PERFORMANCE ANALYSIS OF CLIPPED STBC CODED MIMO OFDM SYSTEM

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International Journal of Electronics and Communication Engineering & Technology

(IJECET) Volume 7, Issue 1, Jan-Feb 2016, pp. 28-44, Article ID: IJECET_07_01_004 Available online at http://www.iaeme.com/IJECET/issues.asp?JType=IJECET&VType=7&IType=1 Journal Impact Factor (2016): 8.2691 (Calculated by GISI) www.jifactor.com ISSN Print: 0976-6464 and ISSN Online: 0976-6472

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PERFORMANCE ANALYSIS OF CLIPPED

STBC CODED MIMO OFDM SYSTEM

Koiloth S R S Jyothsna and Tummala Aravinda Babu

Department of Electronics and Comunication Engineering Chaitanya Bharathi Institute of Technology

Gandipet, Hyderabad, India

ABSTRACT

A combination of Multiple-Input Multiple-Output Spatial Division Multiplexing technology and Orthogonal Frequency Division Multiplexing technique, namely MIMO-OFDM systems, been well-known as a potential

technology to provide high speed data transmission and spectrum efficiency to attain throughput of 1 Gbit/sec and beyond improves link reliability for

modern wireless communications. The rising development of Internet related contents and demand of multimedia services leads to increasing curiosity to high speed communications. It has been shown that by using MIMO system, it

is possible to increase that capacity considerably. To use advantage of MIMO diversity to overcome the fading then we need to send the same signals

through the different MIMO antennas and at the receiver end the different antennas will receive the same signals travelled through diverse paths. Efficient implementation of MIMO OFDM system is based on the FFT

algorithm and MIMO encoding like Alamouti Space Time Block coding (STBC). In this paper, MIMO-OFDM based on Almouti Space Time Block

Codes is described and the BER performance of this system is observed for various antenna configurations .The channel capacity per unit bandwidth is evaluated as a function of SNR and the MIMO channel capacity for different

transmit and receive antennas is observed. Finally, Peak to Average Power Ratio (PAPR) is reduced using clipping technique and the BER performance

of the ASTBC system with clipping and without clipping is observed.

Key words : MIMO, OFDM, STBC and PAPR

Cite this Article: Koiloth S R S Jyothsna and Tummala Aravinda Babu.

Performance Analysis of Clipped STBC Coded MIMO OFDM System. International Journal of Electronics and Communication Engineering &

Technology, 7(1), 2016, pp. 28-44. http://www.iaeme.com/IJECET/issues.asp?JType=IJECET&VType=7&IType=1

Performance Analysis of Clipped STBC Coded MIMO OFDM System


1. INTRODUCTION

MIMO (Multiple Input, Multiple Output) is an antenna technology for wireless

communications in which multiple antennas are used at both the source (transmitter) and the destination (receiver). The antennas at each end of the communications circuit

are combined to minimize errors and optimize data speed. MIMO is one of several forms of smart antenna technology, the others being MISO (Multiple Input, Single Output) and SIMO (Single Input, Multiple Output). In conventional wireless

communications, a single antenna is used at the source, and another single antenna is used at the destination. In some cases, this gives rise to problems with multipath

effects. When an electromagnetic field (EM field) is met with obstructions such as hills, canyons, buildings, and utility wires, the wave fronts are scattered, and thus they take many paths to reach the destination. The late arrival of scattered portions of the

signal causes problems such as fading, cut-out (cliff effect), and intermittent reception (picket fencing). In digital communications systems such as wireless Internet, it can

cause a reduction in data speed and an increase in the number of errors. The use of two or more antennas, along with the transmission of multiple signals (one for each antenna) at the source and the destination, eliminates the trouble caused by multipath

wave propagation, and can even take advantage of this effect.

MIMO technology has aroused interest because of its possible applications in

digital television (DTV), wireless local area networks (WLANs), metropolitan area networks (MANs), and mobile communications.

2. MIMO SYSTEM

MIMO systems are composed of three main elements, namely the transmitter (TX), the channel (H), and the receiver (RX). In NT is denoted as the number of antenna

elements at the transmitter, and Nr is denoted as the number of elements at the receiver. It is important to note that the system is described in terms of the channel. For example, the Multiple-Inputs are located at the output of the TX (the input to the

channel), and similarly, the Multiple-Outputs are located at the input of the RX (the output of the channel).

