𝑅 Γ— 𝑁𝑁𝑇𝑇 matrix representing the scattering effects of the channel. For simplicity the channel matrix 𝐻𝐻 is considered to be known at the receiver. The main drawback of this system is that the utilized linear antenna arrays suffer from their limited array gains. Traditionally to increase the array gain, the array size or number of antenna elements should be increased. Consequently, the number of RF chains, number of data streams, system complexity, and cost are increased. It is required to find a promising solution to achieve higher array gains without changing the RF front end structure of the existing MIMO system. Figure 1: Traditional 𝑁𝑁𝑇𝑇 Γ— 𝑁𝑁𝑅𝑅 MIMO system model. 3. Proposed MIMO Signal Model The traditional MIMO system employs uniform linear antenna arrays at both transmitting and receiving sides as shown in Figure (1). To mitigate the aforementioned problems of the traditional MIMO, The limited gain ULA is replaced by a synthesized higher gain non-uniform feeding linear antenna array using the same number of antenna elements, 𝑁𝑁𝑇𝑇 and 𝑁𝑁𝑅𝑅, and the same number of data streams which is given by: 𝑁𝑁𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = min (𝑁𝑁𝑇𝑇 ,𝑁𝑁𝑅𝑅) (2) When applying array synthesis, the excitation coefficients are no longer uniform. In this case, the MIMO system model can be redrawn as shown in Figure (2). For this purpose, the MOM/GA array synthesis technique introduced in [10] is used to synthesis the radiation pattern of a chosen large size antenna array with reduced number of antenna elements which equals the number of antenna elements of the traditional MIMO system as shown in Figure (2). The original large size array and the synthesized array patterns have almost the same characteristics such as side lobe level (SLL), half power beamwidth (HPBW), array gain, and directivity. The array factor of original large size array 𝐴𝐴𝐴𝐴(πœƒπœƒ) and the array factor of the synthesized array 𝐴𝐴𝐴𝐴𝑠𝑠𝑠𝑠𝑠𝑠(πœƒπœƒ) should be American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2018) Volume 49, No 1, pp 95-105 98 close to each other which can be expressed as follows: 𝐴𝐴𝐴𝐴(πœƒπœƒ) β‰ˆ 𝐴𝐴𝐴𝐴𝑠𝑠𝑠𝑠𝑠𝑠(πœƒπœƒ) (3) Equation (3) can be written as [10] βˆ‘ π‘Žπ‘Žπ‘ π‘ π‘€π‘€βˆ’1 𝑠𝑠=0 𝑒𝑒𝑗𝑗𝑗𝑗𝑠𝑠𝑗𝑗 cos(πœƒπœƒ) β‰ˆ βˆ‘ π‘Žπ‘Žπ‘ π‘  π‘π‘π‘‡π‘‡βˆ’1 𝑠𝑠=0 𝑒𝑒𝑗𝑗𝑗𝑗𝑠𝑠𝑗𝑗𝑠𝑠 cos(πœƒπœƒ) (4) where 𝑀𝑀 is the number of antenna elements of the large size array and 𝑁𝑁𝑇𝑇 is the number of elements of the synthesized array where 𝑀𝑀 > 𝑁𝑁𝑇𝑇 . π‘Žπ‘Žπ‘ π‘  and π‘Žπ‘Žπ‘ π‘  are the excitation coefficients of the original and synthesized arrays respectively. 