Energy Efficient MIMO Wireless Communication Systems Performance Analysis

Energy Efficient MIMO Wireless Communication Systems Performance Analysis

Ngosa Willie1, Jin Wang2

Department of Electronics Engineering, Tianjin University of Technology and Education, Tianjin, P.R, China

Abstract

Multiple Input Multiple Output (MIMO) systems with multiple antenna elements at both Transmitter and Receiver ends are an efficient solution for future wireless communications systems. They provide high data rates by exploiting the spatial domain under the constraints of limited bandwidth and transmit power. Space-Time Block Coding (STBC) is a MIMO transmit strategy which exploits transmit diversity and high reliability. The proposed work presents a comprehensive performance analysis of orthogonal space-time block codes (OSTBCs) with transmit antenna selection under uncorrelated Rayleigh fading channel employing Alamoutis code. The transmitted symbols belong to BPSK, QPSK and Quadrature amplitude modulation (QAM). The objective of this paper is to analyze the performance of MIMO wireless systems in Rayleigh channel using various modulations schemes such as BPSK, QPSK, 16-QAM, and 64-QAM

1. Introduction

   Multiple Input Multiple Output (MIMO) technology holds the promise of higher data rates with increased spectral efficiency. All commercial wireless systems operate in high multipath environments and it is the benefit of multipath that provides the performance improvement when using multiple antenna configurations [1]. Diversity is often used in wireless channels to combat multipath fading effect. The main idea behind diversity is to provide different replicas of the transmitted signal to the receiver [2]. If these different replicas fade independently, it is less probable to have all copies of the transmitted signal in deep fade simultaneously and the receiver can reliably decode the transmitted signal. The replica of the

   transmitted signal can be sent through different means, MIMO utilizes Antenna diversity to combat fading by combining signals from two or more independently faded channels. [3].In this paper, we have used Alamouti Space Time Coding (STC) that sends the same user data to both transmit antennas. The remainder of the paper is organized as follows: Section 2 defines the MIMO system model; section 3 provides a theoretical analysis. Section 4 shows the performance analysis of the channel and its impact on the performance of OSTBC .In section 5, we summarize the study.

2. MIMO System Model

   In a MIMO system where there are M transmit and N receive antennas as shown in fig. 1.0 below, the transmitted data signals pass through multiple paths to get to the receiving antennas. Though not shown on the diagram, but there is also noise that interferes with the data signals along the paths [4].

   In order to design efficient communication algorithms for MIMO systems and to understand the performance limits, it is important to understand the nature of the MIMO channel. For a system with M transmit antennas and N receive antennas, assuming frequency-flat fading over the bandwidth of interest, the MIMO channel at a given time instant may be represented as an M x N matrix.

   y1

   x1 p1

   p2

   pM

   n1

   y

   y

   x h

   2

   2

   2

   2

   n

   n

   h h 2

   =

   21 22

   2M +

   (1.2)

   y N

   xM hN1

   hN 2

   hNM

   nM

   From which the received signal vectors are;

   Figure 1.0 Basic M-transmit by N-receive MIMO system

   y1 x1p1 x2 p2 …………… xM pM n1

   y2 x1p1 x2 p2 …………… xM pM n2

   Figure 1.0 above shows a MIMO transmission systems consisting of M transmit antennas and N receive antennas. The channel H is presumed to be a rich scattering environment. MIMO uses the multi antenna spatial diversity at both ends of the link, treating the multiplicity of the different scattering paths as separate parallel sub channels.

   yN x1hN1 x2 hN 2 …………… xM pM nN

   For a 2×2 MIMO system, the expression for equation (1.1) reduces to;

   y1 = p1

   p2 x1

   + n1

   (1.3)

   y h

   h x

   n

   The received signal vector y can be expressed in terms of the channel matrix H as:

   2 21

   22 2

   2

   y = Hx + n (1.1)

   Where,

   y is the received signal vector

   x is the transmitted signal vector

   n is the additive white Gaussian noise vector with zero mean and a variance of 2

   Equation 1.1 can also be represented as a system of linear equations given by:-

3. Space-Time Block Coding (STBC)

One of the methodologies for exploiting the capacity in MIMO system consists of using the additional diversity of MIMO systems, namely spatial diversity, to combat channel fading. This 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 [5]. The antennas in a MIMO system are used for supporting a transmission of a SISO system since the targeted rate of is that of a SISO system. 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 Nt transmit antennas and Nr

receive antennas has potentially full diversity (i.e.

maximum diversity) gain equal to

Nt xN 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).

1. The Alamouti 2×2 MIMO Scheme

   Where * denotes complex conjugation. A generalized code matrix for Alamouti 2×2 is shown below.