The channel with Nr outputs and Nt inputs is denoted as a Nr X Nt matrix

where each entry hi;j denotes the attenuation and phase shift (transfer function)

between the jth transmitter and the ith receiver. It is assumed that the MIMO channel behaves in a “quasi-static” fashion, i.e. the channel varies randomly between burst to burst, but fixed within a transmission. This is a reasonable and commonly used

assumption as it represents an indoor channel where the time of change is constant and negligible compared to the time of a burst of data. The MIMO signal model is

described as

r = Hs + n (1)

where, r is the received vector of size NR×1, H is the channel matrix of size NR ×NT , s is the transmitted vector of size NT×1, and n is the noise vector of size NR×1. Each

noise element is typically modelled as independent identically distributed (i.i.d.) white Gaussian noise, with variance NT=2. An explanation for this model is as follows. The



transmitted signals are mixed in the channel since they use the same carrier frequency. 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. 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 spacing, they are typically spaced at least c=2, where c is the

wavelength of the carrier frequency. 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 (NR;NT) and therefore the maximum number of streams that a MIMO system can support is upper-bounded by min(NR;NT). Since the performance of MIMO

systems depends highly on the channel matrix, it is important to model the channel matrix realistically. The following section provides an overview of typical channel models used for computer simulations.

3. SPACE–TIME BLOCK CODES (STBC)

Space–time block coding is a technique used in wireless communications to transmit

multiple copies of a data stream across a number of antennas and to exploit the various received versions of the data to improve the reliability of data-transfer. The fact that the transmitted signal must traverse a potentially difficult environment with

scattering, reflection, refraction and so on and may then be further corrupted by thermal noise in the receiver means that some of the received copies of the data will

be 'better' than others.

Transmit antennas

Time slots

An STBC is usually represented by a matrix as shown above. Each row represents a time slot and each column represents one antenna's transmissions over time. Here,

Sij is the modulated symbol to be transmitted in time slot i from antenna j. There are to be T time slots and nT transmit antennas as well as nR receive antennas. This block is usually considered to be of length T. The code rate of an STBC measures how

many symbols per time slot it transmits on average over the course of one block. If a block encodes k symbols, the code-rate is r=k/T. Only one standard STBC can

achieve full-rate Alamouti's code. STBCs as originally introduced, and as usually studied, are orthogonal. This means that the STBC is designed such that the vectors representing any pair of columns taken from the coding matrix are orthogonal. The

result of this is simple, linear, optimal decoding at the receiver.

3.1 ALAMOUTI Space Time Block Code

Alamouti code is the first STBC that provides full diversity at full data rate for two transmit antennas. Fig.1 shows the block diagram of the Alamouti space-time

encoder. S1= [ ,



Figure 1 A block diagram of the Alamouti space-time encoder

The information bits are first modulated using an M-ary modulation scheme. The encoder takes the block of two modulated symbols s1and s2 in each encoding

operation and hands it to the transmit antennas according to the code matrix

(2)

The first row represents the first transmission period and the second row the second transmission period. During the first transmission, the symbols s1 and s2 are

transmitted simultaneously from antenna one and antenna two respectively. In the second transmission period, the symbol

is transmitted from antenna one and the

symbol from transmit antenna two. It is clear that the encoding is performed in

both time (two transmission intervals) and space domain (across two transmit

antennas). The two rows and columns of S are orthogonal to each other and the code matrix is orthogonal

(3)

Where I2 is a (2 × 2) identity matrix. This property enables the receiver to detect s1 and

s2 by a simple linear signal processing operation. Let us look at the receiver side now. Only one receive antenna is assumed to be available. The channel at time t may be modelled by a complex multiplicative distortion h1(t) for transmit antenna one and

h2(t) for transmit antenna two as shown in equation 3.3 and 3.4. Assuming that the fading is constant across two consecutive transmit periods of duration T, we can write

h1(t)= h1(t+T)=h1= (4)

h2(t)= h2(t+T)= h2= (5)

Where, |hi | and θi , i = 1, 2 are the amplitude gain and phase shift for the path from

transmit antenna i to the receive antenna. The received signals at the time t and t + T can then be expressed as

= (6)

=

(7)

Where, r1 and r2 are the received signals at time t and t + T, n1 and n2 are complex random variables representing receiver noise and interference.