𝑑𝑑 and 𝑑𝑑𝑠𝑠 are the element spacing of the original and synthesized arrays respectively. Figure 2: Proposed MIMO system model with synthesized transmitting and receiving antenna arrays. Consider (𝑁𝑁𝑇𝑇 = 𝑁𝑁𝑅𝑅 ) MIMO system whose antenna arrays are radiating in the broadside direction and aligned together. In this case, the synthesized arrays steering vectors are identical such that 𝐴𝐴𝑠𝑠 = 𝐴𝐴𝑠𝑠 = 𝐴𝐴. Where 𝐴𝐴𝑠𝑠 and 𝐴𝐴𝑠𝑠 are the synthesized steering vectors of the transmitting and receiving antenna arrays respectively. To derive the MIMO signal model, consider applying array synthesis at transmitting side only. Then received signal will be: 𝑦𝑦 = 𝐻𝐻 (𝐴𝐴 βˆ™ 𝐻𝐻) + 𝑣𝑣 (5) where (βˆ™) is the dot product. When applying array synthesis at receiving side, the total received signal 𝑦𝑦𝑠𝑠 can be written as: 𝑦𝑦𝑠𝑠 = (𝐻𝐻 (𝐴𝐴 βˆ™ 𝐻𝐻) + 𝑣𝑣).𝐴𝐴 (6) or American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2018) Volume 49, No 1, pp 95-105 99 𝑦𝑦𝑠𝑠 = 𝐻𝐻 (𝐴𝐴2 βˆ™ 𝐻𝐻) + 𝐴𝐴. 𝑣𝑣 (7) Let π‘Šπ‘Š = π‘‘π‘‘π‘šπ‘šπ‘Žπ‘Žπ‘‘π‘‘(𝐴𝐴2) is a square matrix of dimensions (𝑁𝑁𝑇𝑇 Γ— 𝑁𝑁𝑅𝑅 ) and (𝑁𝑁𝑇𝑇 = 𝑁𝑁𝑅𝑅 ) . Also let = 𝐴𝐴. 𝑣𝑣 . Then Equation (7) can be written as: 𝑦𝑦𝑠𝑠 = π‘Šπ‘Š 𝐻𝐻 𝐻𝐻 + π‘šπ‘š (8) For more simplicity let Ξ¨ = π‘Šπ‘Š 𝐻𝐻, then Equation (8) is written as follows: 𝑦𝑦𝑠𝑠 = Ξ¨ 𝐻𝐻 + π‘šπ‘š (9) To express Equation (9) in matrix form, consider the steering vectors 𝐴𝐴𝑠𝑠 = 𝐴𝐴𝑠𝑠 = 𝐴𝐴 which are derived from the synthesized array factor 𝐴𝐴𝐴𝐴𝑠𝑠𝑠𝑠𝑠𝑠(πœƒπœƒ) substituting πœƒπœƒ = πœƒπœƒπ‘–π‘– . As stated previously, the transmitting and receiving antenna arrays are aligned together in broadside direction, hence πœƒπœƒπ‘–π‘– = 90Β° with respect to the array line. The steering vectors at broadside direction can be written as follows: 𝐴𝐴𝑠𝑠 = 𝐴𝐴𝑠𝑠 = 𝐴𝐴 = 𝐴𝐴𝐴𝐴𝑠𝑠𝑠𝑠𝑠𝑠(90Β°) (10) 𝐴𝐴𝑠𝑠 = 𝐴𝐴𝑠𝑠 = 𝐴𝐴 = οΏ½ π‘Žπ‘Ž0 π‘Žπ‘Ž1 π‘Žπ‘Ž2 … … … β€¦π‘Žπ‘Žπ‘π‘π‘‡π‘‡βˆ’1οΏ½ 𝑇𝑇 (11) Also, the remaining parameters can be expressed in matrix form as follows 𝐻𝐻 = [𝐻𝐻1(π‘šπ‘š) 𝐻𝐻2(π‘šπ‘š) 𝐻𝐻3(π‘šπ‘š) … … … … 𝐻𝐻𝑁𝑁𝑇𝑇(π‘šπ‘š)]𝑇𝑇 (12) 𝐻𝐻𝑠𝑠(π‘šπ‘š) = [𝐻𝐻𝑠𝑠(1) 𝐻𝐻𝑠𝑠(2) 𝐻𝐻𝑠𝑠(3) … … … … 𝐻𝐻𝑠𝑠(𝑁𝑁)]𝑇𝑇 (13) π‘šπ‘š = [π‘šπ‘š1(π‘šπ‘š) π‘šπ‘š2(π‘šπ‘š) π‘šπ‘š3(π‘šπ‘š) … … … … π‘šπ‘šπ‘π‘π‘‡π‘‡(π‘šπ‘š)]𝑇𝑇 (14) π‘šπ‘šπ‘ π‘ (π‘šπ‘š) = [π‘šπ‘šπ‘ π‘ (1) π‘šπ‘šπ‘ π‘ (2) π‘šπ‘šπ‘ π‘ (3) … … … … π‘šπ‘šπ‘ π‘ (𝑁𝑁)]𝑇𝑇 (15) 𝑦𝑦𝑠𝑠 = [𝑦𝑦1(π‘šπ‘š) 𝑦𝑦2(π‘šπ‘š) 𝑦𝑦3(π‘šπ‘š) … … … … 𝑦𝑦𝑁𝑁𝑅𝑅(π‘šπ‘š)]𝑇𝑇 (16) 𝑦𝑦𝑠𝑠(π‘šπ‘š) = [𝑦𝑦𝑠𝑠(1) 𝑦𝑦𝑠𝑠(2) 𝑦𝑦𝑠𝑠(3) … … … … 𝑦𝑦𝑠𝑠(𝑁𝑁)]𝑇𝑇 (17) where [ ]𝑇𝑇 is the matrix transpose. 