International Journal of Computer & Organization Trends –Volume 3 Issue 10 – Nov 2013
The Evaluation Of The Performance Of Space–Time Block Codes In Wireless Communications Dindigala Pallav Kumar#1, Rapaka Satish*2 #1
#2
M.Tech, Department of E.C.E & Sir C.R.Reddy College of Engineering Asst.Proffesor, Department of E.C.E & Sir C.R.Reddy College of Engineering Eluru, India
Abstract-- Traditionally, wireless communication entails a sender using a single antenna to transmit a signal and then received by a single antenna at the receiver. In a Multiple-input, Multipleoutput (MIMO) scheme, on the other hand, the sender uses multiple antennas for transmission, and the receiver uses multiple antennas for reception, to increase the data rate by sending different data streams on the different channels. Alternatively, by sending the same signal on each of the different channels, the bit error rate (BER) performance at the receiver can be improved. This project studies the performance of Multiple-Input Multiple-Output (MIMO) systems that use SpaceTime Block Coding (STBC). We propose a systematic method for designing a space-time orthogonal MIMO scheme that employs an arbitrary number of transmitting and receiving antennas, and we evaluate the performance improvements that can be attained by employing our design approach. Key words: Wireless communication, MIMO systems, Diversity, Space–Time Block Codes (STBC), Beam forming, Multipath channels.
I.
Introduction
Wireless networks widely used today include: cellular networks, wireless mesh networks (WMNs), wireless Local Area Networks (WLANs), personal area networks (PANs), and wireless sensor networks (WSNs). The increasing demand for these networks has turned spectrum into a precious resource. For this reason, there is always a need for methods to pack more bits per Hz. A particular solution that has caught researcher‟s attention is the use of multiple antennas at both transmitter (Tx) and receiver (Rx) and such a system is called a Multiple-Input Multiple-Output (MIMO) system. In most situations, due to destructive addition of multipath in the propagation Media and to interference from other users the wireless channels are suffered from attenuation. Most probably the channels are Rayleigh and the main problem with Rayleigh channels are, makes it difficult for the receiver to reliably determine the transmitted signal unless some less attenuated replica of the signal is provided to the receiver. This technique is called as “diversity”, which can be provided using temporal, frequency, polarization, and spatial resources [1], [2], [3]–[4], [5], [6], [7]. To provide significant gain over the communication channel which deals by MIMO, the space– time block coding has been proposed [12] which combines signal processing at the receiver with coding techniques appropriate to multiple transmits antennas. The advantages of
ISSN: 2249-2593
the spatial time block coding are, signal can be coded through the transmit antennas; creating redundancy, which reduces the outage probability and the bandwidth efficiency increases up to three–four times that of current systems. A set of streams can be transmitted in parallel, each using a different transmit antenna element. The receiver can then perform the appropriate signal processing to separate the signals. The aim of this paper is the evaluation of the performance of the space–time block codes and to provide the details of the encoding and decoding procedures. We then provide simulation results confirming that with space–time block coding and multiple transmit antennas, a significant performance gain can be achieved at almost no processing expense. The remaining of this paper is discussed as follows. In Section II, the complete architecture of the system model is explained with the help of channel matrix and in the same section the channel matrix is introduced and briefly explained. Section III is the core part of this entire project, which is aimed to discuss about space time block coding with Alamouti‟s, Alamouti space time encoding STBC & Receiver of Alamouti scheme. Section IV is also a very important part of this paper, which explains the concept of Orthogonal Space-Time Block Codes. Finally, Section V presents simulation results and analysis of paper. II. System Model There are three important elements in MIMO system, named as transmitter (TX), channel (H), and the receiver (RX). Figure 1 depicts such MIMO system block diagram.
