Performance Analysis of a Combined STBC-SVD MIMO-OFDM System
Mohamed Shawky Osman
Faculty of Engineering
Port-Said University
Port-Said, Egypt
Sherif Mohamed Abuelenin
Faculty of Engineering
Port-Said University
Port-Said, Egypt
Heba Yousef Soliman
Faculty of Engineering
Port-Said University
Port-Said, Egypt
Khairy Sayed Al-Barbary
Faculty of Engineering
Suez-Canal University
Ismailia, Egypt
International Journal of Enhanced Research Publications, ISSN: XXXX-XXXX
Vol. 2 Issue 4, April-2013, pp: (1-4), Available online at: www.erpublications.com
Abstract—In this paper we introduce a combined Singular Value Decomposition (SVD) Alamouti Space Time Block Coding (STBC) for future generation WLANs. The introduced scheme improves the Symbol Error Rate (SER) performance of Multiple-Input Multiple-Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) systems. The scheme is applied on a (2×2) MIMO antenna configuration. MATLAB® simulations show that the proposed system performed better over its Alamouti-STBC and SVD counterparts .
Keywords—Multiple-Input Multiple-Output (MIMO); Space Time Block Code (STBC; Singular Value Decomposition (SVD); Symbol Error Rate (SER).
I. Introduction
Multiple-Input Multiple-Output (MIMO) systems [1] use multiple transmit and receive antennas to achieve high spectral efficiency for increased throughput using the same bandwidth. Multipath propagation usually occurs and causes the MIMO channels to be frequency selective [2]. To combat the effect of frequency selective fading, MIMO is generally combined with orthogonal frequency-division multiplexing (OFDM) technique. OFDM transforms the frequency selective fading channels into parallel flat fading sub channels [2]. MIMO-OFDM technique has been adopted in the WLAN standards of IEEE 802.11 [3], [4] and the IEEE 802.16 [5], [6]. Different techniques are used to enhance the performance of MIMO-OFDM systems such as Space Time Block Coding (STBC) and Singular Value Decomposition (SVD). STBC improves the performance by exploiting spatial diversity [7]; its utilization enhances the bit error rate (BER) performance of WLANs [8], [9], [10]. SVD [11] can be used to decompose the MIMO channel matrix H into a set of equivalent independent and parallel single-input single-output (SISO) channels. SVD provides the gains of these independent channels, which can be used to find weightings for the transmitting and receiving antennas. This allows antenna beamforming and greatly increases the system performance [12].
In this paper, we study the performance of a combined STBC-SVD scheme in WLANs and evaluate the SER of the combined system with two transmitting and two receiving antennas. The rest of the paper is organized as follows. Section II presents MIMO techniques that are used in this paper. Section III outlines the structure of the STBC-SVD combined system. Results and analysis of the system are shown in section IV. The conclusion is presented in section V.
II. MIMO TECHNIQUES
Use of efficient coding scheme can improve the performance of MIMO-OFDM systems [13]. This section discusses two common MIMO coding techniques; STBC and SVD.
A. Space Time Block Coding
In STBC, the coding is applied over temporal and spatial dimensions [10]. Adding redundancy improves system performance. In [14] Alamouti proposed a simple transmit diversity scheme. The scheme was generalized later by Tarokh [15] to form the class of Space Time Block Codes. STBC codes achieve the same diversity advantage as maximal ratio combining (MRC). The transmit diversity scheme can be easily applied to OFDM in order to achieve a diversity gain over frequency selective fading channels [8], [9]. In Alamouti's encoding scheme two signals are transmitted simultaneously from the two transmitting antennas. The transmission matrix is given by [7]:
G = (1)
where, in the case of OFDM, x1, x2 are the transmitted signals on a given subcarrier k (from two consecutive OFDM symbols) [10].
Fig. 1: STBC MIMO-OFDM system.
Fig.1 shows a block diagram of the STBC MIMO-OFDM system.
The system first encodes the signal using Alamouti coding. The signal is converted to parallel format before having its IFFT computed. Next, a cyclic prefix (CP) is inserted. A part of the OFDM time-domain waveform is replicated from the back to the front to create a guard period. Duration of the guard period must be longer than the worst-case delay spread of the target multi path environment [16]. Finally, parallel to serial conversion (P/S) is applied before transmission at each antenna.
