BER reduction in OFDM systems susceptible to ICI using the exponential linear pulse

Abstract

Intercarrier interference severely limits orthogonal frequency-division multiplexing (OFDM) performance. Nevertheless,it can be mitigated by using pulse shaping filters. In OFDM-based systems, we assess the exponential linear (EL)
pulse and compare it with the best Nyquist-I pulses. EL pulse is characterized by having one additional design parameter, knows as β. It is first optimized through extensive numerical simulations. We discovered that EL pulse outperforms the rest of pulses in terms of the bit error rate. This finding was explained by its frequency response, which presents both a broad main-lobe and negligible lateral-lobes. For EL pulse and the best pulse shaping functions, we finally determined the signal-to-noise ratio and frequency offset requirements in a real scenario.

Full text

BER Reduction in OFDM Systems Susceptible to
ICI Using the Exponential Linear Pulse
David Zabala-Blanco, Gabriel Campuzano
Department of Electrical and Computer Engineering
Tecnologico de Monterrey, Monterrey, Mexico
Emails: davidzabalablanco@hotmail.com, campuzano@itesm.mx
Cesar A. Azurdia-Meza
Department of Electrical Engineering
Universidad de Chile, Santiago, Chile
Email: cazurdia@ing.uchile.cl
Abstract—Intercarrier interference severely limits orthogonal
frequency-division multiplexing (OFDM) performance. Never-
theless, it can be mitigated by using pulse shaping filters. In
OFDM-based systems, we assess the exponential linear (EL)
pulse and compare it with the best Nyquist-I pulses. EL pulse is
characterized by having one additional design parameter, knows
as β. It is first optimized through extensive numerical simulations.
We discovered that EL pulse outperforms the rest of pulses in
terms of the bit error rate. This finding was explained by its
frequency response, which presents both a broad main-lobe and
negligible lateral-lobes. For EL pulse and the best pulse shaping
functions, we finally determined the signal-to-noise ratio and
frequency offset requirements in a real scenario.
Index Terms—Bit error rate, exponential linear pulse, inter-
carrier interference, orthogonal frequency division multiplexing,
Nyquist-I pulses.
I. INTRODUCTION
Due to the robustness against intersymbol interference pro-
duced by multipath effects in wireless channels, orthogonal
frequency-division multiplexing (OFDM) has been adopted in
several applications [1]–[3]. These include worldwide inter-
operability for microwave access (WiMax), wireless fidelity
(WiFi), long-term evolution (LTE), digital subscriber line
(DSL), digital video broadcasting (DVB), among others [1],
[3]. The massive adoption of OFDM as modulation technique
is furthermore based on its high spectral efficiency (orthogonal
subcarriers) and simplicity of transmitters and receivers (fast
Fourier transform by utilizing digital signal processors) [1]–
[3].
For an OFDM signal to perform correctly, its subcarriers
must be orthogonal during the symbol transmission, and all
the way to the detection process [1], [3]. Unfortunately,
some physical impairments destroy this orthogonality, such
as oscillator frequency detuning and phase noise [3], [4].
We will focus on the former. Carrier frequency offset (CFO)
comes from receiver crystal oscillator inaccuracy or Doppler
spread [1], [2], and produces subcarrier phase rotation, known
as common phase error (CPE), and intercarrier interference
(ICI) [5], [6]. Through pilot-aided phase-noise correction, CPE
is usually suppressed since it is included in most OFDM
implementations to estimate the wireless channel [2]. ICI
is however not easy to eliminate. To do this, consequently,
many proposals exist, including windowing, coding, ICI self-
canceling, and frequency equalization, for example, have been
proposed [2], [7]–[9]. In this manuscript We will focus on the
pulse shaping method.
The impact of Nyquist-I pulses on the performance of
OFDM systems with oscillator frequency detuning has been
extensively studied by several scholars [10]–[22]. Tan et. al.