Information source

Alamouti

Code S

Modulator



3.2 Equivalent Virtual (2 × 2) Channel Matrix (EVCM) of the Alamouti

Code

Conjugating the signal r2 in that is received in the second symbol period, the received signal may be written equivalently as r

= (8)

=

(9)

Thus the equations 3.8 and 3.9 can be written as

=

+

(10)

or in short notation as

y = Hvs + (11)

Where, the modified receive vector y = [ ] T has been introduced. Hv will be

termed the Equivalent Virtual MIMO Channel Matrix (EVCM) of the Alamouti

STBC scheme. It is given by

Hv=

(12)

Thus, by considering of the elements of y as originating from two virtual receive antennas (instead of received samples at one antenna at two time slots) one could

interpret the (2 × 1) Alamouti STBC as a (2× 2) spatial multiplexing transmission using one time slot. The key difference between the Alamouti scheme and a true (2 ×

2) multiplexing system lies in the specific structure of Hv. Unlike to a general i.i.d. MIMO channel matrix, the rows and columns of the virtual channel matrix are orthogonall.

=

)I2 = I2 (13)

where I2 is the (2 × 2) identity matrix and h 2 is the power gain of the equivalent

MIMO channel with =(

). Due to this orthogonality the receiver of the

Alamouti scheme (discussed in detail in the following subsection) decouples the MISO channel into two virtually independent channels each with channel gain h2 and

diversity d = 2. It is obvious that the EVCM depends on the structure of the code and the channel coefficients. The concept of the EVCM simplifies the analysis of the STBC transmission scheme. The existence of an EVCM is one of the important

characteristics of STBCs.

3.3 ASTBC Based MIMO OFDM System Model

Consider a space time block coded MIMO-OFDM system equipped with transmit antennas and receive antennas as illustrated in Figure 2. The message bit sequence is

mapped into a sequence of BPSK symbols which will be converted into N parallel symbol streams after serial to parallel conversion. Each of the N parallel symbol

streams is then encoded by the space-time block code encoder

i=1,2,3.....NT

into where is the antenna index and is the symbol time index.



Figure 2 Block Diagram of MIMO OFDM System using STBC coding.

The number of symbols in a space-time codeword is N=NT×NR. Then the symbol streams are subjected to inverse fast Fourier transform operation followed by cyclic

prefix insertion between two consecutive OFDM symbols in order to reduce the effect of the delay spread of the multipath channels. The length of the CP is adjustable and must be set in order to keep a bandwidth efficient system without occurring inter

symbol interference or inter carrier interference. At the receiver, after removing the CP and applying FFT, the transmitted symbol stream

is estimated using the

received signal

Assume the channel gain follows the Rayleigh distribution

from the ith transmit antenna to jth the receive antenna over the tth symbol period. If the

channel gains do not change during T symbol periods, the symbol time index can be omitted and as long as the transmit antennas and receive antennas are spaced

sufficiently apart, NT NR fading gain {hij} can be assumed to be statistically

independent. If is the transmitted signal from the ith transmit antenna during tth

symbol period, the received signal at the jth receive antenna during tth symbol period is

given by

=

(14)

where is the noise process at the jth receive antenna during tth symbol period, which

is modelled as the zero mean circular symmetric complex Gaussian (ZMCSCG) noise of unit variance, and is the average energy of each transmitted signal.

In general we can write as

Y=

(15)

3.3.1 BER Performance Evaluation

In order to make an investigation of performance analysis of the MIMO-OFDM system with Alamouti Space Time Block Code as the transmit diversity and MRC

diversity technique as the receive diversity over a Rayleigh fading channel, we deal with MATLAB simulation using the parameters based on IEEE802.a standard. BPSK

modulation was used to determine the BER versus SNR performance of the system.



