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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 71, 2022 5501211
Design and Testbed Implementation of Blind
Parameter Estimated OFDM Receiver
Mahesh Shamrao Chaudhari ,Graduate Student Member, IEEE, Sushant Kumar , Rahul Gupta ,
Manish Kumar , and Sudhan Majhi ,Senior Member, IEEE
Abstract— Designing an intelligent or adaptive transceiver
system is becoming a promising technology for upcoming gener-
ations of wireless communication systems due to its adaptivity,
spectrum efficiency, and low-latency characteristics. However,
there is no work available until now that characterizes and
demonstrates complete adaptation in the physical layer for
orthogonal frequency-division multiplexing (OFDM) systems.
In this article, we propose and implement sequential blind
parameter estimation methods for OFDM signals using radio fre-
quency (RF) testbed setup in a realistic scenario. The estimations
include the number of subcarriers, symbol duration, cyclic prefix,
oversampling factor, symbol timing offset (STO), and carrier
frequency offset (CFO). The proposed algorithms also include
blind modulation classification for linearly modulated signals
over a frequency-selective fading channel. The parameter esti-
mation has been carried out through a cyclic cumulant process.
The modulation formats are classified by using normalized
fourth-order cumulant in the frequency domain. The STO and
CFO are estimated by a proposed modified maximum likelihood
algorithm. The performances of parameter estimations, modula-
tion classification, and synchronization are measured through
analytical, simulation, and measurement studies. The overall
performance of the OFDM system is provided in terms of the
received constellation diagram and bit error rate (BER) over an
indoor propagation environment.
Index Terms—Adaptive receiver, cumulant, cyclic cumulant
(CC), intelligent receiver, maximum likelihood (ML), modu-
lation classification, orthogonal frequency-division multiplexing
(OFDM), testbed implementation.
NOMENCLATURE
16-QAM 16 quadrature amplitude modulation.
AWG Arbitrary waveform generator.
Manuscript received August 7, 2021; revised October 13, 2021; accepted
October 20, 2021. Date of publication November 2, 2021; date of current
version March 3, 2022. This work was supported in part by the Ministry of
Electronics and Information Technology, Government of India, under Project
13 (2)/2020-CC&BT and in part by the Empowerment and Equity Oppor-
tunities for Excellence in Science Schemes by the Science and Engineering
Research Board through the Department of Science and Technology, Govern-
ment of India, under Project EEQ/2018/000201. The Associate Editor coordi-
nating the review process was Dr. Huang-Chen Lee. (Corresponding author:
Sudhan Majhi.)
Mahesh Shamrao Chaudhari is with the Department of Electrical Engineer-
ing, IIT Patna, Patna 801103, India (e-mail: mahesh.pee17@iitp.ac.in).
Sushant Kumar is with the Department of Electronics and Communica-
tion, National Institute of Technology Patna, Patna 800005, India (e-mail:
sushant.ec@nitp.ac.in).
Rahul Gupta is with Mavenir Systems Pvt. Ltd., Bengaluru 560045, India
(e-mail: rahul.gupta1@mavenir.com).
Manish Kumar is with the Communications and Signal Processing Group,
DA-IICT, Gandhinagar 382007, India (e-mail: manish_kumar@daiict.ac.in).
Sudhan Majhi is with the Department of Electrical Communication Engi-
neering, Indian Institute of Science, Bengaluru 560012, India (e-mail:
smajhi@iisc.ac.in).
Digital Object Identifier 10.1109/TIM.2021.3124833
AWGN Additive white Gaussian noise.
BER Bit error rate.
BMC Blind modulation classification.
BPSK Binary phase shift keying.
BWR Blind wireless receiver.
CC Cyclic cumulant.
CFO Carrier frequency offset.
CP Cyclic prefix.
CSI Channel state information.
DFT Discrete Fourier transform.
GSM Global System for Mobile Communications.
ICI Intercarrier interference.
IF Intermediate frequency.
ISI Intersymbol interference.
LTE Long-term evolution.
MAP Maximum a-posteriori.
ML Maximum likelihood.
M-PSK M-ary phase shift keying.
M-QAM M-ary quadrature amplitude modulation.
MSK Minimum shift keying.
OFDM Orthogonal frequency-division multiplexing.
OQPSK Offset quadrature phase shift keying.
RF Radio frequency.
SDR Software-defined radio.
STO Symbol timing offset.
VERT Vertical antenna.
VSA Vector signal analyzer.
VSG Vector signal generator.
WiMAX Worldwide interoperability for microwave
access.
I. INTRODUCTION
THE intelligent or adaptive transceiver is going to be a
key feature for upcoming generations of wireless commu-
nication [1]. Sixth-generation (6G) wireless communications
are looking for integrated artificial intelligence in the physical
layer of the wireless device. The adaptive receiver has sev-
eral applications in signal monitoring [2], signal intelligence,
smart spectrum sharing, modulation classification, throughput
enhancement, and channel prediction that can be implemented
in SDR [3]. A similar system can be implemented by using a
statistical signal processing model as described in [4]–[7].
OFDM is the key element in diverse communications
standards [8]. It is the underlying technology in the phys-
ical layer for IEEE 802.11, digital audio and video broad-
casting, WiMAX, LTE, and many more. It is robust to
frequency-selective fading environments as serial high-speed
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5501211 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 71, 2022
data can be transformed into multiple parallel low-speed
data streams that are transmitted through multiple orthogonal
subcarriers.