   The encoding and transmission sequence for the two

   s1

   s2

   transmit antennas in the Alamouti scheme is shown in

   G2

   s* s*

   (1.4)

   Table 1 [6]

   Table 1: Encoding and transmission sequence for the Alamouti two transmit antennas.

   2 1

   Time

   Time

   Space

2. Orthogonal Space Time Block Coding

   (OSTBC)

   	Antenna 1	Antenna 2
   Time t	s1	s2
   Time t + T	2	s* 1

   • s*

   	Antenna 1	Antenna 2
   Time t	s1	s2
   Time t + T	2	s* 1

   • s*

   In this section, we consider another type of STBC called orthogonal space time block codes (OSTBC) for the case of 3 and 4 transmit antennas. The transmit diversity scheme designed by Alamouti can be used only in a system with two transmit antennas. It turns out that this technique belongs to a general class of codes named Space-Time Block Codes or, more precisely, Orthogonal STBCs, since they are baed on the theory of orthogonal designs. The authors of [8] introduced the theory of generalized orthogonal designs in order to create codes for an arbitrary number of transmit antennas. The general idea behind STBCs construction is based on finding coding matrices X that can satisfy the following condition:

   XX H

   p n | x |

   i

   i

   i1

   2

   .IM

   T

   (1.5)

   In this equation, X H

   is the Hermitian of X, p is a

   M

   M

   constant, I

   T

   is the identity matrix of size MT xM T ,

   Figure 2.0 Space Time Coding with Two transmit

   and two receive antenna

   MT represents the number of transmit antennas, and n

   is the number of symbols xi transmitted per

   The data input is first modulated using any of the M- ary modulation schemes. The encoded symbols are then sent to Alamouti STBC encoder. In this system, two different symbols are simultaneously transmitted from the two antennas during any symbol period. During the first time period t, the first symbol in the sequence, s1 is transmitted from antenna 1 while the second symbol, s2 is simultaneously transmitted from antenna

   2

   2

   s

   s

   1

   1

   2. During the next symbol time t + T, the signal s* is transmitted from antenna 1 and the signal * is transmitted from antenna 2 [7].

   transmission block in X. The generalized theory of orthogonal design is exploited to provide codes that satisfy Equation 1.5. The orthogonality property of STBCs is reflected in the fact that all rows of X are orthogonal to each other. In other words, the sequences transmitted from two different antenna elements are orthogonal to each other for each transmission block. [8]

   The Alamouti scheme discussed in Section 3.1 of this paper is part of a general class of STBCs known as Orthogonal Space-Time Block Codes (OSTBCs) [8]. The authors of [9] apply the mathematical framework of orthogonal designs to construct both real and

   complex orthogonal codes that achieve full diversity. For the case of real orthogonal codes, it has been shown that a full rate code can be constructed [9]. However, for the case of complex orthogonal codes, it is unknown if full rate and full diversity codes exist for Nt > 2 [8]. Complex modulation techniques are of interest in this paper and therefore real orthogonal codes are not discussed.

3. Orthogonal Space-Time Block Codes

   With the code matrix G4 , four symbols are taken at a time and transmitted via four transmit antennas in eight time slots, resulting in a transmission rate of 1/2 as well.

4. OSTBC with a rate of 3/4

for Nt = 3 and Nt =4

The following code matrices H 3

and H 4

are

For any arbitrary complex signal constellation, there are OSTBCs that can achieve a rate of 1/2 for any given number of Nt transmit antennas. For example, the code

complex generalized designs for OSTBC with rate 3/4 for three and four transmit antennas, respectively [9]

matrices G3 and G4 are OSTBCs for three and four

s s

s3

transmit antennas, respectively and they have the rate 1/2 [9].

1 2

s2

s* s*

3

2 1

H 3 s* s*

(s

2

s* s* )

(1.8)

s1 s2 s3

3 3 1 1 2

s s s

2 2 2

2 1 4

s* s* (s s* s s* )

3

3

4

4

1

1

s s s

3 3 2 2 1 1

G

(1.6)

2 2 2

3 s4 s3 s2

s

s

s

s

s

s

* * *

1 2 3

2

2

s

s

s*

* s*

As can be observed, (1.8) transmits 3 symbols every 4

4

4

1

1

s* s* s*

time intervals, and therefore has rate 3/4.