In digital transmission, the number of bit errors is the number of received bits of a data stream over a communication channel that has been altered due to noise,

interference, distortion or bit synchronization errors. The bit error rate or bit error ratio (BER) is the number of bit errors divided by the total number of transferred bits

during time interval.

In a noisy channel, the BER is often expressed as a function of the normalized carrier-to-noise ratio measure denoted Eb/N0, (energy per bit to noise power spectral

density ratio), or Es/N0 (energy per modulation symbol to noise spectral density). While in wireless communication, BER (dB) vs. SNR (dB) is used. The BER may be

analyzed using stochastic computer simulations.

3.4 Channel Capacity of MIMO OFDM System

It is the maximum amount of information that can reliably be transmitted over any communication channel at any given instant. It is denoted by ‘C’ and can be given as

(16)

Where, B is Bandwidth in Hertz , S/N is Signal to Noise Ratio in watts or volts2. For MIMO the capacity is given by

(17)

Where, M is the minimum of MT (number of transmitting antennas) or MR (number of

receiving antennas).

3.4.1 Performance Analysis of MIMO OFDM System

The water filling algorithm has been employed to measure the performance of MIMO OFDM integrated system.

3.4.1.1. Water Filling Algorithm

Water filling refers to a technique whereby the power for the spatia l channels are adjusted based on the channels gain. The channel with high gain and signal to noise

ratio gives more power. More power maximizes the sum of data rates in all sub channels. The data rate in each sub channel is related to the power allocation by Shannon’s G formula C = B log(1 + SNR). However, because of t is a logarithmic

function of power, the data rate is usually insensitive to the exact power allocation. This motivates the search for simpler power allocation schemes that can perform close

to the optimal. The water filling algorithm is based on an iterative procedure. The process of water filling algorithm is similar to pouring the water in the vessel .The total amount on water filled (power allocated) is proportional to the Signal to Noise

Ratio of channel.

Power allocated by individual channel is given by

(19)

Where Pt is the power budget of MIMO system which is allocated among the different channels and H is the channel matrix of system. The capacity of a MIMO is the

algebraic sum of the capacities of all channels and given by

(20)



We have to maximize the total number of bits to be transported .As per the scheme following steps are followed to carry out the water filling algorithm.

Algorithm Steps:-

1. Take the inverse of the channel gains.

2. Water filling has non uniform step structure due to the inverse of the Channel gain.

3. Initially take the sum of the total power Pt and the inverse of the channel gain.

It gives the complete area in the water filling and inverse power gain

(21)

4. Decide the initial water level by the formula given below by taking the average

Power allocated

(22)

5. The power values of each subchannel are calculated by subtracting the inverse Channel gain of each channel

(23)

In case the power allocated value become negative stop iteration.

3.5 Peak to Average Power Ratio (PAPR) in OFDM

The PAPR is the relation between the maximum power of a sample in a given OFDM

transmit symbol divided by the average power of that OFDM symbol. PAPR occurs when in a multicarrier system the different sub-carriers are out of phase with each

other. At each instant they are different with respect to each other at different phase values. When all the points achieve the maximum value simultaneously; this will cause the output envelope to suddenly shoot up which causes a 'peak' in the output

envelope. Due to presence of large number of independently modulated subcarriers in an OFDM system, the peak value of the system can be very high as compared to the

average of the whole system. This ratio of the peak to average power value is termed as Peak-to- Average Power Ratio. For the discrete-time version x[n],PAPR is expressed as

(24)

Where E[ ] is the expectation operator. PAPR is evaluated per OFDM symbol. An

OFDM signal consists of a number of independently modulated sub-carriers which can give a large PAPR when added up coherently. When N signals are added with the

same phase they produce a peak power that is N times the average power of the signal. So OFDM signal has a very large PAPR, which is very sensitive to nonlinearity of the high power amplifier.