Thus, blind parameter estimation, BMC, and blind tim-
ing and frequency synchronization for OFDM signals have
become the focus of many research communities. In cognitive
radio, the secondary transmitter often changes the signal para-
meters to suit the availability of spectrum and channel from
the primary users [9]. The secondary transmitter has to send
the information to the secondary receiver about the changes
made at the transmitter. As a result, additional overhead needs
to be introduced in the transmitted signal to train the secondary
receiver. Thus, the spectrum efficiency, i.e., overall information
throughput, gets reduced and provides high latency to the
communication [10]. Hence, the blind parameter estimated
receiver is desirable in these situations as it can blindly retrieve
the information at the receiver without any prior knowledge
of transmitted signal parameters, modulation formats, and CSI.
In fact, using no or minimal training sequence, blind or semi-
blind parameter estimated receiver can substantially improve
the spectral efficiency of the communication system [11].
Even though training sequences are desirable for some com-
munication systems to estimate various parameters from the
signal, the properties of the training sequence get significantly
affected under severe channel conditions. Therefore, training
sequences may not be used for parameter estimation or signal
synchronization in such scenarios [12]. Recently, it has been
noticed that the physical layer security can also be enhanced by
adapting the signal parameters at the transmitter [13]. Hence,
blind parameter estimated receiver, intelligent, or adaptive
transceiver has many key features for the future wireless
communication systems.
II. RELATED WORK
There are several research works available in the literature
to estimate specific parameters blindly for the OFDM signal.
The estimation of OFDM signal parameters includes symbol
duration, useful symbol duration, CP length, oversampling
factor, and the number of subcarriers. In [14], the parameter
extraction is carried out in three successive stages. At the first
stage, the Gaussian test is applied to differentiate between sin-
gle carrier (SC) signal or OFDM signal. At the second stage,
the cyclostationarity test is applied to differentiate between the
OFDM signal and the AWGN. At the last stage, correlation
is applied to carry out parameter estimation, such as the
number of the OFDM symbol and CP duration. It has very low
computational complexity but yields poor performance over
frequency-selective fading channel and the limited number of
physical layer parameters has been considered in this work.
Alternatively, OFDM signal parameters can also be estimated
blindly by exploiting the cyclostationary properties of the
signal as presented [15]. The error in the parameter estimation
process further affects the synchronization process, which
eventually makes it impossible to reconstruct the desired con-
stellation points. Similar signal identification and parameter
estimation algorithms are investigated in [15] and [16].
The BMC for OFDM is a sensitive part of the demodulation
process, and the success rate of the BMC needs to be very high
for retrieving the transmitted data. OFDM signal’s modulation
classification is an important research problem in the presence
of synchronization impairments, i.e., timing, frequency, and
phase offsets. There are only a few BMC algorithms available
in the literature for the OFDM systems [5], [17]–[19]. The
BMC algorithms based on MAP and ML [17], [19] work for
both known or unknown CSI. However, both algorithms con-
sider a perfectly synchronized OFDM signal while classifying
the M-PSK or M-QAM modulation formats. Nevertheless,
the BMC algorithms for OFDM signal discussed in [19] are
limited to known CSI and/or perfect synchronization systems.
The receiver of the OFDM system is also extremely sen-
sitive to STO and CFO errors. The presence of slight error
in STO and CFO estimations introduces ISI and ICI, respec-
tively [20]–[23]. As a result, the signal cannot be reconstructed
properly at the receiver. Therefore, it is of paramount impor-
tance to implement efficient synchronization schemes before
the DFT operation at the receiver.
There are various STO and CFO estimation methods dis-
cussed in the literature [6], [24]–[34]. The blind STO esti-
mators mainly utilize the ISI information associated with
the STO and develop a cost function to minimize or maxi-
mize it for the estimation. An STO estimator in [24] mini-
mizes the variance of the frequency domain signal after the
DFT operation. The power difference between subcarriers and
the phase shift induced by the timing error has been exploited
to estimate the STO [25]. The methods in [26] and [27] use
the second- and fourth-order cyclostationarity properties of the
received signal to estimate the STO.
The different spectrally efficient-based blind CFO estima-
tion methods are discussed in [6], [28], and [29]. These meth-
ods utilize the CFO information possessed by the covariance
matrix. The cost function given in [28] is based on the min-
imization of nondiagonal elements of the covariance matrix
of the frequency domain signal. However, it requires a fairly
large number of OFDM symbols. The method in [6] uses the
phase shift present between the oversampled symbols because
of the CFO; however, it requires a higher order polynomial for
estimating the CFO. To the best of the authors’ knowledge,
there exists no integrated receiver where all blind parameter
estimation, BMC, and blind synchronization algorithms are
considered in one platform and analyzed the overall BER
performances for the OFDM systems. This work is just a
preliminary work for 6G communication where SDR will be
fully automated and we just need a software upgradation to
move from one generation to other.
In this work, the estimation of OFDM signal parameters,
modulation classification, and synchronization is performed.
The blind parameter estimated receiver for SC is provided in
one of our previous works [10]. In this article, the blind para-
meters estimated receiver for OFDM signal is designed, imple-
mented, and measured the performance over RF testbed. The
main contributions of this article are summarized as follows.
1) This article is primarily divided into three main parts,
namely, parameters estimation, modulation classifica-
tion, and synchronization. Finally, the signal constella-
tion and information bits are reconstructed by integrating
these three steps.
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CHAUDHARI et al.: DESIGN AND TESTBED IMPLEMENTATION OF BLIND PARAMETER ESTIMATED OFDM RECEIVER 5501211
2) The CC method has been proposed to estimate the
important OFDM signal parameters, such as the number
of subcarriers, symbol duration, useful symbol duration,
CP length, and oversampling factor.