3 4 1

s* s* s*

4 3 2

With the code matrix G3 , four complex symbols are taken at a time and transmitted via three transmit

s s s3

s3

antennas in eight time slots. Thus, the symbol rate is 1/2

1 2

s

s

2 2

s

s* s* 3

3

(1.9)

2 1 2 2

s

s

1 1 2 2

1 1 2 2

2 2 1 1

2 2 1 1

3

3

s1 s2

s3 s4

H 4 *

s

s

3

* (s s* s s* )

(s s* s s* )

s2

s1 s4

s3

2 2 2 2

2 2 1 1

2 2 1 1

s3 s4

s1 s2

s

3

s3

(s s* s s* )

(s s* s s* )

1 1 2 2

s

G 4

• s3 s2

s1

(1.7)

2 2 2 2

4 s* s* s* s*

1 2 3 4

Obviously, some transmitted signal samples are scaled

2

2

s

s

s

s

s*

* s* *

linear combinations of the original symbols.

4

4

1

1

3

3

s* s* s* s*

3 4 1 2

s* s* s* s*

4 3 2 1

1. Simulations

   Simulations were done in MATLAB using the Rayleigh channel model. The Rayleigh model assumes NLOS, and is used for environments with a large number of scatterers. The Rayleigh model has independent identically distributed (i.i.d.) complex, zero mean, unit variance channel elements and is given

   by [10]. We simulate G2 , G3 , G4 ,

   H 3 , and

   H 4 ,

   for the case of Nt

   = 1 up to Nr

   = 4. We modulate

   using BPSK, QPSK, 4-QAM, 16-QAM, and 64-QAM

   gray mapping constellations. For each sample, blocks of 104 symbols are simulated until at least 100 bit errors are obtained, or until 104 blocks are simulated. The simulation is stopped when the SNR reaches 40dB or after simulating 104 blocks without errors. Consequently, each value obtained for the bit-error rate (BER) of 107 with 100 errors has a 99.9% confidence level.

2. Simulation Results and Analysis

Figure 3: Bit error rate versus SNR of OSTBC for Nr = 1.

For the case Nr = 1. The result is shown in Figure 3 above. As expected, for each different code blocks, the performance degrades as more bits per symbol are transmitted. It can be observed that for a particular modulation and high SNR, the best performance is

obtained by G4 followed by H 4 , G3 , H 3 , and G2 .

Keeping all other variables the same, the results obtained for BPSK and QPSK are nearly identical, and we therefore present data for QPSK and omit that of BPSK. Since the data is nearly identical, the reader can safely assume that the performance of BPSK is that of QPSK. We study the performance of each block code discussed earlier for the different cases of

However, for any modulation and low SNR, G3 out performs H 4 even when H 4 greater gain has. The result is that the best performance at low SNR is obtained by G4 followed by G3 , H 4 , H 3 , and G2 .

constant Nt

Nr , rate, and diversity order

Figure 4: Bit error rate versus SNR of OSTBC for Nr = 4.

Figure 4 shows the case where Nr is fixed to 4. As can be observed, for a particular modulation, the best

performance is obtained by G4

followed

by G3 , H 4 , H 3 , and G2 . This order is the same as for

the case of Nr = 1 and low SNR where G3

outperforms

H 4 even with

H 4 having higher gain.

One possible reason for this behaviour is that the higher rate of H 4 causes lower channel gain per symbol and therefore higher BER for a particular SNR.

The BER curve for the case of keeping Nt = 4 constant while varying Nr from 1 to 4 for different modulations is depicted in Figure5 below.

Figure 6: Bit error rate versus SNR of OSTBC at 3 bits/sec/Hz.

In order to fairly compare all the block code schemes, a comparison with equal data rate and a comparison with equal diversity gain is needed. For the case of equal data rate, we simulate H 3 and H 4 with constellation 16-QAM, and G3 and G4 with constellation 64 QAM. Since H 3 and H 4 have code rate 3/4, using 16-QAM (4 bits/symbol) leads to 3 bits/sec/Hz. Similarly, since

G3 and G4 have code rate 1/2, using 64-QAM (6

Figure 5: Bit error rate versus SNR of OSTBC for Nt = 4.

It can be observed that for any modulation and block code, the gain of using 3 more antennas is approximately 14dB. However, between Nr = 1 and Nr

= 2 the gain is approximately 8dB, between Nr = 2 and Nr = 3 the gain is approximately 4dB, and between Nr

= 3 and Nr = 4 the gain is approximately 2dB. This result suggests diminishing returns as Nr increases. Another observation is that for any Nr and modulation

bits/symbol) leads to 3 bits/sec/Hz. The result for Nr = 1, Nr = 2, and Nr = 4 is presented in Figure 7. As expected, having more receive diversity leads to better performance on all cases. In general, there is a 3dB gain when using the 16-QAM lower order constellations with higher code rate 3/4 over using the 64-QAM higher order constellation with lower code rate 1/2 for the same number of transmit antennas. It is particularly interesting to notice that at high SNR and Nr = 1, 64-QAM G4 outperforms 16-QAM H 3 while

at low SNR and Nr = 1, 16-QAM H 3 outperforms 64-

scheme, G3

and G4

has a 3dB gain over H 3

and

QAM G4

H 4 respectively. An interesting observation is that the

performance of G4

with Nr = 2 is similar to that of

H 4 with Nr = 3, while G4

with Nr = 1 is

outperformed by H 4 with Nr = 2, and G4 with Nr = 3 outperforms H 4 with Nr = 4.