[10] presented the better than raised cosine function, a pulse
that outperforms the rectangular and raised cosine pulses
based on the fact that the filter frequency response exhibits
a broad main-lobe and negligible side-lobes. Numerous pulse
shaping filters with better results than the raised cosine pulse
have been also proposed [11], [12], [14]–[22]. Among these,
the sinc parametric exponential (SPE) and sinc parametric
linear (SPL) pulses may be highlighted [17]. Both functions
possess two additional design parameter, excluding the roll-off
factor, in order to enhance the bit error rate (BER). Improved
modified Bartlett-Hanning (IMBH) [16], improved parametric
linear combination (IPLC) [19], and sinc exponential (SE)
[22] pulses are currently considered the best in this regard.
Nevertheless, the study of novel pulses of Nyquist-I is still
a significant issue owing to continuous increase of wireless
traffic demand.
For peak-to-average power ratio (PAPR) reduction in single-
carrier frequency-division multiple access (SC-FDMA), the
exponential linear (EL) pulse has been revealed in [23]. It
is characterized by having two design parameters, βand the
roll-off factor, where the former provides an extra degree of
freedom to compensate ICI. In this paper, we evaluate and
compare the performance of EL pulse with IMBH, IPLC,
SPE, SPL, and SP pulses in OFDM-based systems. The roll-of
factor is fixed to 0.22 because the 3rd Generation Partnership
Project (3GGP) has suggested this value for the pulse shaping
function implementation at the transmitter and receiver of the
base station and user equipment [24], [25]. We first optimized
EL pulse via extensive numerical simulations. Our results then
revealed that EL pulse outperforms the other pulses in terms of
the BER. Without CPE and given a BER threshold, we finally
found the signal-to-noise ratio (SNR) per bit and normalized
frequency offset requirements for the mentioned pulse shaping
filters. Once again, EL pulse is the best option. The reason
behind all these results is attributed to the lobes of the spectral
function.
The rest of the paper is organized as follows: Section II
describes an OFDM signal over an additive white Gaussian

noise (AWGN) channel with both CFO and Nyquist-I pulses.
In Section III, EL pulse is exposed, optimized, and compared
with the other filters in the frequency domain. For all these
functions, the BER is extensively discussed in Section IV, and
conclusions are reported in Section V.
II. SY ST EM MO DE L AN D EVALUATI ON METRIC
At the baseband, a single transmitted OFDM symbol ac-
quires the form of [10]:
x(t) =
N−1
X
m=0
cmp(t)exp[j2πfmt],(1)
where Ndenotes the number of subcarriers, cmis the m-
th constellation symbol (M-PSK or M-QAM), p(t)is the
pulse shaping filter, and fm=m/T represents the m-th
frequency subcarrier where Tis the OFDM symbol period
in order to obtain orthogonal frequencies [2]. The OFDM
signal is afterwards corrupted by both CFO and AWGN
[10], [13], [18], [20]–[22]. Whereas the former comes from
oscillator frequency detuning or Doppler spread, the latter is
added to account for thermal noise [1], [2]. After frequency
down-conversion, the complex-valued input to the OFDM
demodulator results in [2]:
y(t) =
N−1
X
m=0
cmp(t)exp[j2π(fm+ ∆f)t+θ] + n(t),(2)
with ∆f,θ, and n(t)representing the frequency offset, time-
invariant phase shift, and AWGN, respectively. Obviously, the
received OFDM signal exposes not only phase noise but also
amplitude noise.
It is well-know that the BER is the most relevant perfor-
mance measure of communication systems [1], [3], [13] . For
a BPSK-OFDM system with pulse shaping, CFO, and AWGN,
the BER is given by [13]:
BER = 1 −(1 −BERsy m)N,(3a)
BERsym =1
2Qcos(θ)P(∆f) + pPIC I p2Eb/N0
+Qcos(θ)P(∆f)−pPIC I p2Eb/N0,(3b)
where BERsym is the BER per symbol, Q[.]is the Gaussian
co-error function, P(f)is the Fourier transform of p(t),PIC I
is ICI power, and Eb/N0is the SNR per bit. If the main-lobe
of P(f)is much greater than the spectral summation of its
lateral-lobes, i.e. P(∆f)PN−1
m=0,m6=k|P[(m−k)/T −∆f]|,
the BER per symbol can be approximated as [13]:
BERsym ≈Qcos(θ)P(∆f)p2Eb/N0.(4)
Taking into account the relationship between side-lobes and
the central-lobe of P(f), see Fig. 2, we hence assess the BER
according to Eq. (4).
