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International Journal of Electronics Engineering Research.

ISSN 0975-6450 Volume 9, Number 3 (2017) pp. 409-427

© Research India Publications

http://www.ripublication.com

Performance Analysis of MIMO-OFDM Using NCT Companding Transform

Dr. K. Srinivasa Rao1 and Mrs. N. Roopa Vathi2

1G. V. P. College of Engineering for Women, Visakhapatnam

2G. V. P. College of Engineering for Women, Visakhapatnam

Abstract In this paper a new non-linear companding transform (NCT) technique based on

inverse hyperbolic cosine function is proposed and implemented along with Carrier

Frequency Estimation (CFO) techniques in order to improve the performance of

Multi Input and Multi Output Orthogonal Frequency Division Multiplexing (MIMO-

OFDM) systems. In this proposal, significant PAPR reduction and an improved bit

error rate (BER) performance can be achieved simultaneously, since the power

distribution of the companded signal can be reallocated more reasonably while

maintaining the average power level unchanged. An effective trade-off between the

PAPR and Bit Error Rate (BER) performance is achieved by introducing an inflection

point and variable companding parameters in the companding function, such that it

enables more design flexibility and freedom in companding form. Desired PAPR

threshold can be achieved by proposing technique, since it introduces the companding

distortion as small as possible with appropriate selection of the companding

parameters and forms. Different CFO estimation techniques are implemented to

estimate ICI along with proposed methods to analyze the performance of MIMO-

OFDM systems. The analytical expressions regarding the achievable PAPR reduction

transform gain G, and signal attenuation factor are derived. Simulation results

demonstrate that NCT and CFO estimation techniques substantially improve

performance of MIMO-OFDM system.

Keywords: MIMO-OFDM, PAPR, ICI, Nonlinear companding transform (NCT),

Carrier Frequency 0ffset (CFO), high power amplifiers (HPA).

1. INTRODUCTION Robust, high spectral efficiency and immunity to the interference caused by multipath

fading of OFDM and very high data rate transmission of MIMO highlights the

combination of MIMO-OFDM systems [1, 2]. MIMO-OFDM has been adopted in

mailto:[email protected]

mailto:[email protected]

410 Dr. K. Srinivasa Rao and Mrs. N. Roopa Vathi

3GPP-LTE and IEEE 802.16 (WI-MAX) standards [3]. However, this system has two

major limitations viz., High Peak-to-Average Power Ratio (PAPR) of the transmitted

signals and Intercarrier interference (ICI). High PAPR leads to in-band distortion

across subcarriers and undesired spectral growth if the linear range of higher power

amplifier (HPA) is not sufficient at the OFDM transmitter [4]. ICI leads to distortion

in received OFDM signal as orthogonality is destroyed among subcarriers of OFDM

signal

Many different types of PAPR reduction methods have been proposed in the literature

[5-18], e.g. Clipping and filtering, selective mapping (SLM), partial transmit sequence

(PTS), block coding, active constellation extension (ACE), and companding transform

techniques. Among existing methods, clipping and filtering is a simple procedure to

obtain the desired PAPR reduction, but it yields additional clipping noise, resulting in

significant out-of-band interference (OBI) and other methods SLM, PTS are complex

and require Side Information (SI) to recover the OFDM signal at the receiver. An

approach called non-linear companding transform (NCT) was proposed to overcome

the drawback of OBI. This technique was first introduced in [11], in which mu-law

companding was implemented which efficiently outer performs the clipping.

However, after implementing such logarithmic based compression on OFDM symbol,

its average power increases, leads to more sensitive to the HPA. Since then, many

different proposals have been made to refine NCT schemes in which two careful

designs are considered to improve its overall performance. The first design focuses on

optimizing the nonlinear characteristics of the companding profiles. The second one is

to employ the statistical distribution of the OFDM signal. To achieve more significant

PAPR reduction of OFDM signal, a novel technique based on the inverse hyperbolic

cosine function is proposed. In this proposal, significant PAPR reduction and an

improved bit error rate (BER) performance can be achieved simultaneously, since the

power distribution of the companded signal can be reallocated more reasonably while

maintain the unchanged average power level. Moreover, an effective trade-off

between the PAPR and BER performance can be achieved by adjusting the variable

companding parameters; also it allows more flexibility and freedom in the

companding form. Both theoretical analysis and simulation results confirm the

effectiveness of this technique.