Figure 7: Bit error rate versus SNR of OSTBC with spatial diversity 12.

Figure 7 displays a BER curve for the case of equal diversity gain. To accomplish this, we simulate G2 with Nr = 6, G3 and H 3 with Nr = 4, and G4 and H 4 with Nr = 3. The diversity gain in each case is therefore 12. From Figure 7 we see that having fewer number of transmit antennas and more number of receive antennas results in better performance. G3 and H 3 with Nr = 4 have a 2dB performance gain over

way of increasing capacity. Employing multiple antennas at transmitter as well as both transmitters and receiver sides enables considerable performance enhancement in wireless communications systems.

We have provided a basic overview of MIMO systems and briefly discussed a basic introduction to Space- Time Coding provided by presenting Alamoutis scheme. We then discussed block codes schemes with different code rates for the cases of 3 and 4 transmit antennas. Simulation results were then presented. It was observed that higher diversity gain does not always imply better performance. This was observed when G3

outperformed H 4 at low SNR for Nr = 1 and at any SNR for Nr = 2 up to Nr = 4. Similarly, it was observed that equal diversity gain does not imply equal performance. This was particularly demonstrated when G3 outperformed all others for equal diversity gain. The penalty of having more transmit antennas, which consequently reduces the energy per transmit antenna was observed. Also, we observed diminishing returns for every scheme as the number of received antennas increased. It was particularly interesting to find that although H 3 and H 4 have higher rate than G3

and G4 , the performance of G3 and G4 is greater and could therefore be preferred in some scenarios.

G4 and G4

with Nr = 3 respectively. It is also

interesting to see that G2 with Nr = 6 has similar performance as to G4 with Nr =3. This observation suggests that there is an upper limit at which using few Nt transmit antennas and more Nr receive antennas becomes equivalent to using more Nt transmit antennas and fewer Nr receive antennas. This is conceived to be more economical and practical as, for example, it would only require multiple antennas at the base station in comparison to multiple antennas for every mobile in a cellular communications system

5.0 Conclusion

This paper has presented an investigation into the performance of MIMO wireless systems in Rayleigh channel using various modulations schemes such BPSK, QPSK, 16-QAM, and 64-QAM, and has

focused on techniques for improving the system performance and spectral efficiency. It has investigated techniques that exploit Space time block coding as a

6.0 References

[1]. Carmela Cozzo, and Brian L. Hughes, Space Diversity in Presence of Discrete Multipath Fading Channel IEEE Transactions On Communications, Vol. 51, No. 10, October 2003

[2]. Hamid Jafarkhani Space-Time Coding Theory And Practice , university Of California, Irvine

[3]. G. J. Foschini and M. J. Gans, On limits of wireless communication in a fading environment when using multiple antennas, Wireless Pers. Communication., vol. 6, no. 3, pp. 311355, Mar. 1998.

1. A. S. Mindaudu and A. M. Miyim BER Performance of MPSK and MQAM in 2×2 Alamouti MIMO Systems, International Journal of Information Sciences and Techniques (IJIST) Vol.2, No.5, September 2012

2. J. Winters, On the capacity of radio communication systems with diversity in a Rayleigh fading environment, IEEE Journal on Selected Areas in Communications, vol. 5, no. 5, pp. 871878, 1987.

[6]. S. M. Alamouti, A simple transmitter diversity scheme for wireless communications, IEEE J. Select. Areas Commun., vol. 16, pp. 14511458, Oct. 1998.

[7]. A. J. Paulraj and B. C. Ng, Spacetime modems for wireless personal communications, IEEE Pers. Commun.

Mag., pp. 3648, Feb. 1998

1. G. Tsoulos, MIMO system technology for wirelesscommunications. CRC Press, 2006.

2. V. Tarokh, H. Jafarkhani, and A. Calderbank, Space-time block codes from orthogonal designs, IEEE Transactions on Information Theory, vol. 45, no. 5, pp. 14561467, 1999.

3. G. J. Foschini and M. J. Gans, On limits of wireless communications in a fading environment when using multiple antennas, Wireless Personal Communications, vol. 6, pp. 311-335, 1998