The performance of a PAPR reduction scheme is usually demonstrated by three main factors: the Complementary Cumulative Distributive Function (CCDF), Bit

Error Rate (BER), and transmitted signal power. These factors are explained below



3.5.1. Complementary Cumulative Distributive Function (CCDF)

In practice, the empirical CCDF is the most informative metric used for evaluating the

PAPR. PAPR reduction capability is measured by the amount of CCDF reduction achieved. CCDF provides an indication of the probability of the OFDM signal’s

envelope exceeding a specified PAPR threshold within the OFDM symbol and is given by

CCDF[ PAPR(xn(t))] =prob(PAPR(x

n(t)> )) (25)

Where PAPR (xn(t)) is the PAPR of the nth OFDM symbol and is some threshold. Based on the CLT, the envelope of the OFDM signal follows the Rayleigh

distribution and consequently its energy distribution becomes an exponential, or equivalently, a central chi-square distribution with two degrees of freedom and zero

mean with a CDF given by

CDF( )=(1- ) (26)

The probability that the PAPR of the OFDM signal with N subcarriers is below a

threshold is the probability that all the N samples are below the threshold. Assuming

that the OFDM samples are mutually independent, this probability can be given as

prob(PAPR< )= CDF[ PAPR(xn(t))] = (27)

3.5.2. Bit Error Rate

The performance of a modulation technique can be quantified in terms of the required signal to noise ratio(SNR) to achieve a specific bit error rate (BER). Although the

main focus of PAPR reduction techniques is to reduce the CCDF, this is usually achieved at the expense of increasing the BER. Clipping the high peaks of the OFDM signal by the PA causes a substantial in-band distortion that leads to higher BER.

Other techniques may require that side information be transmitted as well. If the side information is received incorrectly at the receiver, the whole OFDM symbol is

recovered in error and the BER performance degrades.

3.5.3. Transmitted signal power

Some PAPR reduction techniques require that the average power of the transmitted

signal be increased. If the linear region of the PA is not stretched to accommodate the new signal, the signal will traverse the nonlinear region leading to higher distortions and degraded BER performance. However, this solution increases the hardware cost.

3.6 PAPR Reduction Techniques

PAPR reduction techniques vary according to the requirement of the system and are dependent on various factors such as PAPR Spectral efficiency, reduction capacity,

increase in transmit signal power, loss in data rate, complexity of computation and increase in the bit-error rate(BER) at the receiver end are various factors which are taken into account before adopting a PAPR reduction technique of the system.

3.6.1 PAPR Reduction by Clipping

One of the simplest signal distortion methods is the method of clipping the high peaks

of the OFDM signal prior to passing it through the PA. This method employs a clipper that limits the signal envelope to a predetermined clipping level (CL) if the signal exceeds that level; otherwise, the clipper passes the signal without change as defined

by



(29)

where x[n] is the OFDM signal, CL is the clipping level and x[n] is the angle of x[n].

Clipping is a nonlinear process that leads to both in-band and out-of-band distortions. While the latter one causes spectral spreading and can be eliminated by filtering the

signal after clipping, the former can degrade the BER performance and cannot be reduced by filtering. However, oversampling by taking longer IFFT can reduce the in-

band distortion effect as portion of the noise is reshaped outside of the signal band that can be removed later by filtering. Filtering the clipped OFDM signal can preserve the spectral efficiency by eliminating the out-of band distortion and, hence, improving

the BER performance but it can lead to peak power re growth.

The simulations are conducted for the OFDM signal without clipping and when

clipping is used with a clipping ratio (CR) of 1dB and 5dB. The CR is related to the clipping level by the expression

(30)

Where, E[x[n]] is the average of the OFDM signal x[n].

4 BER PERFORMANCE OF MIMO OFDM SYSTEM

At first the performance of Alamouti’s Space Time Block Coded MIMO-OFDM system under Rayleigh fading channel is investigated with various antennas configurations. The simulation model employs BPSK modulation scheme and

Alamouti’s coding scheme using two transmit antennas and more than one receive antennas. Table 1 shows the OFDM parameters considered for simulation.

Table 1 OFDM parameters considered for simulation

Parameters Value

Modulation BPSK

FFT size 64

No of symbols 10^4

No of sub carriers 52

Figure 3 BER performance of ASTBC based MIMO OFDM system for various antenna configurations

0 5 10 15 20 2510

-5

10-4

10-3

10-2

10-1

SNR dB

Bit E

rror

Rate

BER Performance of Alamouti’s STBC for Various Antenna Configuration

Alamouti STBC (NT=2, NR=1)






4.1. BER Performance with and without clipping

The simulations are conducted for the OFDM signal without clipping and when clipping is used with a clipping ratio (CR) of 1dB and 5dB. The CR is related to the

clipping level by the expression. Figure below shows the BER performance of the system with and without clipping and Empirical CCDF with and without clipping for

different values of CR.