3) Cumulant method in the frequency domain has been
proposed for BMC, which can classify the linearly mod-
ulated signals such as BPSK, quadrature PSK (QPSK),
OQPSK, MSK, and 16-QAM over a frequency-selective
fading channel.
4) A modified ML method has been proposed to estimate
STO and CFO jointly and thereafter compensate them
for the OFDM system.
5) The key performance metrics of signal classification,
parameters estimation, modulation classification, and
synchronization are provided through analysis, simula-
tion, and measurement results and compared with the
existing results.
6) Compared to the existing methods, the proposed work
has a substantial contribution in terms of the overall
performances of OFDM receiver over simulation and
measurement. We have built a National Instrument (NI)
RF testbed setup using a configurable RF front end over
an indoor propagation environment. The testbed is the
integration of all the estimation methods and optimized
them end-to-end to obtain the BER performance of the
system.
The rest of this article is organized as follows. Section III
describes the OFDM signal model. Section IV discusses
parameter estimation methods. The modulation classification
is elaborated in Section V. Section VI presents the details of
STO and CFO estimation. Section VII provides the complexity
of the entire system with the comparison of various algorithms.
Section VIII describes the implementation and measurement
setup of the blind receiver testbed. Section IX provides the
simulation and experimental results of all the blind parameter
estimators and blind receiver. Finally, Section X concludes this
article. The abbreviation used in the rest of this article is listed
in Nomenclature.
III. OFDM SIGNAL MODEL
In the OFDM system, serial data streams are converted into
parallel blocks that are modulated using inverse DFT (IDFT).
The discrete-time OFDM signal in the baseband can be written
as
sm[n]=1
√K
K
k=1
dm[k]ej2πkn/Nu,0≤n<Nu(1)
where dm[k]is the transmitted data symbol of mth OFDM
symbol and Kis the total number of subcarriers. Useful data
and CP length are represented by Nu=ρ×Kand Ncp, respec-
tively, where ρis the oversampling factor. They make up the
total number of samples in OFDM symbol Ns, i.e., Ns=Nu+
Ncp. The transmitted baseband signal can be represented as
s[n]=∞
m=−∞
sm[n−mN
s−θ]
=sr[n]+jsi[n],(2)
where θis the STO and sr[n]and si[n]represent in-phase (I)
and quadrature-phase (Q) components, respectively. The
equivalent transmitted passband signal can be written as
x[n]=Re(sr[n]+jsi[n])ej2πfcn
=sr[n]cos
(2πfcn)−si[n]sin
(2πfcn).(3)
Without loss of generality and better to relate practical
implementation, the above signal can be represented as an
IF signal where fcis represented as IF frequency. The channel
response corresponding to the IF signal can be written as
f[n]=Reej2πfcn
L
i=1
hi[n]δ[n−˜τi],(4)
where hi[n]is the baseband channel response, Lis the number
of sample-spaced channel taps, and ˜τiis the delay of each
tap. In this article, the channel is assumed to be constant
over an OFDM symbol, but time-varying in nature across the
OFDM symbols, which is a reasonable assumption for low
and medium mobility scenarios. At the receiver, the signal
is captured along with the noise. After the downconversion
of RF-to-IF signal and subsequent filtering, the simplified
IF signal of the received signal can be formulated as
u[n]=x[n]⊗f[n]+v[n]
=ej2πfcn
L
i=1
s[n−˜τi]hi[n]+v[n],(5)
where v[n]is the IF AWGN noise and ⊗represents the
cyclic convolution operation. Similarly, after downconversion
to baseband signal and filtering, the received baseband signal
can be expressed as
y[n]=ej2πn/Nu
L
l=1
s[n−l−θ]h[˜τl]+w[n],(6)
where is the normalized CFO, Lis the number of multipath,
h[˜τl]is the channel coefficient at time ˜τl,w[n]is the baseband
AWGN with zero mean, variance σ2
w=E{|w[n]|2},ands[·],
h[·],andw[·] are uncorrelated.
IV. OFDM SIGNAL PARAMETERS ESTIMATION
From the baseband signal model, the problem statement can
be defined as: {y[n]}N
n=1is given, and Ns,Nu,Ncp ,θ,and
need to be estimated without any prior knowledge of the
transmitter signal and CSI.
A. Useful Symbol Length Estimation
To retrieve the signal at the receiver, one has to know the
useful symbol length of the OFDM symbol. The number of
samples in the useful OFDM symbol is estimated using the
second-order cyclostationarity. The time-varying correlation
function of the received signal can be expressed as
cy[n;τ]=Ey[n+τ]y∗[n]
=1
Kσ2
de−j2πτ/Nu
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5501211 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 71, 2022
×
L
l=1
h[˜τl]∞
m1=−∞
g[n+τ−˜τl−m1Ns−θ]
×
L
q=1
h∗˜τq∞
m2=−∞
g∗n−˜τq−m2Ns−θ
×
K−1
k=0
ej2πk(τ−˜τl+˜τq−Ns(m1−m2))/Nu
+Rww[n;τ],(7)
where g[·] is the pulse shaping filter, τis the time lag,
σ2
dis the signal power, and Rww[n;τ]is the time-varying
correlation function of noise components. The second-order
cyclostationarity of y[n]can be expressed as
Cy[α;τ]=1
N
N−1
n=0
cy[n;τ]e−j2παnτ=0,1,...,τ
max
=1
KNsσ2
de−j2πτ/Nue−j2παθ/Ns
×
L
l=1
h[˜τl]∞
m1=−∞
g[n+τ−˜τl−m1Ns−θ]
×
L
q=1
h∗˜τq∞
m2=−∞
g∗n−˜τq−m2Ns−θ
×e−j2παn
K−1
k=0
e−j2πk(τ−˜τl+˜τq−Ns(m1−m2))/Nu
+Rww[α, τ ],(8)
where αis the cyclic frequency, τmax is the maximum time
lag, Rww[α, τ ]is the CC of AWGN, and
{α}=α∈[−1/2,1/2)|α=mN−1
s,mis an integer.