N t Is used to denote the number of antenna elements at the transmitter side, and N r denotes the number of antenna elements at the receiver.
http://www.ijcotjournal.org
Page 457
International Journal of Computer & Organization Trends –Volume 3 Issue 10 – Nov 2013 spacing, they are typically spaced at least λ c 2 where λ c is the wavelength of the carrier frequency [8]. The second reason correlation can occur is due to lack of multipath components. It is for this reason that rich multipath is desirable in MIMO systems. The multipath effect can be interpreted by each receive antenna being in a different channel. For this reason, the rank of a MIMO channel is defined as the number of independent equations offered. It is important to note that rank(H) min(N r , N t) ……. (3)
And therefore the maximum number of streams that a MIMO system can support is upper-bounded by min(N r , N t) Figure: 1 MIMO system block diagram
The channel with N r outputs and N t inputs is denoted as a N r N t matrix H.
h1,1 H h 2,1 h Nr,1
h1, 2 h2, 2 hN ,2 r
h1,N h2, N …….. (1) h N , N t
t
r
t
Where each entry of h i, j denotes the attenuation and phase shift (transfer -function) between the jth transmitter and ith receiver. Throughout this paper assumed that channel is fixed with in a transmission but varies randomly between burst to burst i.e. Channel behaves in a “quasi-static” fashion. Therefore the signal model for MIMO is defined as
r H S n ………. (2) H is the channel matrix of size N r N t , S is the transmitted data vector of size N t 1 , r is the received vector of size
Nr 1 and n is the noise vector of size N r 1 . Each noise element is considered as independent identically distributed (i.i.d) white Gaussian noise [8], [9] with variance N t (2.SNR) .
The Explanation for this model is, since we are using the same carrier frequency for all transmitting signals, all transmitted signals are mixed in the same channel. At the receiver side, the received signal is composed of a linear combination of each transmitted signal plus noise. The receiver can solve for the transmitted signals by treating as a system of linear equations [10]. If the channel H is correlated, the system of linear equations will have more unknowns than equations. One reason correlation between signals can occur is due to the spacing between antennas. To prevent correlation due to the
ISSN: 2249-2593
III.
Space-Time Block Coding
For exploiting the capacity of MIMO system, one of the best methodologies is of using additional diversity of MIMO system, especially “spatial diversity”. Spatial diversity can be achieved by transmitting several replicas of the same information through each antenna. By doing this, the probability of losing the information decreases exponentially [10]. Here the diversity order or diversity gain of a MIMO system is defined as the number of independent receptions of the same signal. A MIMO system with transmit antennas and N r receive antennas has potentially full diversity (i.e. maximum diversity) gain equal to N t . N r . The different replicas sent for exploiting diversity are generated by a space-time encoder which encodes a single stream through space using all the transmit antennas and through time by sending each symbol at different times. This form of coding is called Space-Time Coding (STC). Due to their decoding simplicity, the most dominant form of STCs is “Space-Time Block Codes (STBC)”. A. Alamouti’s STBC: The Alamouti‟s scheme is historically the first space-time block code to provide full transmit diversity for systems with two transmit antennas [12]. The Alamouti STBC scheme uses two transmit antennas and N r receive antennas and can accomplish a maximum diversity order of 2. N r . The Alamouti scheme has full rate (i.e. a rate of 1) since it transmits 2 symbols for every 2 time intervals. Next, a description of the Alamouti scheme is provided for both 1 and 2 receive antennas, followed by a general expression for the decoding mechanism for the case of N r receive antennas. B. Alamouti space time encoding: Figure 2, Shows the block diagram for Alamouti space time encoding with two transmitting Antennas. Assume that an M-
http://www.ijcotjournal.org
Page 458
International Journal of Computer & Organization Trends –Volume 3 Issue 10 – Nov 2013 ary modulation scheme is used. In the Alamouti‟s space-time encoder [5], each group of m information bits is first modulated, where m log M . Then, the encoder takes a block 2 of two modulated symbols x1 and x 2 in each encoding operation and maps them to the transmit antennas according to a code matrix given by x1 x 2 G2 ……. (4) x 2 x1
Figure: 2 Alamouti space time encoding
The encoders outputs are transmitted in two consecutive transmission periods from two transmit antennas. During the period of first transmission the two signals x1 and x 2 are transmitted simultaneously from antenna one and antenna two respectively. In the second transmission period, signal x is 2 transmitted from transmit antenna one and signal x from 1 Transmit antenna two, where x is the complex conjugate of 1 . It is clear that the encoding is done in both the space and x1 time domains. Let us denote the transmit sequence from antennas one and two by x1 and x 2 , respectively.
time „t‟ are denoted by h1(t) and h 2 (t) ,respectively. Assuming that the fading coefficients are constant across two consecutive symbol transmission periods, they can be expressed as follows h1(t) h1(t T) h1 eiθ1 h 2 (t) h 2 (t T) h 2 eiθ 2 ……………….. (8) Where h i and i are the amplitude gain and phase shift for the path from transmit antenna to the receive antenna, and T is the symbol duration.