In addition to the high PAPR, OFDM is more sensitive to Inter Carrier Interference

(ICI). It occurs due to mainly two reasons, viz. One is a mismatch in carrier

frequencies due to Doppler shift. Because of this effect, orthogonality among

subcarrier fails, in turn distortion occurs in recovered signal and hence BER

performance degraded significantly. In the literature [19-21], several ICI mitigation

techniques have been proposed, and mainly classified into two types, time and

frequency doamain mitigation techniques. Time domain mitigation techniques

include time doamin windowing and ICI cancellation schemes. Time doamin

windowing technique utilizes a sharping filter to mitigate the ICI effect.The frequency

Performance Analysis of MIMO-OFDM Using NCT Companding Transform 411

domain include CFO estimation and detection which utilizes estimated pilot symbol.

In this subsection discusson some CFO estimation and detection techniques are

analyzed.

The remainder of this paper is organized as follows: section 2 reviews a typical

MIMO-OFDM system. Proposed technique, its corresponding theoretical analysis,

and CFO estimation techniques are described in section 3. Section 4 present

simulation results and compared with existing NCT techniques. Final conclusions are

given in section 5.

2. PAPR of OFDM signals in MIMO-OFDM. Consider full rate Alamouti STBC-OFDM system with two transmitter and receiver

antennas and as shown in Fig: 1. The bit stream from information source is mapped

by digital modulator either M-PSK or M-QAM. Then these modulated symbols are

encoded by Space Time Block encoder and output is fed to OFDM modulator. The

following steps are performed to each of the parallel output streams corresponding to

a particular transmit antenna to get OFDM signals.

Pilot symbol insertion, IFFT operation.

Addition of CP.

After adding CP, proposed NCT compression is performed on OFDM symbols and

up converted to RF frequeucy, then propagated through the MIMO channels. At

receiver, CP is removed from the received signals and decompanding is perfromed by

proposed NCT decompanding function, then reverse of OFDM operation (FFT) is

performed on decompanded signals then passed through the channel estimator, in this

stage CFO estiamtion is carried out and subsequently optimal ML detection is

performed to detect the transmitted signal.

MTx Antenn

a

S/P

Sou

rce

S/P

Decompanding

& FFT

Source

Channel

Estimation

Source

MIMO

Detector

Demodulator

CP

CP

P/S

Pilot allocation

IFFT & CP

Source

NCT

Compandin

g

Source

NCT

Compandin

g

Source

P/S

Sou

rce

P/S

Sou

rce

Pilot allocation

IFFT & CP

S/P

Alamouti ST

Encoder

Symbol

Mapping

Decompanding

& FFT

Source

I/P

Bits

O/P

Bits MRx

Antenna

Figure 1: Block diagram of MIMO-OFDM system using proposed NCT techniques


The frames 1mx and 2

mx are generated from xm as follows:

)(*

)1(*

)1()(

)1(2

)(2

)1(1

)(1

vmxvmx

vmxvmx

vmxvmx

vmxvmx (1)

where v = 1, 2, …, Ns. Rows represents antenna indices and columns represents time

intervals i.e. xm(v) and xm(v+1) are generated from antenna 1, and -xm*(v+1) and

xm*(v) are generated from antenna 2 during first and second time intervals.

In the following subsections antenna index and time index are omitted from MIMO-

OFDM signal for the sake of analysis convenience.

Symbols )1(),0( XX and )0(),1( ** XX are transmitted over antennas 1 and 2 at tones ‘n’ and

‘n+1’ respectively. Let TNpXPXPXPX )]1(),...,1(),0([ be the frequency domain sequence

from the thp transmit antenna to be transmitted, where N is the number of subcarriers.

Since Nyquist rate samples are not sufficient to represent the peaks of the continuous

time signal, it is preferable to have the PAPR performance on the over-sampled time

domain vector TLNpxpxpxpx )]1(),...,1(),0([ , is obtained after performing LN point IFFT,

where L represents the oversampling factor. Thereby the thn element of px can be

expressed as

)2.

exp(.1

0

1

LNnkjN

k kXLN

nx

, 1,...,1,0 LNn (2)

where 1j , and n is the time index.

