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Carrier Frequency Offset Impact on LTE-OFDM Systems: Proceedings of the
Fourth ICMEET 2018
Chapter in Lecture Notes in Electrical Engineering · January 2019
DOI: 10.1007/978-981-13-1906-8_42
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Andhra University
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Carrier Frequency Offset Impact
on LTE-OFDM Systems
Chanamala Vijay, Gottapu Sasibhushana Rao and Minchula Vinodh Kumar
Abstract The Carrier Frequency Offset (CFO) occurs in an LTE-OFDM system
due to the mismatched frequencies on the received signal and the local oscillator at
the receiver. The reason for this offset is caused due to the Doppler shift resulting in
Inter-Carrier Interference (ICI) and Inter-Symbol Interference (ISI) where its performance degrades with an increase in the Bit Error Rate (BER). This paper analyses the
BER performance for various modulations with different ranges of frequency offset.
The results indicate that for BPSK modulation technique, it provides better BER at
null carrier frequency offset when compared to other modulation techniques (QPSK,
8PSK, 16PSK, 32PSK, 64PSK, and 16QAM) and other ranges of offset frequency.
Keywords OFDM · CFO · ICI · ISI · SNR · BER
1 Introduction
OFDM is an established modulation scheme in current broadband wireless mobile
communication systems due to its high spectral efficiency and robustness against
multipath interference. Its system model with offset is as shown in Fig. 1. The notable
drawback of the OFDM system is its sensitivity to carrier frequency offset caused
by oscillator inaccuracies and the Doppler shift in the channel. Doppler shift occurs
when the transmitter of a signal is moving in relation to the receiver [1–3]. The
relative movement shifts the frequency of the signal, making it different at the receiver
than the transmitter. CFO causes frequency differences between the transmitter and
C. Vijay (B) · G. Sasibhushana Rao · M. V. Kumar
Andhra University College of Engineering (A) Andhra University, Visakhapatnam 530003,
Andhra Pradesh, India
e-mail: vchanamala@gmail.com
G. Sasibhushana Rao
e-mail: sasigps@gmail.com
M. V. Kumar
e-mail: vinodh.edu@gmail.com
© Springer Nature Singapore Pte Ltd. 2019
G. Panda et al. (eds.), Microelectronics, Electromagnetics
and Telecommunications, Lecture Notes in Electrical Engineering 521,
https://doi.org/10.1007/978-981-13-1906-8_42
401
402
S(k)
C. Vijay et al.
S/P
Signal
Mappe
r
B(k)
Adding B(n) Adding
Cyclic
Pilots
Prefix
and
and P/S
IFFT
b(t)
DAC
Channel k(t)
z(t)
j 2πδ 1 x 0
δ 1=
ε
e
X
Δf
Gaussian noise w(t)
a(n)
A(k)
S(k)
P/S
Signal
Demappe
r
FFT
Remove
Cyclic
Prefix
and S/P
ADC
a(t)
r(t)
Fig. 1 Block diagram of OFDM with frequency offset
receiver oscillator, Doppler shift of mobile channels, decrease in power efficiency,
phase shift, and oscillator instabilities.
Merits and Demerits of OFDM are listed as below [4, 5]
(i)
(ii)
(iii)
(iv)
Very easy and efficient in dealing with multipath.
Robust against narrowband interference.
Sensitive to frequency offset and phase noise.
Peak to average power ratio reduces the power efficiency of RF amplifier at the
transmitter.
2 Frequency Offset
In modern communication system engineering, CFO is shifting of the radio frequency
as shown in Fig. 2. The CFO destroys the orthogonality of the carriers and causes
Inter-Symbol Interference (ISI) and Inter-Channel Interference (ICI) [6–8]. There
are two categories of CFO, they are as follows:
Magnitude
Carrier Frequency Offset
Fig. 2 Carrier frequency offset (ε)
Frequency
Carrier Frequency Offset Impact on LTE-OFDM Systems
403
(1) Fractional CFO, which introduces ICI and degrades the performance of Bit
Error Rate (BER) and
(2) Integer CFO, which introduces the cyclic shift of data subcarriers and phase
change.