(9)
The time-varying correlation function has the following
property:
cy[n;τ]=cy[n+Ns;τ],(10)
where
cy[n;τ]=1
N
N−1
α=0
Cy[α;τ]ej2παn,(11)
and Nsis the periodic parameter that refers to the number of
samples in an OFDM symbol period. Again, the correlation
function has the following property:
cy[n;τ]=cy[n+Nu;τ],(12)
for n∈Ncp within the Nssamples. It implies that cyclosta-
tionarity has dual peak properties for OFDM signal: one is
for Nuand other is for Ncp. Thus, the CC Cy{α;τ}provides
cyclic peak at ±k(1/Ts),k=0,1,2,...,mfor τ=Nu,where
Tsis the symbol period, fs=1/Tsis the symbol rate, and
Fs=ρ×fsis the sampling frequency.
Since the OFDM signal exhibits the second-order cyclosta-
tionarity at α=0 and at delay τ=Nu, the estimated number
of samples within a useful OFDM symbol period is derived
as
ˆ
Nu=arg max
τCy[0;τ].(13)
The corresponding useful OFDM symbol duration in terms
of time is obtained as
ˆ
Tu=ˆ
Nu×1/Fs.(14)
B. OFDM Symbol and Cyclic Length Estimation
The knowledge of the OFDM symbol and cyclic length at
the receiver is equally important to eliminate the effects of
ISI from the signal. It has been noticed that the OFDM signal
exhibits the second-order cyclostationary at delay τmalong
with α. Therefore, the OFDM symbol period can be estimated
by exploiting the nonzero peaks in the magnitude of the cyclic
frequency at delay τm=Nuand over the cyclic frequency
range. For the positive cyclic frequency, the nonzero cyclic
frequency appears at an integer multiple of Ns.
From the OFDM signal format, we know that CP length
is not more than half of the useful OFDM symbol length,
i.e., OFDM symbol duration follows the property ˆ
Tu≤Ts≤
ˆ
Tu+0.5∗ˆ
Tu. Therefore, the first symbol rate peak (the peak
at OFDM symbol rate), ±(1/Ts),of[α;Nu]appears in the
interval [(1/( ˆ
Tu+0.5∗ˆ
Tu)), (1/ˆ
Tu)]. The estimated OFDM
symbol duration is derived as
ˆ
Ts1=1
arg max 1
ˆ
Tu+0.5∗ˆ
Tu≤α≤1
ˆ
Tu
Cy[α;Nu].(15)
However, this estimator does not provide a good perfor-
mance. Thus, we have used an averaging over first, second, and
third consecutive peaks. The final estimated OFDM symbol
duration is represented as ˆ
Ts=(1/6)3
m=1ˆ
Tsm. Thus, Nsis
obtained as
ˆ
Ns=ˆ
Ts×Fs.(16)
Finally, cyclic or guard length is estimated as
ˆ
Ncp =ˆ
Ns−ˆ
Nu.(17)
Hence, the cyclic duration ˆ
TCis obtained as
ˆ
Tcp =ˆ
Ncp ×1/Fs.(18)
C. Number of Subcarrier Estimation
The number of the subcarrier of the OFDM signal is another
important parameter that needs to be known to perform the
DFT operation at the receiver. In the OFDM systems, the
number of subcarriers is equivalent to 2k,wherekis an integer
and the signal bandwidth is defined as Bw=K/Tu. We can
easily estimate the OFDM signal bandwidth ˆ
Bw.SinceKis
the form of 2k, we have proposed the number of subcarrier
estimator as
ˆ
K=2log2(ˆ
Bw∗ˆ
Tu),(19)
where · is the nearest integer operator.
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CHAUDHARI et al.: DESIGN AND TESTBED IMPLEMENTATION OF BLIND PARAMETER ESTIMATED OFDM RECEIVER 5501211
D. Oversampling Factor Estimation
In the conventional OFDM systems, the number of samples
in the useful OFDM symbol is usually kept larger than the
number of subcarriers. The oversampling factor is decided by
the sampling rate of the receiver. However, the knowledge of
oversampling is to be known at the receiver to reconstruct
the constellation point or information bits. It implies that the
received signals need to be decimated by an oversampling
factor. The proposed oversampling factor estimator is
ˆρ=ˆ
Nu
ˆ
K.(20)
From the simulation studies, it is noticed that ˆρis always
estimated correctly with a success rate of 100%. However,
ˆ
Nudeviates one or two samples from the true value. This
error propagates to the CP estimator. Thus, we propose a fine
estimator to estimate the useful symbol and CP length as
ˆ
ˆ
Nu=ˆρ׈
K,(21)
and
ˆ
ˆ
Ncp =ˆ
Ns−ˆ
ˆ
Nu.(22)
The above iterative process improves the overall estimation
process. Note that the useful symbol length is dependent on
the proper estimation of the oversampling factor parameter and
the number of subcarriers as presented in (19) and (20).
From (19), it is evident that the estimated number of
subcarriers is always the in-power of 2, i.e., ˆ
K=16,32,64,
and 128. Also, the estimation accuracy of ˆ
Kis very high,
which is discussed in the following. For example, consider
ˆ
Nu=161 (which is offset from its true value by 1), ˆ
Bw=2
MHz, Fs=20 MHz, and ˆρ=10, and then, from (14)
ˆ
Tu=161
2×107=8.05 ×10−6,
from (19)
ˆ
K=2log2(2×106×8.05×10−6)=24.009=24=16,
and from (21)
ˆ
ˆ
Nu=10 ×16 =160.