According to central limit theorem, OFDM signal nx from antenna can be

approximated as a complex Gaussian process for a large value of N (e.g. N ≥ 64).

Thus, with zero mean and a constant variance 2/}2

{2

kXE , the real and imaginary

parts of nx become Gaussian distribution with probability density function (PDF) as

follows

)2

2

exp(.2

2

xxnxf , 0x (3)

It is evident that the maximal amplitude of the OFDM signal may exceed its average

signal amplitude. The probability distribution function (CDF) of nx is given by

2/

2

0

2/

2exp

0

)2

2

exp(.2

2}{Pr)(

x

ydyx yy

xnxobxnxF

),2

2

exp(1

x 0x

(4)

where Prob{B} is the probability of an event B.


PAPR of the mth frame from pth antenna is defined by

2

)()(

2

)()(

max

)(

np

mxE

np

mxnp

m (5)

By employing proposed NCT technique, the PAPR of the original OFDM signal xn is

remarkably reduced. It is useful to treat PAPR is a random variable and use a

statistical description given by the complementary cumulative distribution function

(CCDF) defined as the probability that exceeds a particular threshold PAPR0, i.e.

}0{Pr)0( PAPRxPAPRobPAPRxCCDF (6)

3. THEORETICAL ANALYSIS OF PROPOSED SCHEME. 3.1 Scheme description In this proposal, significant PAPR reduction and an improved bit error rate (BER)

performance can be achieved simultaneously, since the power distribution of the

companded signal can be reallocated more reasonably while maintain the unchanged

average power level. Moreover, an effective trade-off between the PAPR and BER

performance can be achieved by adjusting the variable companding parameters; also it

allows more flexibility and freedom in the companding form. Both theoretical

analysis and simulation results confirm the effectiveness of this technique.

The generic formulae of the proposed scheme are derived in this subsection, whose

companding function is defined by an inverse hyperbolic cosine function with

inflexion point. Using this method, the amplitude, or power of the transmitted signal

can be reallocated with reasonable and flexible manner. Moreover, it has the

advantage of keeping average output power unchanged. Hence, the sensitivity of

companding operation to the non-linearity of the HPA can be reduced.

In MIMO-OFDM system, the companded signal is TLNyyyy ]1,...,1,0[ , represented as

)( nxCompny , 1,...,1,0 LNn (7)

where xn is the original OFDM signal, and Comp(.) represents the companding

function, which is strictly monotonic increasing function and only changes the

amplitude of xn. The inverse of companding function is the de-companding function,

i.e. Comp-1(x). Suppose cAx (0 ≤ c ≤ 1) is the inflexion point of Comp(x), where

}{]1,0[max nxLNnxA is the maximum input amplitude. The proposed companding

function is defined as follows

xcAxxkcAarxxcAxxkarx

xComp),cosh(.).sgn(

),cosh(.).sgn()(

(8)


where sgn(.) is the sign function, and arcosh(.) is the inverse hyperbolic cosine

function is given by

)12

ln()cosh( xxxar (9)

The average power can be adjusted by the parameter ‘ ’ and the degree of

companding is specified by parameter ’k’. Before and after companding operation, the

average power of the signal is same according to the proposed method.

0

)(2

}2

{}2

{ dxxnxfxnxEnyE (10)

Clearly, the parameter ‘ ’ can be determined, when ‘k’ is chosen. The companded

signal can be recovered by the corresponding de-companding function.

)cosh(.1

).sgn()(1

x

kxxComp

(11)

where 2

)cosh(

xexex

is the hyperbolic cosine function.

By solving (10), ‘ ’ is determined as follows

xkcAxcAnxnn

arnxkxcAnxnn

arE2

cosh2

cosh

(12)

Clearly, the parameter ‘ ’ can be determined, when ‘k’ is chosen. The signal is

recovered by the corresponding de-companding function.

Further by making approximate substitution, the CDF of companded signal may be

obtained as

})({Pr}{Pr)( xnxcompobxnyobxnyF

=

)cosh(.,1

)cosh(.0),22

)/(2

coshexp(1

0,0

xkcAarx

xkcAarxk

x

x

(13)

The proposed method is suitable for real time applications as it used in practical

MIMO-OFDM systems through the use of pre-computed look-up tables. Fig: 2 depict

the transform profile of the companding function in (8) with various parameters.