At the receiver antenna, the received signals over two consecutive symbol periods, denoted by r1 and r2 for time t And t+T, respectively, can be expressed as r1 h1,1x1 h1,2x 2 n1 r2 h1,1x 2 h1,2x1 n 2 ………………………. (9)
x1 x1 x 2 x 2 x 2 x1
…………. (5) The key feature of the Alamouti‟s scheme is that the transmit sequences from the two transmit antennas are “orthogonal”, since the inner product of the sequences x1 and x 2 is zero, i.e.
x1.x 2 x1.x2 x 2 .x1 ……… (6) Therefore the code matrix has the following property X.XT X T .X I ………… (7)
Figure 3: Alamouti Space Time Receiving
For Alamouti STBC scheme there is No need of Channel State Information (CSI) at the transmitter and still now, it can be used with 2 transmit antennas and 1 receive antenna while accomplishing the full diversity of 2. In the following section we discuss, having more antennas at the transmitter and receivers side with accomplishing N r .Nt full diversity. IV.
Orthogonal Space-Time Block Codes
STBCs are originally studied as orthogonal i.e. the STBC is designed such that the vectors of any pair of columns are orthogonal.
C. Receiver of Alamouti scheme: Let us assume that one receive antenna is used at the receiver. The block diagram of the receiver for the Alamouti‟s scheme is shown in figure 3.The fading channel coefficients from the first and second transmit antennas to the receive antenna at
ISSN: 2249-2593
http://www.ijcotjournal.org
Page 459
International Journal of Computer & Organization Trends –Volume 3 Issue 10 – Nov 2013 A. OSTBC Encoder
α i,2 j Is the squared magnitude of the channel transfer function
The OSTBC Encoder block is used to encode the input symbol sequence by using orthogonal space-time block code (OSTBC) and the block maps the input symbols block-wise and concatenates the output codeword matrices in the time domain.
h i, j and to estimate the transmitted symbols s1 and s 2 , the calculated ~s and ~s are then sent to a Maximum Likelihood 1
2
(ML) decoder respectively. Case 2: 2 Receive Antennas: The received symbols for the case of two receive antennas, [14] are:
r1(1) h1,1S1 h1,2S2 n1(1) r1(2) h1,1S2 h1,2S1 n1(1)
Fig 4: OSTBC Encoder
N is Number of transmit antennas and N may be 2, 3, 4... For N = 2, R must be 1. For N = 3 or 4, R can be 3/4 or 1/2, indicated by Rate and T is time domain length. Specifically, for N = 2 or R = 1/2, T must be a multiple of 2 and when R = 3/4, T must be a multiple of 3 on the output T/R is the symbol sequence length. B. OSTBC Encoding Algorithms
r2(1) h 2,1S1 h 2,2S2 n (1) 2 r2(2) h 2,1S2 h 2,2S1 n (2) 2 ……………………. (12) The combined signals are
~s (α 2 α 2 α 2 α 2 )S h n (1) h n (2) h n (1) h n (2) 1 1,1 1,2 2,1 2,2 1 1,1 1 1,2 1 2,1 2 2,2 2
Several different OSTBC encoding algorithms are supported by OSTBC Encoder block depending on the selection for Rate and Number of transmit antennas.
~s (α 2 α 2 α 2 α 2 )S h n (2) h n (1) h n (2) h n (1) 2 1,1 1,2 2,1 2,2 2 1,1 1 1, 2 1 2,1 2 2, 2 2
Case 1: ‘1’ Receive Antenna: Decoding of the signal depends on the number of active receive antennas available at R x . The receive signals for the case of one receive antenna are
Decoding decision statistic of Nr receives antennas:
r1(1) r1 (t) h1,1S1 h1,2S2 n1(1)
r1(2) r1 (t T) h1,1S2 h1,2S1 n1(2) ………….. (9)
r1 Is received signal at antenna 1, where h i.j is the channel Transfer function from the jth transmit antenna and the ith receive antenna1, n 1 is a complex random variable representing noise at antenna 1.