4. Simulation Results and Discussions In order to analyze the impact of the proposed technique on the BER, the 8 Γ— 8 LTE MIMO system is taken as the simulation object. It employs two equal size uniform linear antenna arrays at both transmitting and receiving sides with uniform element spacing 𝑑𝑑 = πœ†πœ† 2⁄ . The transmitted signal is modulated using 4-QAM and transmitted over a Rayleigh American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2018) Volume 49, No 1, pp 95-105 100 fading channel. The signal is subjected to an additive white Gaussian noise (AWGN) with zero mean and variance 𝜎𝜎2. Applying the array synthesis algorithm presented in [10], the dedicated 𝑁𝑁𝑇𝑇 = 𝑁𝑁𝑅𝑅 = 8 elements are used to synthesize different larger size antenna arrays from 𝑀𝑀 = 9 to 𝑀𝑀 = 16 as shown in Figure (3). But, as the number of antenna elements 𝑀𝑀 increase, the side lobe level increase. The grating lobes appear significantly at 𝑀𝑀 = 15 and 𝑀𝑀 = 16. The synthesized array parameters and excitations are listed in Table (1). To verify the effectiveness of the proposed technique, two simulation test cases considering ZF and MMSE detectors are presented in the next sections. (a) (𝑀𝑀 = 9,𝑁𝑁𝑇𝑇 = 𝑁𝑁𝑅𝑅 = 8) (b) (𝑀𝑀 = 10,𝑁𝑁𝑇𝑇 = 𝑁𝑁𝑅𝑅 = 8) (c) (𝑀𝑀 = 11,𝑁𝑁𝑇𝑇 = 𝑁𝑁𝑅𝑅 = 8) (d) (𝑀𝑀 = 12,𝑁𝑁𝑇𝑇 = 𝑁𝑁𝑅𝑅 = 8) American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2018) Volume 49, No 1, pp 95-105 101 (e) (𝑀𝑀 = 13,𝑁𝑁𝑇𝑇 = 𝑁𝑁𝑅𝑅 = 8) (f) (𝑀𝑀 = 14,𝑁𝑁𝑇𝑇 = 𝑁𝑁𝑅𝑅 = 8) (g) (𝑀𝑀 = 15,𝑁𝑁𝑇𝑇 = 𝑁𝑁𝑅𝑅 = 8) (h) (𝑀𝑀 = 16,𝑁𝑁𝑇𝑇 = 𝑁𝑁𝑅𝑅 = 8) Figure 3: The synthesized antenna arrays using 𝑁𝑁𝑇𝑇 = 𝑁𝑁𝑅𝑅 = 8 elements for different larger size antenna arrays from 𝑀𝑀 = 9 to 𝑀𝑀 = 16. Table 1: The synthesized array parameters for 𝑀𝑀 = 9 to 𝑀𝑀 = 16 using 𝑁𝑁𝑇𝑇 = 𝑁𝑁𝑅𝑅 = 8 elements 𝑴𝑴 9 10 11 12 13 14 15 16 𝒅𝒅𝒔𝒔 0.564πœ†πœ† 0.626πœ†πœ† 0.701πœ†πœ† 0.75πœ†πœ† 0.869πœ†πœ† 0.879πœ†πœ† 0.915πœ†πœ† 0.944πœ†πœ† π’‚π’‚πŸπŸ 1.0892 1.1930 1.2061 1.3415 1.2964 1.4636 1.4198 0.9000 π’‚π’‚πŸπŸ 1.144 1.2673 1.3920 1.4908 1.3678 1.5052 1.3144 0.7752 π’‚π’‚πŸ‘πŸ‘ 1.1196 1.2494 1.4952 1.5509 1.6494 1.6865 1.3236 0.7216 π’‚π’‚πŸ’πŸ’ 1.1307 1.2518 1.3518 1.479 1.8438 1.8100 1.3414 0.6999 π’‚π’‚πŸ“πŸ“ 1.1307 1.2518 1.3518 1.479 1.8438 1.8100 1.3414 0.6999 π’‚π’‚πŸ”πŸ” 1.1196 1.2494 1.4952 1.5509 1.6494 1.6865 1.3236 0.7216 π’‚π’‚πŸ•πŸ• 1.144 1.2673 1.3920 1.4908 1.3678 1.5052 1.3144 0.7752 π’‚π’‚πŸ–πŸ– 1.0892 1.1930 1.2061 1.3415 1.2964 1.4636 1.4198 0.9000 4.1 ZF Detector Based on Array Synthesis (𝒁𝒁𝒁𝒁𝒔𝒔𝒔𝒔𝒔𝒔) American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2018) Volume 