We are getting ˆ
ˆ
Nu=160 by reestimation of ˆ
Nu=158,159,
and 162, which is offset by 1 or 2 from its true value
Nu=160.
V. M ODULATION CLASSIFICATION
In this section, we discuss the frequency domain cumu-
lant approach to classify the modulation formats for OFDM
signal. The proposed method is robust to STO, CFO, and
phase offset without having proper knowledge of channel
statistics [35]. It is applicable to a more extensive pool of
modulations, i.e., BPSK, QPSK, OQPSK, MSK, and 16-QAM.
To nullify the effect of timing offset in the feature extraction
process, we introduce uniform random timing offsets θu∈
U(−K/2,K/2)in each OFDM symbol. Now, we can write
the modified expression for the mth OFDM symbol as ¯ym[n]=
ym[n−θu]. Fig. 1 shows the block diagram of the BMC.
Fig. 1. Program flow of the proposed BMC algorithm.
Classification is performed in two stages. At the first stage,
the normalized fourth-order cumulant is used on the DFT of
the received OFDM signal to classify OQPSK, MSK, and
16-QAM modulation formats. The sample average estimate of
fourth-order cumulant with two-conjugations can be expressed
as
ˆc42 ¯
Ym=1
N
N
n=1|¯
Ym[v]|4−|1
N
N
n=1
¯
Ym[v]2|2
−21
N
N
n=1|¯
Ym[v]|22
,(23)
where ¯
Ym[v]is the DFT of the modified OFDM symbol ¯ym[n].
In practice, we estimate the normalized fourth-order cumulant
by ˜c42 ¯
Ym=ˆc42 ¯
Ym/((1/N)N
n=1|¯
Ym[v]|2−σ2
w).Now,wetake
the average of all cumulant values, i.e., equal to the total
number of OFDM symbols Mas ˜c42Y=(1/M)M
m=1˜c42 ¯
Ym.
This gives distinct values for OQPSK, MSK, and 16-QAM
modulation formats. At the second stage, the remaining mod-
ulation formats, i.e., BPSK and QPSK, are classified using the
normalized fourth-order cumulant of DFT of a square of the
received OFDM signal and can be written as
˜c42 ¯
Zm=
1
NN
n=1|¯
Zm[v]|4−|ˆc20 ¯
Zm|2−2ˆc2
21 ¯
Zm
ˆc21 ¯
Zm−σ2
w
,(24)
where ¯
Zm[v]is the DFT of ¯y2
m[n],ˆc20 ¯
Zm=(1/N)N
n=1
¯
Zm[v]2,andˆc21 ¯
Zm=(1/N)N
n=1|¯
Zm[v]|2. Similarly, we take
the average of Mcumulant values to classify the BPSK and
QPSK modulation formats as ˜c42Z=(1/M)M
m=1˜c42 ¯
Zm.
VI. SYNCHRONIZATION
The estimation of STO and CFO needs to be compensated
before the DFT operation to remove ISI and ICI. Upon the
observation and successful detection of MOFDM symbols,
the log-likelihood (LL) function of the mth received OFDM
symbol ym[n]can be written as
LLest(θ,)=logM−1
m=0
LLest
m(θ,).(25)
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5501211 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 71, 2022
Substituting f(ym[n]),f(ym[n+Nu]),and f(ym[n],ym[n+
Nu])into (25) [31] and upon further solving
LLest(θ,)=M
n∈Du2ρest [n][n]−ρ2
est [n][n]
σ2
d1−ρ2
est [n]
−log1−ρ2
est [n],(26)
here, ρest [n]=σ−2
d|E{ψm[n]}|,ψm[n]=ym[n]y∗
m[n+
N],φm[n]=(1/2){|ym[n]|2+|ym[n+N]|2},[n]=
1/MM−1
m=0φm[n],(n)=1/MM−1
m=0γm[n],andγm[n]=
Re{ej2πψm[n]},andDu={θ,θ +1,...,θ +L+Ncp −1}.
A. Estimation of CFO
Using (26), LLest
n(θ , ) can be obtained as
LLest
n(θ,)=˜
T1([n]−ρest [n][n])−˜
T2,
where
˜
T1=2ρest [n]
σ2
y1−ρ2
est [n]and ˜
T2=log1−ρ2
est [n].
The maximization of the CFO parameter is dependent only
on [n]. Therefore, we can write
ˆ[n]=arg max
[n]
=arg max
{|[n]|cos(2π +[n])},
where [n]=|[n]|ej[n]and [n]=1/MM−1
m=0ψm[n].
Since |[n]| is independent of , the maximum value of the
argument is obtained when the cosine term is unity, i.e.,
ˆ[n]=−1
2π[n].
The value of ˆ[n]is calculated at all n,wheren∈Du.
Hence,
ˆ=1
Ncp +L
θ+Ncp+L−1
n=θ
ˆ[n].(27)
B. Estimation of STO
Theestimateofθand Lcan be generally obtained as [31]
ˆ
θ, ˆ
L=arg max
(θ, L)
n∈Du
LLest
n(θ, ˆ).