Figure 4 BER performance with and without clipping for different values of CR

Figure 5 Empirical CCDF with and without clipping for different CR

Table 2 shows the parameters used for simulation of clipping technique.

Table 2 Parameters used for simulation of clipping technique

Parameters Value

Modulation BPSK

FFT size 64

No of symbols 10^4

No of sub carriers 52

Clipping Ratio 1dB,5Db

4.2 Deterministic Channel Capacity of MIMO-OFDM System

For a MIMO system with NT transmits and NR receive antennas, a narrowband time-

invariant wireless channel can be represented by NR NT deterministic matrix H . Consider a transmitted symbol vector x which is composed of NT

0 2 4 6 8 10 12 14 16 18 2010

-5

10-4

10-3

10-2

10-1

100

SNR(dB)

BE

R

BER without clipping and with clipping for different values of CR

no clipping

CR = 5dB

CR = 1dB

0 2 4 6 8 10 1210

-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

PAPR threshold(dB)

CC

DF

Empirical CCDF without clipping and with clipping for different values of CR.

no clipping

CR = 1dB

CR = 5dB



independent input symbols x1,x2,x3......... . Then, the received signal y can be

written in a matrix form as follows.

Y=

(31)

where (z=z1,z2,z3.......... T is a noise vector which is assumed to be zero mean

circular symmetric complex Gaussian (ZMCSCG). The autocorrelation of transmitted

signal vector is given by

(32)

The capacity of a deterministic channel is defined as

bits/channel use in which f(x) is the probability density function (PDF) of the transmit signal vector x, and is the mutual information of random vectors x and y.

From the fundamental principle of the information theory, the mutual information of the two continuous random vectors x and y is given as

(33)

in which H(y) is the differential entropy of y and is the conditional

differential entropy of y when x is given. Using the statistical independence of the two random vectors z and x in Equation 31, we can write equation 33 as follows

(34)

From the equation 33 we observe that H(z) is a constant, we can see that the mutual information is maximized when H(y) is maximized. Now, the auto-correlation matrix of y is given as

(35)

Putting the value of equation 31 in equation 35 we find

(36)

where, Ex the energy of the transmitted signals and N0 is the power spectral density of

the additive noise The differential entropy H(y) is maximized when y is

ZMCSCG which consequently requires x to be ZMCSCG. The mutual information can be found from equation 34 as follows

= +

) bps/Hz (37)

Then, the channel capacity of deterministic MIMO channel in the case of CSI known to both receiver and transmitter side is expressed as

bps/Hz (38)

When H is not known at the transmitter side, one can spread the energy equally among all the transmit antennas so that the autocorrelation function of the transmit

signal vector x is given as

(39)

Finally the channel capacity is given as



+

)

(40)

where r=min(NT ,NR) denotes the rank of H and denotes the ith eigen value.

4.2.1 Performance of Deterministic MIMO Channel Capacity

The performance of deterministic channel capacity per unit bandwidth is evaluated as

a function of SNR. In this simulation, a highly scattered environment is considered. The capacity of a MIMO channel is analyzed with the antenna configuration as shown

in Table 3 below. Each channel is considered as a parallel flat fading channel. The power in a parallel channel (after decomposition) is distributed as water filling algorithm. Channel matrix H is measured using Rayleigh distribution function.

Table3 Antenna Configuration for MIMO channel capacity

Combination No of Transmitting

antennas

No of Receiving

antennas

1 2 2

2 3 3

3 4 4

4 5 5

This simulation computes channel capacity and PDF of elements in SVD of matrix H, by varying the SNR from -10 dB to 20 dB, where 104 iterations are

performed.