The OFDM transmitter and receiver with CFO equations can be determined as
At transmitter
b(n) k−1
j2π xm
1 B(m)e X
X m0
(1)
At receiver
a(n) b(n)e
j2π xε
X
+ w(n)
(2)
where ε Normalized Carrier Frequency offset, ε 1f f X T and w(n) XT
Noise of the signal, N number of subcarriers.
Channel carrier frequency offset is added to the received signal
A(k) B(k)S(0) +
N −1
B(l)S(l − k) + W (k)
(3)
l0,lk
where k = 0, 2, …, N − 1.
Due to the carrier frequency offset, the Bit Error Rate (BER) performance degrades
as the signal-to-noise ratio (SNR) increases for the selective range of CFO [9, 10].
3 Results
This section illustrates the behavior of OFDM with different CFO ranges in terms
of BER versus SNR for various modulations such as BPSK, QPSK, 8PSK, 16PSK,
32PSK, 64PSK, and 16QAM. All simulations are performed by using MATLAB
software. The offset ranges from 0 to 0.2 with an interval of 0.05 under Gaussian
channel. The simulated results are compared with each modulation techniques for
the above-selected range of CFOs. It is observed that BPSK modulation technique
is having low BER for null offset when compared to other modulation techniques.
The BER results for various modulations versus. SNR in dB under different ranges
of CFOs are plotted in Fig. 3 and tabulated in Table 1.
The BER performance of CFO OFDM system gradually decreases as SNR
increases, whereas at fixed SNR, BER increases with CFO as shown in Table 1.
The BPSK modulation is having least BER when compared to the 16QAM for
CFO “0” and BER is increasing for an increase in CFOs. So, it is observed that BPSK
modulation technique is having low BER for null offset than other modulations.
404
C. Vijay et al.
0
10
-1
10
-2
BER
10
-3
10
CFO 0
CFO 0.05
-4
10
CFO 0.1
CFO 0.15
CFO 0.2
-5
10
-6
10
0
1
2
3
4
5
6
7
8
9
10
SNR
(a) BER for BPSK modulation
0
10
-1
BER
10
CFO 0
-2
CFO 0.05
10
CFO 0.1
CFO 0.15
CFO 0.2
-3
10
0
1
2
3
4
5
6
7
8
9
10
7
8
9
10
SNR
(b) BER for QPSK modulation
0
BER
10
-1
10
CFO 0
CFO 0.05
CFO 0.1
CFO 0.15
CFO 0.2
-2
10
0
1
2
3
4
5
6
SNR
(c) BER for 8PSK modulation
Fig. 3 Performance of BER with SNR for CFO range from 0 to 0.2 by applying various modulation
techniques a BER for BPSK modulation, b BER for QPSK modulation, c BER for 8PSK modulation,
d BER for16PSK modulation, e BER for 32PSK modulation, f BER for 64PSK modulation, g BER
for 16QAM modulation
Carrier Frequency Offset Impact on LTE-OFDM Systems
405
-0.1
10
BER
-0.2
10
CFO 0
-0.3
CFO 0.05
10
CFO 0.1
CFO 0.15
CFO 0.2
-0.4
10
0
1
2
3
4
5
SNR
6
7
8
9
10
7
8
9
10
8
9
10
(d)BER for16PSK modulation
-0.03
10
-0.06
10
BER
-0.09
10
CFO 0
CFO 0.05
-0.12
CFO 0.1
10
CFO 0.15
CFO 0.2
-0.15
10
-0.18
10
0
1
2
3
4
5
6
SNR
(e) BER for 32PSK modulation
-0.01
10
-0.02
10
-0.03
10
-0.04
BER
10
-0.05
10
CFO 0
CFO 0.05
-0.06
10
CFO 0.1
CFO 0.15
-0.07
CFO 0.2
10
-0.08
10
0
1
2
3
4
5
SNR
6
7
(f) BER for 64PSK modulation
Fig. 3 (continued)