Fig: 2 Transform profiles of the proposed companding function with various

parameters.

From Fig: 2, the proposed scheme compresses large amplitude signals while partially

improves the small amplitude signals simultaneously. Moreover, this method does not

increase the average power unlike -law companding method. Thus, this technique

effectively reduces the PAPR by reducing the peak signals and also provides

immunity to small signals from the channel noise.

In the following subsections, its theoretical performance in terms of achievable PAPR

reduction and impact of companding distortion on BER performance is investigated.

3.2 Achievable PAPR reduction

As per the PAPR definition in (5), the maximum PAPR of the companded signal is

expressed as follows.

}2

{

}2

{]1,0[max

nyE

nyLNnyPAPR

=

2

)(2

cosh.2

xkcAar (14)

In order to compare the PAPR values before and after the companding operation, a

transform gain G, is defined as the ratio of the PAPR of original signal to that of

companded signal, i.e.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.5

1

1.5

2

2.5

3

Input Amplitude |Xn|

Outp

ut

Am

plit

ude |Y

n|

c = 0.43, k = 2.3

c = 0.45, k = 2.5

c = 0.47, k = 2.7

c = 0.49, k = 2.9


)cosh(.10log2010log10)(

xkcAar

xA

yPAPR

xPAPRdBG

(15)

The theoretical results of the attainable PAPR reduction and transform gain G,

obtained using (14) and (15), respectively. As seen from Fig: 4 more PAPR reduction

is achieved as c increases.

Furthermore, the CCDF of the achievable PAPR using proposed technique is

formulated as

}0{Pr)0( PAPRyPAPRobPAPRyCCDF

)0)(

2cosh.

2

2

( PAPR

xkcAa

xAxCCDF

(16)

Fig: 4 Theoretical results of transform gain G with different values of c.

3.6 Distortion due to Companding transforms Extra non-linear process is introduced to the transmitted signal by NCT companding

operation, so it is clear that when PAPR reduced, corresponding BER performance

may be degraded. Due to the disadvantages of non-linear distortion, NCT should be

designed carefully such that the amount of clipped signals as little as possible. Hence,

it may be advisable to minimize the impact of companding distortion on BER as small

1 1.5 2 2.5 3 3.5 4-1

0

1

2

3

4

5

6

7

companding degree k

Tra

nsfo

rm g

ain

G(d

B)

c = 0.5

c = 0.6

c = 0.8

c = 0.9


as possible. The companded signal can be represented as the sum of a useful

attenuated input replica and companding noise as per the extension of Bussgang

theorem.

1,...,1,0,. LNnnbnxny (17)

where is an attenuation factor and can be calculated as

dxxnxfxCompx

nxnxE

nxnyE)(

0

).(.2

1

}*

.{

}*

.{

(18)

Considering an additive white Gaussian noise (AWGN) channel, the received signal

nr can be expressed as nwnynr , where nw is channel noise. After the de-

companding operation, the recovered signal 'nx can be expressed as

nw

nxnbnxny

nx

'

(19)

From (31), it is clear that channel noise nw enlarges to

nwafter de-companding

operation. To minimize the signal distortion ‘ ’ must approaches to ‘1’ enough.

Substituting Comp(x) and )(xnxf in (31), the attenuation factor of this technique is

obtained as

xcA xA

xcAdx

xxxkcAardxkxar

xx

0

)2

2

exp(2

)cosh(4

2)cosh()

2

2

exp(2

4

2

(20)

From the simulation results, approaches to ‘1’ for the values of c = 0.8, k = 1.15. It

can be observed that, by choosing the optimal companding parameters the proposed

scheme approached the desired PAPR level.

3.7 Analysis of ICI reduction techniques ICI occurs between orthogonal subcarriers due to CFO (Carrier Frequency Offset)

among subcarrier frequencies. So to mitigate ICI effect, CFO has to be detected and

corrected, two popular methods for CFO estimation [20] are discussed in this

subsection and results are analyzed for comparison purpose.