……………………. (13)
The Maximum Likelihood decoder decision statistic decodes in favour of s and s over all possible values, such that (16) 1 2 are minimized where is given by for Nt 2 2
2 Nr s1 (ri(1) )h i,1 ri(2) h i,2 S1 ψ S1 i1 2
2 Nr s 2 (ri(1) )h i,2 ri(2) h i,1 S2 ψ S2 i1
Nr Nt 2 ψ 1 h i, j i 1 j1
The received signals are combined as follows, before the received signals are sent to the decoder
~s h r (1) h r (2) 1 1,1 1 1,2 1 ~s h r (1) h r (2) 2
1,2 1
As discussed in this section the Orthogonal Space-Time Block Codes for 3 transmitting antennas, codes with 1/2 and 3/4 coding rate and full diversity 3N r
1,1 1
………………….. (10)
N t =3 & with full diversity Rate ½ the OSTBC codes are
(9) & (10) yields:
~s (α2 α2 )S h n (1) h n(2) 1 1,1 1,2 1 1,1 1 1,2 1 ~s (α 2 α 2 )S h n (2) h n (1) 2
1,1
1,2
2
1,1 1
1, 2 1
…………………. (11)
ISSN: 2249-2593
http://www.ijcotjournal.org
Page 460
International Journal of Computer & Organization Trends –Volume 3 Issue 10 – Nov 2013 s1 s2 s 3 s G3 4 s1 s 2 s3 s a
s2 s1 s4 s3 s 2 s1 s 4 s 3
s3 s4 s1 s2 s 3 s 4 s1 s 2
At every 8 time intervals this code transmits 4 symbols, and therefore has rate 1/2.
In this paper, the simulation results for proposed Alamouti STBC scheme is should be identical with the results of MRC, which is shown in below figure 5. From the simulation results it is clear that the estimate of the transmitted symbol with the Alamouti STBC scheme is identical to that obtained from MRC, the BER with above described Alamouti scheme should be same as that for MRC. However, there is a small catch. With Alamouti STBC, we are transmitting from two antennas. Hence the total transmits power in the Alamouti scheme is twice that of that used in MRC. To make the comparison fair, we need to make the total transmit power from two antennas in STBC case to be equal to that of power transmitted from a single antenna in the MRC case.
The decision metrics to minimize by the decoder for detecting s1 , s 2 s 3 and s 4 are given are 2
Nr 2 s1 ri(1) h i,1 ri(2) h i,2 ri(3) h i,3 ri(5) h i,1 ri(6) h i,2 ri(7) h i,3 S1 S1 i1 2
Nr 2 s 2 ri(1) h i,2 ri(2) h i,1 ri(4) h i,3 ri(5) h i,2 ri(6) h i,1 ri(8) h i,3 S2 S2 .. i1 2
Nr 2 s3 ri(1)hi,3 ri(3)hi,1 ri(4)hi,2 ri(5)hi,3 ri(7)hi,1 ri(8)hi,2 S3 S3 .. i1 2
Nr 2 s4 ri(2)hi,3 ri(3)hi,2 ri(4)hi,1 ri(6)hi,3 ri(7)hi2 ri(8)hi,1 S4 S4 .. i1 Similarly by applying the OSTBC scheme for higher order antennas and we can conclude this paper by providing simulation results and their analysis in following sections. Where
Fig 5: Simulation Results of Alamouti Scheme
With this scaling, we can see that BER performance of 2Tx, 1Rx Alamouti STBC case has a roughly 3dB poorer performance that 1Tx, 2Rx MRC case.
is defined as: Nr N t 2 1 2 h i , j i1 j1 V.
Simulation Results
In this section the simulation results for proposed method is discussed clearly with simulation results using MATLAB.