406
C. Vijay et al.
-0.08
10
CFO 0
CFO 0.05
-0.09
CFO 0.1
10
CFO 0.15
BER
CFO 0.2
-0.1
10
-0.11
10
-0.12
10
0
1
2
3
4
5
6
7
8
9
10
SNR
(g) BER for 16QAM modulation
Fig. 3 (continued)
Table 1 CFO OFDM system performance in BER versus SNR for different modulations
CFO
SNR
0
2
4
6
8
10
(a) BER for BPSK modulation
0
0.078644
0.037438
0.05
0.084684
0.042579
0.1
0.101945
0.057871
0.15
0.131541
0.085102
0.2
0.173363
0.12615
(b) BER for QPSK modulation
0.012452
0.015614
0.026447
0.048823
0.085555
0.002327
0.003599
0.009198
0.024485
0.054676
0.000198
0.00044
0.002299
0.010701
0.032775
4.69E-06
2.03E-05
0.000369
0.004013
0.019105
0
0.291712
0.197715
0.05
0.309956
0.21954
0.1
0.360026
0.282652
0.15
0.433372
0.377812
0.2
0.517500
0.487174
(c) BER for 8PSK modulation
0.109498
0.13418
0.209367
0.326538
0.459823
0.045531
0.067938
0.145056
0.278971
0.439834
0.011942
0.026476
0.092691
0.237977
0.423465
1.52E-03
7.34E-03
0.054682
0.203622
0.413179
0
0.05
0.1
0.15
0.2
0.389978
0.432836
0.538837
0.659909
0.75783
0.279327
0.343744
0.496718
0.653526
0.76987
0.17411
0.261075
0.464486
0.660193
0.78765
0.087213
0.18912
0.443959
0.67378
0.805837
0.577309
0.593938
0.641323
0.701901
0.760627
0.490926
0.51873
0.589317
0.676556
0.754763
(continued)
Carrier Frequency Offset Impact on LTE-OFDM Systems
Table 1 (continued)
CFO
SNR
0
2
407
4
6
8
10
0
0.776788
0.726357
0.05
0.786784
0.744514
0.1
0.815534
0.788336
0.15
0.848979
0.838316
0.2
0.881541
0.881165
(e) BER for 32PSK modulation
0.661444
0.691984
0.762869
0.833515
0.885948
0.581534
0.634854
0.744088
0.838197
0.896666
0.487653
0.576304
0.737901
0.851133
0.910405
0.382983
0.524866
0.746335
0.870782
0.925125
0
0.886959
0.86079
0.05
0.892352
0.869707
0.1
0.906378
0.893055
0.15
0.92483
0.918941
0.2
0.940813
0.941132
(f) BER for 64PSK modulation
0.82542
0.84288
0.88023
0.91772
0.943667
0.781804
0.811607
0.871598
0.921059
0.949845
0.727747
0.780671
0.870809
0.929513
0.957452
0.660688
0.754652
0.879839
0.941159
0.965181
0
0.943425
0.929761
0.05
0.945672
0.934871
0.1
0.95322
0.946372
0.15
0.961951
0.959393
0.2
0.970549
0.97053
(g) BER for 16QAM modulation
0.91226
0.920863
0.940327
0.959005
0.971931
0.890116
0.905502
0.936477
0.960477
0.975017
0.861768
0.889098
0.935768
0.96483
0.97901
0.82628
0.875956
0.940466
0.971102
0.98292
0
0.05
0.1
0.15
0.2
0.74987
0.749475
0.749188
0.771145
0.841034
0.74983
0.748851
0.748386
0.765766
0.839796
0.750437
0.749652
0.747768
0.76428
0.838629
0.750481
0.748608
0.749256
0.762372
0.83769
(d) BER for 16PSK modulation
0.74922
0.74883
0.753488
0.782832
0.845952
0.749587
0.748692
0.751015
0.775532
0.843123
4 Conclusions
LTE-OFDM system performance analysis is evaluated for determining the impact
of Carrier Frequency Offset by considering the different modulation techniques.
Further, the impact of different CFO values is analyzed for different modulation
techniques and in which the BPSK provides better performance when compared
to other modulation techniques. It is found that for a BPSK modulation, the BER
increases due to different CFOs as 0.078644 for CFO “0”, 0.084684 for CFO “0.05”,
0.101945 for CFO “0.1”, 0.1315410 for CFO “0.15”, and 0.173363 for CFO “0.2”.
LTE-OFDM system analysis signifies that BPSK is less sensitive to CFO than other
modulation techniques.
408
C. Vijay et al.
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