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 Total Downloads : 1999
 Authors : Kajal H. Tailor, Shweta N. Shah
 Paper ID : IJERTV2IS1409
 Volume & Issue : Volume 02, Issue 01 (January 2013)
 Published (First Online): 30012013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
A Review on Various Interference Effects in a MIMOOFDM System
Kajal H. Tailor1, Prof. Shweta N. Shap
1Electronics and Communication Engineering Department, Govt. Engineering College, Surat
2 Electronics and Communication Engineering Department, SVNIT, Surat, India
Abstract:
The performance of a MIMOOFDM system is severely degraded in presence of RF impairments like phase noise and I/Q imbalance and other interferences like ICI (intercarrier interference) and NBI (narrowband interference). Lowcomplexity estimation and compensation techniques that can jointly remove the effect of these impairments are highly desirable. In this paper, we present a study of various interference effects in a MIMOOFDM system and their compensation techniques.

Introduction
The demand of high data rates over wireless communication channels is everincreasing. To meet such demands, a reliable and robust technology has to be implemented which provides highdatarate wireless access with high QoS (quality of service). MIMO (MultipleInputMultipleOutput) wireless technology meets these demands by offering increased spectral efficiency through spatialmultiplexing gain and improved link reliability due to antenna diversity gain. OFDM is a widely used technology due to its robustness against ISI (Intersymbol Interference) and frequencyselective fading. The combination of MIMO and OFDM system is an attractive airinterface solution for next generation wireless communication systems. It has been specified as a standard in IEEE 802.11n WLAN and in IEEE 802.16e WMAN and
provides a maximum data rate of up to 600 Mbps. It is yet to be standardized for the upcoming WLAN standard amendment i.e., IEEE 802.11ac. However a MIMOOFDM system suffers from major RF impairments like phasenoise and I/Q imbalance due to nonidealities in the transmission chain components. It is also known as dirtyRF signal processing. Phase noise causes a CPE (commonphaseerror), which is constant phase rotation common to all the subcarriers in an OFDM symbol, and ICI, due to interference from the neighbouring subcarriers. I/Q mismatch occurs when the analog components on the I and Q rails are
not exactly matched. Figure. 1 and 2 below shows an NT Ã— NR MIMOOFDM system affected by phase noise and I/Q mismatch. and A represents I/Q phase and amplitude mismatch respectively and (t) represents random phase variations.
Figure 1. MIMOOFDM transmitter with NT transmit branches
Figure 2. MIMOOFDM receiver with NR receive branches affected by phase noise and I/Q imbalance
In addition to phase noise and I/Q imbalance, the performance of a MIMOOFDM system is severely degraded due to narrowband interference. NBI arises when two different systems operate in the same frequency band. For e.g., this kind of interference is
mainly found in unlicensed frequency bands like the ISM (Industrial Scientific Medical) band, where systems such as Bluetooth or microwave ovens interfere with OFDM based WLAN (Wireless Local Area Networks). In this review paper, we present a study of above mentioned interference effects namely, phase noise, I/Q mismatch, ICI and NBI in a MIMO OFDM system and their compensation techniques.