Figure 6 Deterministic MIMO Channel Capacity in Terms of SNR

4.3 Ergodic Channel Capacity of MIMO-OFDM System

In general case, MIMO channels change randomly and hence is a random matrix

which means that its channel capacity is also randomly time varying and follows an ergodic process in practice Then, we consider the following statistical notion of the

MIMO channel capacity.

bps/Hz (41)

-10 -5 0 5 10 15 200

5

10

15

20

25

30

SNR in dB

Channel C

apacity (

bps/H

z)

Deterministic MIMO Channel Capacity in Terms of SNR

nt=2, nr=2

nt=3, nr=3

nt=4, nr=4

nt=5, nr=5



which is frequently known as an ergodic channel capacity. The ergodic channel capacity for the open- loop system without using CSI at the transmitter side from

equation 41 is given as

)} (42)

Similarly, the ergodic channel capacity for the closed loop (CL) system using CSI

at the transmitter side is given as

) (43)

Sometimes the ergodic channel capacity is expressed as a function of the outage

channel capacity. The outage probability can be defined as

(44)

4.3.1 Performance of Ergodic MIMO Channel Capacity

The performance of ergodic MIMO channel capacity per unit bandwidth is evaluated

as a function of SNR. Cumulative density function is also evaluated for ergodic channel capacity.

Figure 7 Ergodic MIMO Channel Capacity in Terms of SNR

4.4 Capacity of MIMO Correlated Fading Channel

In general, the MIMO channel gains are not independent and identically distributed (i.i.d.) and the capacity of the MIMO channel are closely related to the channel

correlation. For this reason, consider the capacity of the MIMO channel when the channel gains between transmit and received antennas are correlated. We model the

correlated channel as follows:

(45)

Where Hw denotes the independent and identically distributed (i.i.d) Rayleigh fading channel gain matrix and Rt is the correlation matrix taking correlations between the

transmit antennas, Rr is the correlation matrix taking correlations between the receive antennas. Then the correlated channel capacity can be represented as

) (46)

-10 -5 0 5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

X

F(X

)

Empirical CDF

NT=NR=1

NT=NR=2

NT=NR=3

NT=NR=4



From the above equations, let us consider two cases for simulation.

Case1: Correlation exists between transmit and receive antennas, transmit

antennas and receive antennas but the correlation matrix Rt and Rr are identical

Figure 8 Capacity of i.i.d and Correlated Channel in Terms of SNR with Correlation exist between the Transmit Antennas and Receive Antennas but Same Correlation Matrix

Observation: Figure8 shows the capacity of i.i.d and correlated channel in terms of SNR with correlation exists between the transmit antennas and receive antennas but

same correlation matrix. From figure 8 I observe that at 15 dB of SNR value 4×4 i.i.d channel provide 16.22 bps/Hz whereas 3×3 i.i.d channel provides 11.8 bps/Hz and 4×4 correlated channel provides12.34 bps/Hz. So i.i.d channel outperforms the

correlated channel.

Case 2: Correlation exists between transmit and receive antennas, transmit

antennas and receive antennas but the correlation matrix Rt and Rr are not identical.

Figure 9 Capacity of i.i.d and Correlated Channel in Terms of SNR with Correlation Exists between the Transmit Antennas and Receive Antennas but different Correlation Matrix

Observation:

Figure 9 shows the capacity of i.i.d and correlated channel in terms of SNR with correlation exists between the transmit antennas and receive antennas but different

-10 -5 0 5 10 15 200

5

10

15

20

25

SNR in dB

Channel C

apacity (

bps/H

z)

Capacity of i.i.d and Correlated Channel in Terms of SNR with Correlation Exists between the Transmit Antennas and Receive Antennas but Same Correlation Matrix

3×3 correlated channel

3×3 i.i.d channel

4×4 i.i.d channel


-10 -5 0 5 10 15 200

5

10

15

20

25

SNR in dB

Channel C

apacity (

bps/H

z)

Capacity of i.i.d and Correlated Channel in terms of SNR with Correlation Exists between the Transmit Antennas and Receive Antennas but Different Correlation Matrix


3×3 i.i.d channel


4×4 i.i.d channel



correlation matrix. In this case I noticed that 4×4 i.i.d channel provide 22bps/Hz whereas 4×4 correlated channel provides 14 bps /Hz. So i.i.d channel outperforms the

correlated channel.