49, No 1, pp 95-105 102 According to Equation (1), the traditional Zero-Forcing detection as a low complexity linear detection algorithm gives the estimate of 𝐻𝐻 as follows [11]: 𝐻𝐻� = 𝐻𝐻† 𝑦𝑦 = 𝐻𝐻 + (𝐻𝐻𝐻𝐻𝐻𝐻)βˆ’1𝐻𝐻𝐻𝐻 𝑣𝑣 = 𝐻𝐻 + 𝑣𝑣�𝑧𝑧𝑧𝑧 (18) The detector thus forces the interference to zero. The matrix 𝐻𝐻† nullifying the interference is given by: 𝐻𝐻† = (𝐻𝐻𝐻𝐻𝐻𝐻)βˆ’1𝐻𝐻𝐻𝐻 (19) where 𝐻𝐻† is the pseudo inverse of the channel matrix 𝐻𝐻. Using the proposed signal model expressed in Equation (9), the ZF detection process applying array synthesis can be summarized as follows where the matrix 𝛹𝛹† nullifying the interference is given by: 𝛹𝛹† = (𝛹𝛹𝐻𝐻𝛹𝛹)βˆ’1𝛹𝛹𝐻𝐻 (20) where 𝛹𝛹† is the pseudo inverse of the matrix 𝛹𝛹. The new symbols estimates 𝐻𝐻�𝑠𝑠𝑠𝑠𝑠𝑠 will be given as follows: 𝐻𝐻�𝑠𝑠𝑠𝑠𝑠𝑠 = 𝛹𝛹† 𝑦𝑦𝑠𝑠 = 𝐻𝐻 + (𝛹𝛹𝐻𝐻𝛹𝛹)βˆ’1𝛹𝛹𝐻𝐻 π‘šπ‘š = 𝐻𝐻 + π‘šπ‘šοΏ½π‘§π‘§π‘§π‘§ (21) Figure 4: The BER versus SNR for different array sizes (𝑀𝑀 > 𝑁𝑁𝑇𝑇) synthesized using the same number of antenna elements 𝑁𝑁𝑇𝑇 = 𝑁𝑁𝑅𝑅 = 8 compared to the traditional ZF detector in a 8 Γ— 8 MIMO system. To verify the effectiveness of the proposed technique, the BER versus signal to noise ratio (SNR) is plotted for the ZF detector applying array synthesis, 𝑍𝑍𝐴𝐴𝑠𝑠𝑠𝑠𝑠𝑠 , as shown in Figure (4). Replacing the 8-elements uniform antenna arrays by the 8-elements synthesized antenna arrays, it is found that the BER performance is significantly enhanced as the number of antenna elements increases from 𝑀𝑀 = 9 to 𝑀𝑀 = 14 as shown in Figure (4). But, for 𝑀𝑀 = 15 and 𝑀𝑀 = 16, the appearance of grating lobes highly degrades the BER performance as shown in Figure (5). For examples, at 𝑆𝑆𝑁𝑁𝑆𝑆 = 0𝑑𝑑𝑑𝑑 and 𝑀𝑀 = 14, the BER is reduced by 0.2867 compared to the American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2018) Volume 49, No 1, pp 95-105 103 traditional ZF detector. Also, the simulation results revealed that (𝑀𝑀 = 14,𝑁𝑁𝑇𝑇 = 𝑁𝑁𝑅𝑅 = 8) system provides the best BER performance. Figure 5: The BER performance degradation of the proposed ZF detector at (𝑀𝑀 β‰₯ 15,𝑁𝑁𝑇𝑇 = 𝑁𝑁𝑅𝑅 = 8) for a 8 Γ— 8 MIMO system. 4.2 MMSE Detector Based on Array Synthesis (𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝒔𝒔𝒔𝒔𝒔𝒔) According to Equation (1), the MMSE detector estimates the transmitted vector 𝐻𝐻 by applying a linear transformation to the received vector 𝑦𝑦. It finds out the estimate 𝐻𝐻�𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 of the transmitted symbol vector 𝐻𝐻 as [11]: 𝐻𝐻�𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 = π‘Šπ‘Šπ‘€π‘€π‘€π‘€π‘€π‘€π‘€π‘€ 𝑦𝑦 = (𝐻𝐻𝐻𝐻𝐻𝐻 + 𝜎𝜎2𝐼𝐼)βˆ’1𝐻𝐻𝐻𝐻y = 𝐻𝐻� + (𝐻𝐻𝐻𝐻𝐻𝐻 + 𝜎𝜎2𝐼𝐼)βˆ’1𝐻𝐻𝐻𝐻𝑣𝑣 = 𝐻𝐻� + 𝑣𝑣�𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 (22) The MMSE weight matrix, π‘Šπ‘Šπ‘€π‘€π‘€π‘€π‘€π‘€π‘€π‘€ , is utilized to maximize the post-detection signal-to interference plus noise ratio (SINR) [11]. While the MMSE receiver requires the statistical information of noise variance 𝜎𝜎2. Its BER performance is superior to ZF detection due to mitigating the noise enhancement. The MMSE weight matrix π‘Šπ‘Šπ‘€π‘€π‘€π‘€π‘€π‘€π‘€π‘€ is given by: π‘Šπ‘Šπ‘€π‘€π‘€π‘€π‘€π‘€π‘€π‘€ = (𝐻𝐻𝐻𝐻𝐻𝐻 + 𝜎𝜎2𝐼𝐼)βˆ’1𝐻𝐻𝐻𝐻 (23) Using the proposed signal model expressed in Equation (9), the MMSE detection process applying array synthesis can be summarized as follows where the MMSE weight matrix π‘Šπ‘Šπ‘€π‘€π‘€π‘€π‘€π‘€π‘€π‘€π‘ π‘ π‘ π‘ π‘ π‘  is given by: π‘Šπ‘Šπ‘€π‘€π‘€π‘€π‘€π‘€π‘€π‘€π‘ π‘ π‘ π‘ π‘ π‘  = (𝛹𝛹𝐻𝐻𝛹𝛹 + 𝜎𝜎2𝐼𝐼)βˆ’1𝛹𝛹𝐻𝐻 (24) American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2018) Volume 49, No 1, pp 95-105 104 The new symbols estimates 𝐻𝐻�𝑠𝑠𝑠𝑠𝑠𝑠 will be given as follows: 𝐻𝐻�𝑠𝑠𝑠𝑠𝑠𝑠 = π‘Šπ‘Šπ‘€π‘€π‘€π‘€π‘€π‘€π‘€π‘€π‘ π‘ π‘ π‘ π‘ π‘  𝑦𝑦𝑠𝑠 = (𝛹𝛹𝐻𝐻𝛹𝛹 + 𝜎𝜎2𝐼𝐼)βˆ’1𝛹𝛹𝐻𝐻𝑦𝑦𝑠𝑠 = 𝐻𝐻 + (𝛹𝛹𝐻𝐻𝛹𝛹 + 𝜎𝜎2𝐼𝐼)βˆ’1𝛹𝛹𝐻𝐻𝑧𝑧 = 𝐻𝐻 + π‘šπ‘šοΏ½π‘€π‘€π‘€π‘€π‘€π‘€π‘€π‘€ (25) Also, replacing the 8-elements uniform antenna array by the 8-elements synthesized antenna arrays, it is found that the BER performance of the MMSE detector is significantly enhanced as the number of elements increase from 𝑀𝑀 = 9 to 𝑀𝑀 = 14 as shown in Figure (6). Also, for 𝑀𝑀 = 15 and 𝑀𝑀 = 16, the appearance of grating lobes highly degrades the BER performance as shown in Figure (7). For examples, at 𝑆𝑆𝑁𝑁𝑆𝑆 = 0𝑑𝑑𝑑𝑑 and 𝑀𝑀 = 14, the BER is reduced by 0.4257 compared to the traditional MMSE detector. The simulation results revealed that (𝑀𝑀 = 14,𝑁𝑁𝑇𝑇 = 8) system provides the best BER performance. Figure 6: The BER versus SNR for different array sizes (𝑀𝑀 > 𝑁𝑁𝑇𝑇) synthesized using the same number of antenna elements 𝑁𝑁𝑇𝑇 = 𝑁𝑁𝑅𝑅 = 8 compared to the traditional MMSE detector in a 8 Γ— 8 MIMO system. Figure 7: The BER performance degradation of the proposed MMSE detector at (𝑀𝑀 β‰₯ 15,𝑁𝑁𝑇𝑇 = 8) for a 8 Γ— 8 MIMO system. 5. Conclusion In this paper, new detection techniques based on antenna arrays synthesis for maximum gain have been introduced. The achieved array gain significantly enhanced the signal to noise ratio of the system giving rise to better BER performance. 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