CFO Estimation Techniques Using Cyclic Prefix (CP)

Frequency-Domain Estimation Techniques for CFO

3.8 CFO Estimation Techniques Using Cyclic Prefix (CP) When there is negligible channel effect between transmitter and receiver, the phase

difference between Cyclic Prefix (CP) and the corresponding rear part of an OFDM


symbol due to CFO is determined as 2πε, where ε is normalized CFO. So, CFO can be

determined by the phase angle of the product of CP and the corresponding rear part of

an OFDM symbol. But this type of CFO estimation suffers from limited range of

CFO. So the range of CFO estimation can be increased by decreasing the distance

among two blocks for correction. This can be done by training symbols that are

repetitive with some shorter time periods. Let a transmitter sends the training symbols

with D repetitive patterns in the time domain, which can be generated by performing

IFFT operation of a comb type signal as follows:

otherwise

DNiiDkifmAnx

;0

)1/(,...,1,0,*;][ (21)

where Am represents an M-ary symbols and N/D is an integer. As ][nx and ]/[ DNnx

are identical (i.e. jenyDNnyny

2][]/[][

* ). A receiver can estimate CFO as follows

1/

0

]/[][*

arg

2

ˆDN

nDNnyny

D

(22)

As estimation range of CFO increases, the MSE performance becomes worse, hence

by taking the average of estimates with repetitive patterns of the shorter period as

)2(

0

)1/(

0

/)1(/*

arg

2

ˆD

m

DN

nDNmnyDmNny

D

(23)

Now MSE performance is improved without reducing the estimation range of CFO.

3.9 CFO estimation using Frequency-Domain techniques If two similar training symbols are transmitted successively, the corresponding signals

with CFO of ε are related with each other as follows

2][1][2

/2][1][2

jekYkY

NNjenyny (24)

Now, the CFO can be estimated in frequency domain as follows:

1

0

][2][*

1

1

0

][2][*

1Im1

tan

2

1ˆ

N

kkYkY

N

kkYkY

(25)

Above (25) is a well-known approach by Moose [21]. And it is applicable only during

the preamble period, during which data symbols cannot be transmitted. To overcome

this drawback, Classen [22] has proposed another technique, wherein pilot subcarriers

are inserted in the frequency domain and transmitted along with OFDM symbol for

CFO tracking and estimation. In this technique the signal is compensated with

estimated CFO in the time domain, after estimating CFO from pilot tones. In this

process, CFO estimation is implemented in two different modes. One is acquisition

and tracking modes. A wide range of CFO estimation including an integer CFO is


possible in the acquisition mode, where as only fine CFO estimation is possible in

tracking mode. The integer CFO is estimated by

]][[][

1

0

*],[

*],[max

2

1ˆ jplXjp

L

jDlXjplYjpDlY

subTacq

(26)

where L, p[j], and Xl[p[j]] denote the number of pilot tones, the location of the jth

pilot tones, and the symbol for which pilot tone located at p[j] in the frequency

domain at the lth symbol period.

In the tracking mode, the fine CFO is estimated as

]][[][

*ˆ],[

*ˆ],[

1

1

arg

2

1ˆ jplXjpDlXacqjplYacwjp

L

jDlY

DsubTf

( 27)

In the acquisition mode acq̂ and f̂ both are estimated and then, the CFO is

compensated by their sum. In the tracking mode, only f̂ is estimated and then

compensated.

3.10 ML detection method Maximum Likelihood (ML) detection method is used at the receiver for Alamouti

space-time coding scheme based on diversity analysis. Two channel gains are

assumed to be time-invariant over two consecutive symbol periods, that is

111)(1)(1

jehhsTthth , and

222)(2)(2

jehhsTthth

(28)

where │hi│ and θi represent the amplitude and phase rotation over the two symbol

periods.

Consider two received symbols, y1 and y2, during time t and t+Ts respectively, then

2*12

*212

122111

zxhxhy

zxhxhy

(29)

where z1 and z2 are AWGN noise samples at time t and t+Ts.

Consider a matrix vector equation by taking complex conjugate of the second

received symbol.

*

1

1

2

1*1

*2

21*2

1

z

z

x

x

hh

hh

y

y (30)


In Alamouti scheme, it is assumed that channel gains are known to the receiver, and

then the transmitted symbols are two unknown variables at the receiver. By

multiplying the Hermitian transpose of channel matrix both sides, the input-output

matrix can be obtained as follows.