5. CONCLUSION

The performance of the ASTBC based MIMO OFDM system under Rayleigh fading channel is evaluated and it is observed that the performance of two transmit antennas with more receive antennas is much better than that of the system with two transmit

antenna and less receive antennas in term of BER due to the more diversity gain of Alamouti’s code. The performance of deterministic, ergodic and correlated MIMO

channel capacity is evaluated. It is observed that the channel capacity increases with the number of antennas added to the system, independent and identically distributed channel outperforms the correlated channel. Finally, to reduce PAPR clipping

technique is applied and I observed that as the CR is reduced, the CL is lowered down and more parts of the OFDM signal are clipped and hence, the BER is increasing and

the empirical CCDF is decreasing.

REFERENCES

[1] Md.Mejbaul Haque, Mohammad Shaifur Rahman and Ki-Doo Kim” Performance Analysis of MIMO-OFDM for 4G Wireless Systems under Rayleigh Fading Channel”, International Journal of Multimedia and Ubiquitous Engineering Vol. 8, No. 1, January, 2013.

[2] Yasir Rahmatallah, Seshadri Mohan” Peak-To-Average Power Ratio Reduction in OFDM Systems:A Survey And Taxonomy”,IEEE Communications Surveys & Tutorials, VOL. 15, NO. 4, Fourth Quarter 2013.

[3] Hemangi Deshmukh , Harsh Goud,” Capacity Analysis of MIMO OFDM System using Water filling Algorithm”, International Journal of Advanced Research in Computer Engineering & Technology (IJARCET) Volume 1, Issue 8, October 2012.

[4] K.Hariprasad reddy, M.Anusha”MIMO-OFDM using Power allocation in WATERFILLING algorithm based on SVD process”, International Journal of Engineering Science & Advanced Technology Volume-3, Issue-5, 197-204.

[5] Shilpa Bavi, Sudhirkumar Dhotre” PAPR Reduction in OFDM System Using Clipping and Filtering Method” , International Journal of Advanced Research in Computer Science and Software Engineering, Volume 5, Issue 2, February 2015.

[6] Nimay Chandra Giri, SK Mohammed Ali, Rupanita Das” BER Analysis and Performance of MIMO-OFDM System using BPSK Modulation Scheme for Next Generation Communication Systems”,International Journal of Engineering Sciences & Research Technology, March, 2014.

[7] Arun Gangwar, Manushree Bhardwaj” An Overview: Peak to Average Power Ratio in OFDM system & its Effect”,International Journal of Communication and Computer Technologies Volume 01 – No.2, Issue: 02 September 2012.

[8] Parneet Kaur , Ravinder Singh” Complementary Cumulative Distribution Function for Performance Analysis of OFDM Signals,“IOSR Journal of Electronics and Communication Engineering, ISSN : 2278-2834 Volume 2, Issue 5,Sep-Oct 2012.

[9] Prof. A.K Jaiswal, Er.Anil Kumar, Anand Prakash Singh”Performance Analysis of MIMO OFDM system in Rayleigh fading channel” ,International Journal of Scientific and Research Publications, Volume 2, Issue 5, May 2012.



[10] Mir Muhammad Lodro, Muhammad Hanif Abro” Ergodic Capacity of MIMO Correlated Channels in Multipath Fading Environment with known Channel State Information”, International Journal of Electrical and Computer Engineering, Vol.2, No.5, October 2012.

[11] Yong Soo Cho,Jaekwon Kim,Won Young Yang,Chung Gu-Kang”MIMO OFDM Wireless communications with MATLAB”,IEEE press.

[12] Ke-Lin DU and M.N.S.Swamy, “Wireless Communication Systems”, Cambridge University Press,2010.

[13] HELMUT BOLCSKEI, ETH ZURICH”MIMO OFDM Wireless Systems: Basics, Perspectives and Challenges”, IEEE Wireless Communications, August 2006.

[14] Asha Ravi, J.Nalini, Kanchana S.R.”Antenna Management of Space-Time Shift Keying Systems” International Journal of Computer Science And Technology, Vol. 3, Issue 1, Jan. - March 2012.

PERFORMANCE ANALYSIS OF CLIPPED STBC CODED MIMO OFDM SYSTEM

Engineering

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