Phase Noise (PN)
Phase Noise is caused due to nonlinearities in the local oscillator and can be considered as a parasitic phase modulation of the oscillators signal. A general signallevel model for a noisy oscillator can be expressed as
osc(t) = e(j2fct)*e(j(t)) (1)
where (t) denotes the timevarying PN and fc is the nominal oscillating frequency i.e., carrier frequency for oscillators. The variation in phase can either be continuous or dicrete. Discrete phase variation produces discrete signals called spurious frequencies and continuous phase fluctuations causes phase noise. The PN of a free running oscillator is assumed to follow Brownian motion (Weiner process). PN causes
modeled separately for transmitter and receiver side. However the impact of PN at the receiver dominates the overall PN effect [1]. Considering receiver side PN, the vector of received samples for mth OFDM symbol after the impact of a multipath channel and removal of the CP is
ym = diag(ejm ) (xm hm) + nm (3)
where is the circular convolution operator, xm is the vector of samples of mth transmitted OFDM symbol, hm is the channel impulse response, and nm is AWGN (Additive White Gaussian Noise) vector. m is a vector containing PN realization samples within mth OFDM symbol, m = [m(0),…, m (N1)]T. The received frequency domain signal vector is given by
Rm = Jm (Xm Â· Hm) + m (4)
Xm is the vector of transmitted subcarrier symbols, Hm is the channel transfer function, m is the FFT of AWGN, and Jm is the FFT of exp( jm). The received signal can be expressed as a summation of two terms
+
+
Rm(k) = Xm(k) Hm(k) Jm(0) + m(k)
the PSD (power spectral density) to exhibit skirts around the carrier frequency resulting in a Lorentzian
N1
l=0,lk
Xm(l)Hm(l)Jm(kl) (5)
m=1
m=1
spectrum. It is measured in units of dBc/Hz. When a strong RF blocker signal convolves with the skirts of the Lorentzian spectrum in the mixer (reciprocal mixing), the reciprocal noise produced would dominate the PN. Thus the errors caused by phase noise cannot be neglected. The interference due to phase noise can be separated into a CPE and an ICI. CPE refers to a constant phase rotation which is
The first and the second parts of the signal are the CPE and ICI terms respectively. For a MIMOOFDM system with NT transmit and NR receive antennas and N subcarriers in one OFDM symbol, considering PN both at the transmitter and receiver, the received samples at receiver antenna n from each of NT transmit antennas are written as
common to all the subcarriers in an OFDM symbol [3]. ICI corresponds to neighbouring subcarriers interfering with each other. When the ratio of the
yn(l) = ejrx ,n (l) NT
(hnm (l) xm (l)ejtx ,m (l)) + nn(l)
(6)
phase noise bandwidth and OFDM intercarrier spacing is small, CPE dominates and when the ratio is closer to unity, ICI dominates [4].

Phase Noise Modeling
In a general OFDM system with N subcarriers, the timedomain waveform samples are obtained by N point IFFT (inverse fast Fourier transform) of the subcarrier data symbols. Thus, at mth OFDM symbol interval, these samples can be written as
where ejrx and ejtx are PN at transmitter and receiver side respectively. hnm is the multipath channel from transmitter m to receiver n. Thus in MIMO systems the PN increases linearly with the increase in the number transmitters.

Phase Noise Compensation
One of the most common ways of phase noise mitigation is estimation using pilot symbols or a known training sequence. Based on the estimation of
x (n) = 1 N1 X
k ej2nk /N (2)
frequency offset on known pilot symbols, the
m N k=0 m
frequency offset is compensated on other data sub
where Xm(k) denotes the kth subcarrier data symbol during mth OFDM symbol interval. A cyclic prefix of size Ng samples is added to an OFDM symbol to combat ISI in a time dispersive channel. PN is
carriers. Correction of CPE is relatively simpler as compared to ICI. According to [1], the CPE term is estimated using known pilot subcarriers Sp. From (5) it results in eq. (7)
Rm(k) = Xm(k)Hm(k)Jm(0) + m(k) (7)
where k Sp. The ICI and AWGN term are combined into a single m(k) term. Assuming a know channel response Hm(k), the term Jm(0) can be estimated using a Least Squares (LS) estimation which is given as
with the phase error. It assumes a varying stepsize, to deal with timevarying channel. It uses squared error between the desired response and the filter output, to calculate the updated weights. [9] uses a ZeroForcing solution for MIMO decoding on a per subcarrier basis i.e., the estimated kth symbol is Xk = WkYk where Wk
k H (k)
k H (k)
kSp Rm k Xm m
is the weight matrix. The ICI and CPE terms are
J 0 =
kSp Xm
(k)Hm
(k)2
(8)
estimated and corrected by using continuous pilots. In
[16] an iterative approach is used where first the CPEIn [3] the estimate of CPE is given as
is estimated using Least Squares (LS) estimation. As the preamble also suffers from a phase rotation, a
Ns lc lc
second level LS estimation is done and the obtained
= i=1 i,l i,l
i=1
i=1
Ns lci,l
(9)
estimate is used for intial correction. The remaining CPE in data symbols is equalised by MMSE equaliser.
where
,
is the reliability estimate, for instance the
ICI which is referred to as higher order phase noise is
compensated by linear MMSE estimation.
estimated subchannel amplitude for subchannel ci,l at symbol l and lci,l is the phase difference between the transmitted phase of subchannel ci,l and the received phase and NS is the number of pilot symbols. For ICI estimation, spectral components around the center frequency are considered in [1] because PSD of phase noise has typically steeply descending lowpass natured spectrum around the nominal oscillating frequency. Thus only the spectral components around the center frequency is considered with circular subcarrier indexing k{ u,…, u }. Thus the received symbol becomes