B. Singular Value Decomposition
One of the most important approaches used to realize a MIMO system is the Singular Value Decomposition (SVD). SVD can be used to decompose the MIMO channel matrix into a set of equivalent independent parallel single-input single-output (SISO) channels. SVD also gives the gains of these SISO channels. These gains are used to calculate weightings for the transmitting and receiving antennas. With aid of the SVD [11] any MIMO channel encountered by a system employing Nt transmit antennas and Nr receive antennas represented by Nr x Nt matrix H may be decomposed as:
(2)
where, S is an Nr x Nt non-negative and diagonal matrix, while U and V are Nr x Nr and Nt x Nt unitary matrices, respectively. Furthermore, the diagonal entries of S are the non-negative square roots of the eigenvalues of the matrix H. If the transmitter transmits VX, where X is the Nt-element transmitted signal vector emanating from the Nt antennas, then the Nr-element received signal vector Y’ may be expressed using the following equation as:
(3)
where n’ is the Nr-element Additive White Gaussian Noise (AWGN) vector. Note that the multiplication of both sides of equation (3) by UH and the multiplication of X by V have only a scaling effect [17]. Hence, we can decouple Y’ into:
(4)
Where we have Y is the estimated signal and n = UHn’. In the SVD MIMO-OFDM system shown in Fig.2, we use two transmitting and two receiving antennas, then S is a diagonal Fig. 2: SVD MIMO-OFDM system.
matrix having two singular values (which are the non-negative
square roots of the eigenvalues of HHH) on its diagonal. Hence, the ith element of Y, i.e. yi depends only on the ith element of X, i.e. on xi and the ith diagonal element of S [16]. Therefore, if X carries different information then multiplexing gain is obtained. While, if X carries identical information then diversity gain is obtained.
III. COMBINED STBC-SVD SYSTEM MIMO TECHNIQUES
A simplified structure of (2×2) combined MIMO system is illustrated in Fig. 3. The incoming bit stream is mapped onto phase shift keying (PSK) constellation points then passed into the Alamouti-STBC encoder. Each of the two output substreams of the STBC encoder is multiplied by the V component matrix, and then OFDM modulated before transmission. Accordingly, the two symbols are transmitted using two antennas over two consecutive symbol periods.
We can write the system received signal equation over two symbol period for a certain subchannel as follows:
= . . + . (5)
where the two subscripts denotes the receiving antenna and the transmitting antenna, consecutively. The received signal is then postcoded by multiplying it by :
= . . . + . (6)
We transform the (2 x 2) channel matrix into simple (2 x 2) S diagonal matrix as follows:
=.+ (7)
Then, a simple decoding algorithm similar to STBC decoding is applied as follows:
(8)
(9)
Fig. 3: The STBC-SVD combined system.
where y1 and y2 are the estimation of the received signals at x1 and x2 respectively, N1 = n1 + n4 and N2 = n2 + n3.
III. RESULTS AND DISCUSSIONS
We performed simulations of the proposed system using MATLAB®. We assumed perfect channel response information to be available for both the transmitter and receiver. System parameters are listed in TABLE 1 below.
We compare the performance of the proposed system to that of STBC and SVD based systems. The comparison is based on calculating the SER in each in a multipath fading channel. A MIMO link with fixed OFDM by assigning a fixed number of data bits on each subcarrier for a fair comparison throughout the simulation. Fig. 4 shows the comparison between (2x2) STBC, (2x2) SVD and (2x2) combined system. By observing the figure above, we can easily tell that the (2x2) combined MIMO-OFDM system has the best performance, followed by the (2x2) STBC system then (2x2) the SVD system.
TABLE I. Fixed Simulation Parameters
Parameters / ValueNumber of subcarrier / 64
OFDM symbol / 64 symbol periods
Guard interval (GI) / 16
Modulation scheme / BPSK
Power delay profile
( TGn channel model D “Typical office“) /
Fig. 4: SER for (2x2) STBC and (2x2) SVD compared to (2x2) combined MIMO-OFDM system.
Fig. 5: SER for (3x2) STBC and (3x3) SVD compared to (2x2) combined MIMO-OFDM system.
Moreover, Fig.5 above shows a performance comparison between the introduced system and the performances of a (3x2) STBC and (3x3) SVD systems. The figure clearly shows that the combined (2x2) system performs approximately to the (3x2) STBC system and outperforms the (3x3) SVD system with respect to the SER. This indicates that the combined system can be used to reduce the system physical complexity as it saves including additional antenna in the receiving side of the STBC systems.
IV. CONCLUSION
In this paper a combined (2x2) STBC-SVD scheme was investigated for next generation WLANs. This scheme combines SVD and Alamouti STBC techniques to provide both increased throughput and diversity. Performance results for MIMO-OFDM WLANs employing the combined technique were presented and compared to the STBC and SVD MIMO-OFDM systems. Symbol Error Rate performance results under IEEE TGn (Task Group N) D channel [18] verifies the superiority of the proposed STBC-SVD combined scheme relative to a standard (2x2) Alamouti STBC and (2x2) SVD approaches. In addition, the combined system with two transmitting and two receiving antennas approximately gave the same results of the STBC system with two transmitting and three receiving antennas and outperform the SVD system with three transmitting and three receiving antennas which means that a reduction in physical complexity is obtained using the proposed system.
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