Note that L∈Z1{0,1,...,Ncp −1},θ∈Z2
{0,1,...,Ns−1}. For each value of θ,thereareNcp com-
binations of Du.(θ =0,L=0)gives one set of Du,i.e.,
Du={0,1,...,Ncp −1}.(θ =Ns−1,L=Ncp −1)gives
Du={Ns−1,Ns,...,Nu+3Ncp −3}. In all, there is a total
of Ncp ×Nscombinations of Du. In this context, the proposed
timing function ˜
G(r1,r2)is defined as
˜
G(r1,r2)=
r1+Lcp−1
n=r1+r2
E{[n]}−2
th
r1+Lcp−1
n=r1+r2
E{[n]},
(28)
TAB L E I
COMPLEXITY OF OVERALL SYSTEM
TAB L E I I
COMPLEXITY COMPARISON WITH EXISTING SCHEMES
where r1∈Z1,r2∈Z2,andth =(E{|ym[n]|2}−
E{|w[n]|2})/E{|ym[n]|2}=σ2
t/σ 2
y. Here, the function
˜
G(r1,r2)is computed for all the values of r1and r2.
Therefore, upon further calculations, it can be observed
that ˜
G(r1,r2)yields the maximum value at r1=θand
r2=L, i.e.,
ˆ
θ, ˆ
L=arg max
(r1,r2)
˜
G(r1,r2).(29)
ˆ
θis used to find the starting point of the OFDM symbol.
VII. COMPUTATION COMPLEXITY
The computational complexity of the entire system is pro-
vided in this section. Also, the proposed schemes are compared
with the existing ones. The end-to-end complexity of the
proposed method is shown in Table I. The complexity of
each of the algorithms is calculated first, and then, end-to-end
complexity is calculated from it.
Here, Nuis the useful symbol length, Ncp is the length of
the CP, Mis the total OFDM symbol used for estimation,
and Kis the number of subcarriers. Also, the comparison
of the proposed schemes with the existing schemes is shown
in Table II.
From Table II, it is clear that the complexity for the
proposed parameter estimation scheme is the same as that
of the scheme in [15] and [36]. Also, the complexity of the
proposed STO and CFO estimation scheme is equal to the
ML method [31]. However, the proposed CFO estimation
scheme is having less complexity than that of the scheme
in [29]. The complexity of the STO estimation scheme in [24]
and the proposed scheme is dependent on the choice of values
used for Nu,Ncp,andM. However, the performance of
the proposed scheme is much better than that of the power
difference method [24], which is discussed in Section VIII.
VIII. MEASUREMENT AND TESTBED
IMPLEMENTATION SETUP
The testbed measurement and implementation consist
of hardware and software parts as described in [10].
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CHAUDHARI et al.: DESIGN AND TESTBED IMPLEMENTATION OF BLIND PARAMETER ESTIMATED OFDM RECEIVER 5501211
Fig. 2. LabVIEW front panel of the OFDM transmitter.
The NI chassis is equipped with (NI PXIe-8135) embedded
controller, VSGs (NI PXIe-5673) are used at the transmitter
end, and VSAs (NI PXIe-5663) are used at the receiver end.
The transmitter and receiver consist of a VERT-2450 antenna
for transmission and reception of the RF signal with dual band
(2.4–2.5 and 4.9–5.9 GHz). The carrier frequency used for
transmission and reception is 2.3 GHz. The measurement and
implementation setup of BWR for OFDM is organized at the
Signal Processing for Wireless Communication (SPWiCOM)
Laboratory, IIT Patna.
A. Transmitter Setup
The binary and modulated data can be generated with the
help of mathscript or it can be generated in the LabVIEW
itself. These binary data are given to the AWG, which can
generate baseband I and Q signals at the data rate of up
to 200 Ms/s. AWG generates I-Q data that are upconverted
by an RF upconverter with the help of a local oscillator
that has a frequency range of 500 kHz–6.6 GHz. The power
level and the carrier frequency of transmission can be easily
changed through the front panel of the OFDM transmitter,
as shown in Fig. 2. Other parameters, such as the number
of subcarriers, the number of symbols in one OFDM block
of transmission, length of CP, modulation scheme, and trans-
mission symbol rate, are controlled through the same front
panel. Oversampling is done by a factor of 10 at the transmitter
end. Finally, the oversampled signal is fed up to the transmit-
ter antenna, which has an omnidirectional radiation pattern,
50 impedance, and a peak gain of 3 dBi for wireless
transmission.
B. Laboratory Setup
The laboratory wireless environment is quite dynamic due
to the movement of human traffic. Fig. 3 shows the floor
plan of the SPWiCOM laboratory. It is equipped with modern
instruments and amenities. It has a dimension of 10 m ×
12 m ×4 m and has several cabins for students and staff.
The antenna (VERT-2450) is installed at the receiver and the
transmitter and a height of 1 m from the level of the floor. The
cabins and human traffic in the laboratory act as scatterers
Fig. 3. Laboratory setup for measurements and implementation of blind
parameters estimated OFDM receiver.
for the electromagnetic (EM) wave that is originating from
the transmitter antenna. Apart from the scatter path, a clear
line-of-sight path is also available between the transmitter
and receiver antenna. Thus, multipath propagation is available
between transmitter and receiver. The typical delay spread for
laboratory setup is 50–100 ns. Thus, the coherence bandwidth
for the setup is 2–4 MHz. The channel path loss is also
about 25–35 dB.
C. Receiver Setup
A wireless signal is captured by the receiver antenna
(VERT-2450) and given to the receiver part for analysis.
A receiver is made up of three sections: RF acquisition, IF,
and baseband signal processing. The RF signal acquisition is
done by the VSG module of NI and it is further processed by
the mathscript node of MATLAB in real time, as shown in the
right of Fig. 4. The signal acquisition and processing of it is
carried out as described in [10].