III. EXPONENTIAL LINEAL PUL SE
As mentioned, an OFDM symbol is composed by N orthog-
onal signals. Loss of this orthogonality generates ICI, which
means system degradation [1]–[3]. To compensate it, the pulse
shaping function must fulfill the Nyquist-I criterion [26]. In
frequency domain, it is defined as:
P(f) = (1, f = 0
0, f =±1/T, ±2/T, ... (5)
This means that at the separation between OFDM subcarriers,
ICI does not exist and the OFDM signal can be then demod-
ulated. It is worth to note that a pulse shaping filter with a
no-narrow main-lobe and the smallest lateral-lobes is the last
goal [10], [26].
Based on the linear-1 pulse [27], the EL pulse was proposed
to reduce PAPR for SC-FDMA in [23]. Its frequency response
is given by:
P(f) = exp[−0.5πβ(f T )2]sinc(fT )sinc(αf T ),(6)
where αrepresents the roll-off factor and βis an extra design
parameter. We fixed the roll-off factor to 0.22 since it has
been suggested by the 3GPP [24], [25]. βvaries from 0
to 1 and allows a reduction of the side-lobes of P(f)at
expense of decreasing its central-lobe. The EL is evidently
a Nyquist-I pulse because it fully satisfies Eq (5). Further, the
EL pulse thus becomes linear-1 pulse if βis equal to 0. Fig. 1
depicts how the frequency profile evolves for various β. As β
increases, the lateral-lobes decreases, however, the main-lobe
also decreases. Through extensive numerical simulations, a β
of 0.2 was finally found to improve the performance of the
system.
0 0.5 1 1.5 2
f T
-0.2
0.2
0.6
1
P (f)
0
0.25
0.5
0.75
1
Fig. 1. Frequency domain of the exponential lineal pulse with βas parameter.
By using the optimal β, EL pulse is compared with the best
performance Nyquist-I pulses [22]. For comparison purposes,
the design parameters of the other filters are the ones that
minimize the BER in OFDM-based systems [16], [17], [19],
[22]. Fig. 2 shows their spectra. It is expected that IMBH pulse
has the worst system performance by its narrow central-lobe.
On the other hand, SE and EL functions outperform the other

pulses due to not only their broad central-lobes but also their
negligible side-lobes. The almost same frequency responses of
these require a quantitative result, such as the BER, to known
which can be chosen as the best.
0 0.5 1 1.5 2
f T
-0.2
0.2
0.6
1
P (f)
EL, =0.2
IMBH, =1.52, n=2
IPLC, =2.5, =0.1, =1
SPE, b=0.5, =1
SPL, b=0.5, p=1
SE, =0.55, =1
Pulse
Fig. 2. Nyquist-I pulses frequency profile.
IV. PERFORMANCE EVALUATION
An OFDM signal with 64 subcarriers is employed to
evaluate the performance of the system. For a ∆fT = 0.25
and θ= 25o, the BER in terms of the SNR per bit with
Nyquist-I pulse as parameter is displayed in Fig. 3. As the
SNR per bit increases, of course, the BER enhances. Whereas
IMBH pulse exhibits the worst result, EL pulse presents the
best performance. Notice that EL and SE pulses have similar
behavior by their almost same spectra, see Fig. 2. For all
these filters, moreover, Fig. 4 depicts the SNR per bit and
normalized frequency offset requirements at a forward error
correction (FEC) limit equal to 10−3, which could be reduced
to 10−12 using modern FEC architectures [28]. There is not
phase noise because it is easily suppressed through pilot-
assisted equalization [2]. The minimum SNR per bit is 8.5
dB. Below this value, AWGN limits the system performance
and so compensate CFO does not make sense. The residual ICI
increases as the SNR per bit increases, too. This relationship
depends on which pulse shaping function is utilized, being
thus less demanding by EL pulse. For example, if a given
application imposes a SNR ber pit of 15 dB, IMBH and EL
pulses allow a normalized frequency offset up to 0.28 and 0.36,
respectively. All this means that EL function outperforms the
rest of the pulses in terms of the BER.