ISSN: 2249-2593
http://www.ijcotjournal.org
Page 461
International Journal of Computer & Organization Trends –Volume 3 Issue 10 – Nov 2013 [7] J. Winters, J. Salz, and R. D. Gitlin, “The impact of antenna diversity on the capacity of wireless communication systems,” IEEE Trans. Commun., vol. 42. no. 2/3/4, pp. 1740–1751, Feb./Mar./Apr. 1994. [8] A. Molisch, Wireless Communications. Wiley-IEEE Press, 2005. [9] G. Tsoulos, MIMO system technology for wireless communications. CRC Press, 2006. [10] D. Gesbert, M. Shafi, D. Shiu, P. Smith, and A. Naguib, “From theory to practice: an overview of MIMO space-time coded wireless systems,” IEEE Journal on selected areas in Communications, vol. 21, no. 3, pp. 281–302, 2003. [11] B. Vucetic and J. Yuan, Space-Time Coding, England, Wiley, 2003. [12] V. Tarokh, H. Jafarkhani, and A. Calderbank, “Space-time block coding for wireless communications: performance results,” IEEE Journal on selected areas in communications, vol. 17, no. 3, pp. 451–460, 1999. [13] S. M. Alamouti, "A simple transmit diversity technique for wireless communications", IEEE(R) Journal on Selected Areas in Communications, Vol. 16, No. 8, pp. 1451-1458, October 1998 [14] S. Alamouti, “A simple transmit diversity technique for wireless communications,”IEEE Journal on selected areas in communications, vol. 16,no. 8, pp. 1451–1458, 1998. [15] V. Tarokh, H. Jafarkhani, and A. Calderbank, “Space-time block codes from orthogonal designs,” IEEE Transactions on Information Theory, vol. 45, no. 5, pp. 1456–1467, 1999.
Fig 6: Performance comparison of STBC Similarly transmitting the same data on multiple transmit antenna does not provide diversity gain efficiently, since in the case of 2 transmit antenna case the resultant effective channel h1 h 2 is a Rayleigh channel again therefore the Bit Error Rate performance is identical to 1 transmit 1 receive Rayleigh channel case. If the transmit symbols are multiplied by a complex phase to ensure that the phases align at the receiver, there is diversity gain. However, the BER performance seems to be slightly poorer than the 1 transmit 2 receive MRC case. As we guess, the noise is scaled by
h1 h 2
BIO DATA
D.Pallv Kumar, pursuing his M.Tech degree in Sir C.R.Reddy college of Engineering, Affiliated to Andhra University. He was graduated from JNTU Kakinada in the year of 2011. Presently he is working as a MATLAB developer for ICOM Technologies, India.
in the case of transmit beam
forming, whereas the noise scaling is different in the case of Maximal Ratio Combining. Thus the simulation results are used to compare The Evaluation of the Performance of Space– Time Block Codes in Wireless Communications REFERENCES [1] N. Balaban and J. Salz, “Dual diversity combining and equalization indigital cellular mobile radio,” IEEE Trans. Veh. Technol., vol. 40, pp 342– 354, May 1991. [2] J.-C. Guey, M. P. Fitz, M. R. Bell, and W.-Y. Kuo, “Signal design for transmitter diversity wireless communication systems over Rayleigh fading channels,” in Proc. IEEE VTC’96, Apr. 1996, pp. 136–140. [3] A. Hiroike, F. Adachi, and N. Nakajima, “Combined effects of phase sweeping transmitter diversity and channel coding,” IEEE Trans. Veh. Technol., vol. 41, pp. 170–176, May 1992. [4] G. Raleigh and J. M. Cioffi, “Spatio-temporal coding for wireless communications,” in Proc. IEEE GLOBECOM’96, Nov. 1996, pp. 1809– 1814. [5] C.-E. W. Sundberg and N. Seshadri, “Coded modulation for fading channels: An overview,” invited paper, European Trans. Telecomm. Related Technol., pp. 309–324, May 1993.
R.Satish, presently working as an Assistant Professor in Sir C.R.Reddy Engineering College, Eluru. He has done much amount of work towards the new concepts in the era of Antennas & wave propagation, EMF theory. In this interesting journey he four conferences and published two journal papers in the span of just 8 years.He has great working knowledge in MATLAB and solved somany concpets.
[6] V. Weerackody, “Diversity for direct-sequence spread spectrum system using multiple transmit antennas,” in Proc. IEEE ICC’93, May 1993, pp. 1775–1779.
ISSN: 2249-2593
http://www.ijcotjournal.org
Page 462