2~1

~

2

12

2

2

12

~1

~

z

z

x

xhh

y

y

(31)

where

*2

1

2*2

2*1

2~

1~

y

y

hh

hh

y

y, and

*2

1

1*2

2*1

2~1

~

z

z

hh

hh

z

z

From (23), it is clear that, the interference signal x2 is dropped out from y1, while the

interference signal x1 is dropped out from y2. This is the result of complex

orthogonality of Alamouti code. This particular attribute reduces the complexity of

ML receiver structure as follows.

.2,1,2

2

2

1

~

,ˆ

i

hh

iyQMLiX (32)

where Q(.) represents the slicing function that decides a transmit symbol for the given

constellation set. x1 and x2 can be determined separately to reduce the complexity of

original ML-detection algorithm from │C│2 to 2│C│, where C is the constellation

for the modulation symbols x1 and x2. This is possible due to orthogonal structure of

Alamouti ST codes. Scaling factor, 2

2

2

1 hh guarantees the second order diversity,

which is the main feature of Alamouti code.

4. SIMULATION RESULTS Alamouti STBC 2 X 2 MIMO-OFDM with 1024 subcarriers using 16-QAM is

simulated. For the performance comparison purpose, existing PAPR reduction

techniques include -law companding [11], NCT [18], SLM [5] and PTS [5] were

also simulated along with proposed NCT technique.

4.1 PAPR reduction performance Fig: 5 represents the CCDF Vs PAPR plots for the original MIMO-OFDM signal and

companded signals using three different NCT methods, SLM, and PTS.


Fig: 5 PAPR-CCDF comparisons among different PAPR reduction.

As seen from the Fig: 5, proposed method improves the PAPR by 9.7dB over original

MIMO-OFDM. Particularly this technique with c = 0.45 and k = 2.5 surpasses -

law, NCT, SLM, and PTS by 4 dB, and 5.3 dB, 5.7 dB, and 7 dB respectively at clip

rate 10-3 (CCDF).

4.2 PSD performance Fig: 6 depict the power spectral density of companding schemes, and give the

measure of Out-of-band Interference (OBI). From Fig: 6, proposed NCT has lower

out of band radiation 20dB than mu-law companding, 5 dB lower than existing NCT,

and just 2 dB higher than original MIMO-OFDM signal. So, the proposed NCT has

reduced considerable out-of-band radiation when compared to existing schemes.

0 2 4 6 8 10 1210

-3

10-2

10-1

100

PAPR in dB

CC

DF

(xi) =

Pr(

xi >

PA

PR

)

Original

u-law

NCT

NCT-cos

SLM

PTS


Fig: 6 PSDs of different companding techniques.

4.3 BER performance Fig: 7 present the BER performance Vs SNR curves employing different methods

over an AWGN channel with digital modulations 16QAM,. As a reference, the curve

of ideal performance bound also given. As it evident BER performance of proposed

NCT is little degraded, while it significantly reduces the PAPR. All the BER curves of

companded signals are on right of the ideal bound. As can be seen in Fig: 5.6 to

achieve a BER level of 10-4, the required Eb/No for proposed NCT with c = 0.45 and

k = 2.5 is 12dB, which is about 2 dB better to other schemes. In addition, it should be

significant that the BER performance is only about 0.2 dB worse than the ideal bound.

As anticipated, the impact of companding distortion on the BER performance can be

efficiently reduced because the power of transmitted signal has been reallocated more

reasonably.

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-90

-80

-70

-60

-50

-40

-30

Normalized frequency ( rad/sample)

PS

D (

dB

/rad/s

am

ple

)

Original MIMO-OFDM

NCT

Proposed NCT

mu-law


Fig: 7 BER comparisons between the original signal and the companded signal

employing different methods using 16-QAM.

Fig: 8 MSE performance comparison plots of three CFO methods.

0 2 4 6 8 10 12 14 16 18 2010

-4

10-3

10-2

10-1

100

Eb/No(dB)

BE

R

Original MIMO-OFDM

mu-law

NCT

Proposed NCT(c = 0.5, k = 2.5)

0 5 10 15 20 25 3010

-8

10-7

10-6

10-5

10-4

10-3

SNR[dB]

MS

E

CFO Estimation

NCT with CP-based technique

NCT with Moose (Preamble-based)

NCT with Classen (Pilot-based)


From Fig: 8, it clear that MSE performance of Classen with proposed NCT is superior

to other two techniques and signal is detected using ML method.