V. CONCLUSION
We initially introduced EL pulse in OFDM-based systems.
It was optimized via extensive numerical simulations and
compared with the optimized IMBH, IPLC, SPE, SPL, and SP
pulses through their frequency responses. EL and SE pulses
showed almost the same and also the best frequency behavior.
To conclude, we discovered that EL pulse outperformed the
rest of pulses for any normalized frequency offset. This is
done through the SNR per bit and the frequency offset times
OFDM symbol period requirements in a real scenario, i.e. at
the FEC limit and with pilot-assisted equalization.
ACKNOWLEDGMENT
This work was partially assisted by Tecnologico de Monter-
rey scholarships. The present investigation was also supported
by the Project FONDECYT Iniciacion No. 11160517, Fondo
Nacional de Desarrollo Cientifico y Tecnologico.
0 3 6 9 12 15
Eb/N0 (dB)
10-5
10-4
10-3
10-2
10-1
100
BER
EL, =0.2
IMBH, =1.52, n=2
IPLC, =2.5, =0.1, =1
SPE, b=0.5, =1
SPL, b=0.5, p=1
SE, =0.55, =1
Pulse
Fig. 3. BER vs. SNR per bit with Nyquist-I pulses as parameter for ∆f T =
0.25 and θ= 25o.
0 0.1 0.2 0.3 0.4 0.5
f T
5
15
25
35
Eb/N0 (dB)
EL, =0.2
IMBH, =1.52, n=2
IPLC, =2.5, =0.1, =1
SPE, b=0.5, =1
SPL, b=0.5, p=1
SE, =0.55, =1
Pulse
Fig. 4. SNR per bit as a function of the normalized frequency offset for
several Nyquist-I pulses and a BER threshold equal to 10−3and without
phase error.
REFERENCES
[1] L. Hanzo and M. Munster and B. J. Choi and T. Keller, OFDM and
MC-CDMA for Broadband Multi-User Communications, WLANs and
Broadcasting. Wiley-IEEE Press, 2003.
[2] T. Hwang, C. Yang, G. Wu, S. Li, and G. Y. Li, “OFDM and its Wireless
Applications: A Survey,” IEEE Transactions on Vehicular Technology,
vol. 58, pp. 1673–1694, 2009.
[3] W. Shieh and I. Djordjevic, OFDM for Optical Communications. El-
sevier, 2010.
[4] J. Armstrong, “OFDM for Optical Communications,” Journal of Light-
wave Technology, vol. 27, pp. 189–204, 2009.
[5] P. H. Moose, “A Technique for Orthogonal Frequency Division Multi-
plexing Frequency Offset Correction,” IEEE Transactions on Communi-
cations, vol. 42, no. 10, pp. 2908–2914, Oct 1994.

[6] T. Pollet, M. V. Bladel, and M. Moeneclaey, “BER Sensitivity of OFDM
Systems to Carrier Frequency Offset and Wiener Phase Noise,” IEEE
Transactions on Communications, vol. 43, pp. 191–193, 1995.
[7] J. Armstrong, “Analysis of New and Existing Methods of Reducing
Intercarrier Interference due to Carrier Frequency Offset in OFDM,”
IEEE Transactions on Communications, vol. 47, pp. 365–369, 1999.
[8] A. A. M. Al-Bassiouni and M. Ismail and W. Zhuang, “An Eigenvalue
Based Carrier Frequency Offset Estimator for OFDM Systems,” IEEE
Wireless Communications Letters, vol. 2, pp. 475–478, 2013.
[9] C. H. Tseng and C. D. Chung, “Concatenated Precoded OFDM for CFO
Effect Mitigation,” IEEE Transactions on Vehicular Technology, vol. 62,
pp. 2618–2632, 2013.
[10] P. Tan and N. C. Beaulieu, “Reduced ICI in OFDM Systems Using
the ”Better than” Raised-Cosine Pulse,” IEEE Communications Letters,
vol. 8, pp. 135–137, 2004.
