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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
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
412 Dr. K. Srinivasa Rao and Mrs. N. Roopa Vathi
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.
Performance Analysis of MIMO-OFDM Using NCT Companding Transform 413
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)
414 Dr. K. Srinivasa Rao and Mrs. N. Roopa Vathi
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.
Performance Analysis of MIMO-OFDM Using NCT Companding Transform 415
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
416 Dr. K. Srinivasa Rao and Mrs. N. Roopa Vathi
)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
Performance Analysis of MIMO-OFDM Using NCT Companding Transform 417
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
418 Dr. K. Srinivasa Rao and Mrs. N. Roopa Vathi
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
Performance Analysis of MIMO-OFDM Using NCT Companding Transform 419
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)
420 Dr. K. Srinivasa Rao and Mrs. N. Roopa Vathi
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.
Performance Analysis of MIMO-OFDM Using NCT Companding Transform 421
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
422 Dr. K. Srinivasa Rao and Mrs. N. Roopa Vathi
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
Performance Analysis of MIMO-OFDM Using NCT Companding Transform 423
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)
424 Dr. K. Srinivasa Rao and Mrs. N. Roopa Vathi
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
Performance Analysis of MIMO-OFDM Using NCT Companding Transform 425
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.
428 Dr. K. Srinivasa Rao and Mrs. N. Roopa Vathi