Following Tables: 1, 2, and 3 illustrate the comparison study PAPR of proposed NCT

method with respective to existing methods, BER comparison, and MSE graphs for

ICI reduction to evaluate overall performance of 2 X 2 STBC MIMO-OFDM systems.

Table: 1 PAPR comparisons for proposed NCT with existing techniques

Different types of PAPR reduction

schemes PAPR reduction gain (at clip

rate 10-3)

Proposed NCT 9.7 dB

mu-law 4 dB

NCT1 5.2 dB

SLM 2.7 dB

PTS 3.7 dB

Table: 2 BER comparisons for proposed NCT method with existing

techniques.

Different types of PAPR reduction

schemes SNR at BER of 10-4

Proposed NCT 12dB

Mu-law 14dB

NCT1 13dB

MIMO-OFDM 11.8dB

Table: 3 MSE comparisons for different CFO estimation methods along with

proposed PAPR reduction technique.

Different CFO estimation with

proposed NCT technique MSE at SNR of 30dB

Cp-based technique 1.77e-7

Moose (preamble-based) 4.252e-8

Classen (Pilot-based) 3.242e-8


5. CONCLUSION In this work, inverse hyperbolic cosine function Nonlinear Companding transform has

been proposed, and evaluated with CFO estimation techniques to analyze of 2 X 2

STBC-OFDM systems performance. Power distribution of the companded signal is

reallocated more reasonably by compressing large signals, with partially enhancing

smaller amplitudes simultaneously, thus, it provides immunity to small signals from

the channel noise with improved bit error rate (BER) performance. This scheme

achieves considerable PAPR reduction with suitable choice of the variable

companding parameters and inflexion point in the companding function.

From the simulation results, it is observed that the proposed NCT showed

improvement of 6 dB and 4 dB in PAPR reduction as compared to mu-law and

existing NCT respectively at a clip rate of 10-3. Also, the proposed NCT scheme has

reduced the OBI by 5 dB, and 20 dB than existing NCT, and mu-law companding

techniques respectively. This technique has achieved BER of 10-4 at Eb/No of 12 dB,

which is almost 1 dB improvement compared to existing NCT. The BER of proposed

NCT is less degraded than existing NCT and MIMO-OFDM signal but still better

than existing schemes and it is achieved the Eb/No gain of 1 dB and good MSE

performance. Thus, the BER performance of proposed NCT is less degraded than

existing NCT and MIMO-OFDM signal. Proposed NCT with Classen (Pilot-based)

CFO estimation technique has achieved good MSE performance, as MSE of estimated

CFO errors decreases with respect to SNR and finally symbols are detected by the ML

detector in MIMO receiver.

Hence, from the simulation results, it is concluded that the proposed NCT has

achieved moderate performance compared to existing companding techniques in

terms of PAPR reduction, BER, and OBI reduction.

ACKNOWLEDGMENTS The authors sincerely thanked Prof. G.T Rao, E.C.E Department, G.V.P College of

Engineering (Autonomous) for his immense support and valuable suggestions.

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Biographical notes:

Dr.K.Srinivasa Rao received B. Tech degree in Electronics and

Communication Engineering from Nagarjuna University, Guntur, M. Tech

degree in I & CS and Ph.D from J.N.T University College of Engineering.

Kakinada, presently he is working as an Associate Professor in the

department of Electronics and Communication Engineering, G.V.P. College of

Engineering for Women, Visakhapatnam. His research interests include Wireless

Communications, Digital Signal processing and embedded systems. He is a Life

Member of IETE.

Mrs.N.Roopa Vathi received B.Tech degree in Electronics and

Communications Engineering from J.N.T.University, Kakinada, M. Tech

degree in Radar and Microwave from Andhra University. Presently she is

working as an Assistant Professor in the department of Electronics and

Communication Engineering, G.V.P. College of Engineering for Women,

Visakhapatnam. Her research interests include Digital Communications and Digital

Signal processing. She is a Life Member of ISTE.