IX. SIMULATION AND MEASUREMENT RESULTS
In this section, the overall performance of the blind para-
meter estimated receiver is evaluated through simulation and
experimental studies. The details of the experimental steps are
already described in Section VIII. For the simulation process,
we have used 5 MHz carrier frequency and 2 MS/s symbol
rate. For the experimental analysis, we have used carrier fre-
quency and symbol rate as 2.3 GHz and 2 MS/s, respectively,
to avoid any influence from other wireless systems, such
as GSM, LTE, and WiMAX. Furthermore, we specify the
modulation type as QPSK, the number of OFDM subcarriers
as 64, and the CP length as 1/4 of symbol length referring
to 802.11a. Accordingly, parameters, such as useful OFDM
symbol length, length of OFDM symbol, CP length, number of
subcarriers, oversampling factor, and modulation type, would
be estimated blindly at the receiver. Finally, the constellation
points and information bits are obtained.
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5501211 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 71, 2022
Fig. 4. Process flow of blind parameters estimated OFDM receiver in the LabVIEW environment.
Fig. 5. (a) Estimation performance for symbol length. (b) Estimation performance for useful symbol length. (c) Estimation performance for number of
subcarrier.
For the receiver setup, we have used the frequency spanning
method of hardware to acquire the signal in the desired band of
frequency. Start and stop frequency (in Hz) is provided to the
VSA so that it only observes that frequency span. A reference
level of −30 dBm is set up for signal reception and a signal
above this level is chopped off. The acquisition rate of 20
MS/s is given to VSA, which is the same as the transmitter
sampling rate after oversampling [10].
We have compared the proposed OFDM parameter
estimation (K,Nu,and Ns) performance with [37]. The pro-
posed OFDM parameter estimator gives slightly better perfor-
mance for parameters K=32, Ns=400, and Nu=320
against [37]. The proposed method carries out OFDM para-
meter estimation in both simulation and measurement environ-
ments without any knowledge of synchronization parameters.
Fig. 5(a) shows the performance of OFDM symbol length
estimation in terms of normalized mean square error (NMSE)
for both simulation and experimental study, where suffixes “S”
and “M” stand for simulation and measurement, respectively.
From Fig. 5(a), it has been observed that the experimental
performance approximates theoretical performance at a high
signal-to-noise ratio (SNR), although the experimental channel
is an indoor channel. As we increase the OFDM symbol
length, we get lower NMSE because we have more samples
to process, which ultimately enhances the estimation accuracy.
However, it increases the capturing time and buffers size of
the system, and thus, we have to trade off between accuracy
and computation time.
Fig. 5(b) shows the NMSE of useful OFDM symbol
length for both simulation and experimental results. It can
be observed that the simulation result almost coincides with
the experimental measure at high SNR. Although the different
channel is considered in both conditions, it has a little effect
on their performance because of insensitivity of OFDM signal
to multipath. Similar to the OFDM symbol length estimation
performance, the NMSE of useful OFDM symbol length
estimation varies with the SNR changes, and it can mainly
be decided by the number of processed symbols. However,
from the measurement and simulation results, we can say that
a less number of the processed symbol increases the NMSE
of useful OFDM symbol length.
Fig. 5(c) shows the performance of the subcarrier estima-
tor ( ˆ
K) for both simulation and experimental results. We have
carried out the performance for K=16, 32, 64, and 128.
The accuracy of the estimator increases with an increase
in SNR.
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CHAUDHARI et al.: DESIGN AND TESTBED IMPLEMENTATION OF BLIND PARAMETER ESTIMATED OFDM RECEIVER 5501211
Fig. 6. (a) NMSE of STO estimation of the proposed method for OFDM with different SNRs. (b) NMSE versus SNR of the CFO estimators. (c) Simulation
and measurement results: Pcc versus SNR for different modulation formats.
Fig. 6(a) shows the NMSE versus SNR curve of STO
estimation for the proposed algorithm, the ML estimator [31],
and the power difference measurement algorithm [24] under
the AWGN channel. The number of subcarriers is taken as
Nu=128 and the CP is set as Ncp =32. In the simulation
process, we have introduced θ=100 and =0.002. The
ML algorithm, power difference algorithm, and the proposed
scheme demonstrate the performance improvement with an
increase in SNR. It can be noted that the proposed STO esti-
mator outperforms the ML and power difference methods over
the range of moderate-to-high SNR, thereby demonstrating the
comparative robustness of the estimation algorithm.
The NMSE for measurement results cannot be obtained
in the case of STO because we do not guarantee that the
timing offset signal at the transmitter will exactly appear at
the receiver. This is because we cannot start transmission
and reception exactly at the same time. Fig. 6(b) shows
the NMSE comparison of the proposed CFO estimator with
the existing ML estimation [31] and ESPRIT-based estima-
tion [29]. The plot also presents the derived Cramer–Rao
lower bound (CRLB) of the CFO estimator under the
frequency-selective fading channel. The proposed estimator
outperforms the other estimators because the CFO estimate
has been obtained by maximizing LLest(θ , ) at each sampling
instant for better estimation accuracy. Thereafter, at each
sampling instants, the estimated CFO, i.e., ˆ[n], averaged over
the entire range of the fading channel. The performance of the
proposed scheme is also tested for different values of CFOs,
as shown in Fig. 6(b). The NMSE is almost the same for
different CFOs at a particular SNR.
BMC for the OFDM system is proposed in our previous
work [35]. The proposed carries out BMC in the presence
of timing, frequency, and phase offset without knowledge
of CSI. The comparison of the proposed method with the
Kolmogorov–Smirnov (KS) test [5] and cumulant-based [38]
method is carried out in [35]. The measurement results of the
proposed method are shown in Fig. 6(c).