[11] H. M. Mourad, “Reducing ICI in OFDM Systems Using a Proposed
Pulse Shape,” Wireless Personal Communications, vol. 40, pp. 41–48,
2007.
[12] V. Kumbasar and O. Kucur, “ICI Reduction in OFDM Systems by Using
Improved Sinc Power Pulse,” Digital Signal Processing, vol. 17, pp. 997
– 1006, 2007.
[13] K. N. Le, “Insights on ICI and its Effects on Performance of OFDM
Systems,” Digital Signal Processing, vol. 18, pp. 876 – 884, 2008.
[14] T. Peng and N. C. Beaulieu, “Analysis of the Effects of Nyquist Pulse-
Shaping on the Performance of OFDM Systems with Carrier Frequency
Offset,” European Transactions on Telecommunications, vol. 20, pp. 9–
22, 2009.
[15] Alexandru, N. C. and Onofrei, A. L., “ICI Reduction in OFDM Systems
Using Phase Modified Sinc Pulse,” Wireless Personal Communications,
vol. 53, pp. 141–151, 2010.
[16] R. Saxena and H. D. Joshi, “ICI Reduction in OFDM System Using
IMBH Pulse Shapes,” Wireless Personal Communications, vol. 71, pp.
2895–2911, 2013.
[17] S. Kamal and C. Azurdia-Meza and K. Lee, “Nyquist-I Pulses Designed
to Suppress the Effect of ICI Power in OFDM Systems,” in International
Wireless Communications and Mobile Computing Conference (IWCMC),
2015, pp. 1412–1417.
[18] C. A. Azurdia-Meza and S. Kamal and K. Lee, “BER Enhance-
ment of OFDM-based Systems Using the Improved Parametric Linear
Combination Pulse,” in International Conference on Information and
Communication Technology Convergence (ICTC), 2015.
[19] C. A. Azurdia-Meza and H. F. Arra˜
no and C. Estevez and I. Soto,
“Performance Enhancement of OFDM-Based Systems Using Improved
Parametric Linear Combination Pulses,” Wireless Personal Communica-
tions, vol. 85, pp. 809–824, 2015.
[20] S. Kamal and C. A. Azurdia-Meza and K. Lee, “Suppressing the Effect
of ICI Power Using Dual Sinc Pulses in OFDM-Based Systems,” AEU
International Journal of Electronics and Communications, vol. 70, pp.
953 – 960, 2016.
[21] ——, “Family of Nyquist-I Pulses to Enhance Orthogonal Frequency
Division Multiplexing System Performance,” IETE Technical Review,
vol. 33, pp. 187–198, 2016.
[22] ——, “Improved Nyquist-I Pulses to Enhance the Performance of
OFDM-Based Systems,” Wireless Personal Communications, pp. 1–17,
2017.
[23] S. Kamal and C. A. Azurdia-Meza and N. H. Tran and K. Lee, “Low-
PAPR Hybrid Filter for SC-FDMA,” IEEE Communications Letters,
vol. PP, pp. 1–1, 2016.
[24] Third Generation Partnership Project (3GPP), “Universal Mobile
Telecommunications System; Base Station Radio Transmission and
Reception,” European Telecommunications Standards Institute, Tech.
Rep. 125.104, 2014.
[25] ——, “Universal Mobile Telecommunications System ; User Equipment
Radio Transmission and Reception.” European Telecommunications
Standards Institute, Tech. Rep. 125.101, 2014.
[26] H. Nyquist, “Certain Topics in Telegraph Transmission Theory,” Pro-
ceedings of the IEEE, vol. 90, pp. 280–305, 2002.
[27] N. C. Beaulieu and M. O. Damen, “Parametric Construction of Nyquist-I
Pulses,” IEEE Transactions on Communications, vol. 52, pp. 2134–2142,
2004.
[28] A. Tychopoulos and O. Koufopavlou and I. Tomkos, “FEC in Optical
Communications - A Tutorial Overview on the Evolution of Architec-
tures and the Future Prospects of Outband and Inband FEC for Optical
Communications,” IEEE Circuits and Devices Magazine, vol. 22, pp.
79–86, 2006.