Fig. 6(c) shows the accuracy of the percentage of correct
classification (Pcc) versus received SNR for five different
Fig. 7. Reconstructed constellation for 16-QAM.
modulation schemes, i.e., BPSK, QPSK, OQPSK, MSK, and
16-QAM in the simulation and measurement environment.
It has been observed that the performance beyond 10 dB SNR
is saturating, but below 10 dB, it is increasing exponentially.
Due to the RF hardware impairments, such as quadrature skew,
gain imbalance, and dc offset, the simulation performance is
much better than the testbed implementation. The channel
condition is the major affecting factor for the performance
of BMC in simulation and testbed implementation.
After parameter estimation of the OFDM signal, we can
demodulate the information carried by each subcarrier
received after identifying the type of modulation with the
above-described method. Fig. 7 shows the constellation points
of 16-QAM by experimental studies. It has been observed that
the constellations are distinct and this indicates that all the
parameters are estimated correctly, the timing offset error, and
the CFO has been compensated properly.
In the existing literature, the performance of OFDM para-
meter estimation is given individually by considering that other
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5501211 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 71, 2022
Fig. 8. BER plot of simulation and measurement.
parameters are known to the receiver. For instant, for the
existing CFO estimation method, it is assumed that STO and
other parameters were known prior to the receiver end. In this
work, each existing method or algorithm is optimized and its
performance is tested individually in the simulated and mea-
surement environment by considering that other parameters are
also estimated. Moreover, we have also compared the BER
performance of the proposed system with the conventional
receiver [39], as shown in Fig. 8. To carry out the BER
performance, channel estimation is carried out with the scheme
proposed in [40].
X. CONCLUSION
A BWR for the OFDM system testbed is built using config-
urable RF front-end SDR and tested in an indoor environment.
We have optimized each estimator to build an end-to-end
system and calculated the BER. We have proposed the fine
useful symbol length, number of subcarriers, and oversampling
factor estimator. The work in this article develops a complete
BWR by combining individual blind parameter estimation
algorithms sequentially without having knowledge of CSI.
The critically important parameters of the OFDM system,
such as OFDM symbol length, useful symbol length, CP, the
number of subcarriers, STO, CFO, and modulation, have been
estimated. We have measured the performance accuracy of
the individual estimator and overall blind receiver in realistic
indoor scenarios. The CSI is estimated for BER analysis only.
The performance comparison in terms of BER of simulation
and experimental results has been carried out. The detailed
experimental studies carried on the blind receiver ensure that
we can develop a BWR for future wireless communication
systems. In the future, we can implement BWR for the OFDM
system for the outdoor environment using RF and a low noise
amplifier. A similar idea can be extended for building BWR
for the SCFDMA system.
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Mahesh Shamrao Chaudhari (Graduate Student
Member, IEEE) received the B.E. degree in elec-
tronics and communication from the University of
Pune, Pune, India, in 2014, and the M.E. degree in
communication system engineering from BIT Mesra
Patna, Patna, India, in 2017. He is currently pursu-
ing the Ph.D. degree in electrical engineering with
IIT Patna, Patna.
His research interests include wireless communica-
tion and deep learning for wirelesss communication.
Sushant Kumar received the B.Tech. degree in
electronics and communication from ICFAI Uni-
versity, Dehradun, India, in 2011, and the M.Tech.
and Ph.D. degrees in electrical engineering from IIT
Patna, Patna, India, in 2015 and 2020, respectively.
He is currently an Assistant Professor with
the Department of Electronics and Communication
Engineering, National Institute of Technology, Patna.
His research interest is signal processing for wireless
communication.
Rahul Gupta received the B.Tech. degree in elec-
tronics and communication from the Oriental Insti-
tute of Science and Technology, Bhopal, India,
in 2012, and the M.Tech. and Ph.D. degrees in
electrical engineering from IIT Patna, Patna, India,
in 2015 and 2020, respectively.
He was a Post-Doctoral Researcher with the
Department of Electrical and Computer Engineer-
ing, University of Cyprus, Nicosia, Cyprus. He is
currently a Member of Technical Staff II of Research
and Development with Mavenir Systems Pvt. Ltd.,
Bengaluru, India. His research interest is signal processing for wireless
communication.
Manish Kumar received the B.Tech. degree in elec-
tronics and communication from ICFAI University,
Dehradun, India, in 2010, the M.Tech. degree in
digital communication from ABV-IIITM, Gwalior,
India, in 2013, and the Ph.D. degree in electrical
engineering from IIT Patna, Patna, India, in 2018.
He worked as Lead Engineer at the 5G Sys-
tem Engineering Research and Development Team,
Radisys, Bengaluru, India, wholly owned subsidiary
of Reliance Jio Platforms from 2019 to 2021, and
was a Researcher at Ben-Gurion University, Be’er
Sheva, Israel, from 2018 to 2019. He is currently an Assistant Professor with
the Communications and Signal Processing Group, DA-IICT, Gandhinagar,
India. His research interests lie in the domain of 5G communication and
signal processing aspects for wireless communication.
Sudhan Majhi (Senior Member, IEEE) received
the M.Tech. degree in computer science and data
processing from IIT Kharagpur, Kharagpur, India,
in 2004, and the Ph.D. degree from Nanyang Tech-
nological University (NTU), Singapore, in 2008.
He was a Post-Doctoral Researcher with the Uni-
versity of Michigan–Dearborn, Dearborn, MI, USA,
the Institute of Electronics and Telecommunications,
Rennes, France, and NTU. He is currently an Asso-
ciate Professor with the Department of Electrical
Communication Engineering, Indian Institute of Sci-
ence (IISc), Bengaluru, India. His research interest is signal processing for
wireless communication.
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