I/Q Mismatch
I/Q imbalance is the effect when the inphase and quadraturephase branch in the RF frontend are not exactly identical. In SISO/MIMOOFDM systems I/Q mismatch causes interference from the conjugate of the data on the frequency mirror subcarriers which scales with the number of transmit antennas. It can be modelled as a gain, phase and delay mismatch between the I and Qrails. It is categorized as frequency dependent or frequency independent. Frequency independent I/Q imbalance occurs when
R (k) = u X (k l) H (kl)J
(l) + (k) (10)
the effects are constant over the bandwidth of interest
m l=u m
m m m
and frequency dependent I/Q imbalance occurs when
there is a difference in the lowpass filters of both
The variable m(k) has the AWGN terms and all non estimated ICI terms in it. Only a subset of subcarriers k{ l1,…,lP } is considered, p > 2u +1 the received symbol is given as
branches. I/Q gain and phase mismatches are frequency independent whereas I/Q delay mismatch is frequency dependent [8]. In the presence of I/Q gain, delay and phase mismatch, expressed in continuous
Rm,p
=Am,uJ
m,u+
m,u
(11)
time complex baseband notation, the transmit sequence is expressed as
where Am(k) = Xm(k) Hm(k). It is assumed that both Xm(k) and Hm(k) are known for the considered
x m t = Amt xmr t mti ejmti
subcarriers and that estimating Jm,u is done using the pseudo inverse of Am,u as
+ jBmt
xmi
t mtq
ejmtq (13)
m,u = (H ,u m,u )1H ,u Rm,p (12)
where Amt , Bmt are the gains, mti , mtq are the phase
m m
offsets and mti , mtq are the delay offsets on the two
m=1
m=1
The resulting PN spectrum estimate can then be used to deconvolve the effect of the PN out of the system, i.e., ICI can be removed. In [5] a matched filtering approach is utilized for phase noise mitigation. The channel is first estimated using an MMSE (Minimum
rails at transmitter m. xmr and xmi are the real and imaginary parts of xm (t). x m (t) convolves with the channel from transmitter m to receiver n and adds with data from other transmitters at receiver n
Mean Square Error) equalizer. Further for phase noise, a semiblind adaptive equalizer based on an LMS (Least Mean Square) algorithm is used because the
rn t = NT
( x m (t)hnm (t)) + nn (t) (14)
phase noise is randomly varying and only a few pilot tones are available. [6] uses a SSDLMS (Stepsize delta Least Mean Square) adaptive algorithm to deal
Considering I/Q mismatch at the receiver frontend, the corrupted received signal is
rn t = Anr rni (t nri )ejnri
+ jBnr rnq (t nrq )ejnrq + nn (t) (15)
Substituting (13) and (14) in (15), after taking FFT, substituting Xreal(k) = 0.5(X(k) + X*(k)) and Ximag(k)
= 0.5(X(k) X*(k)), gives the expression for frequency domain received subcarrier at receive antenna n which contains the interference terms from
2 n
j( )
j( )
y(n) = x(n)e N h(n) + w(n) (16)
Here x(n) represents the nth sample of the transmitted signal, represents the normalized frequency offset and is given by fÂ·NTs. f is the Doppler shift, Ts is the subcarrier symbol period. The frequency domain representation is
l=0,lk
l=0,lk
the conjugate of the data on the frequency mirror subcarriers of all the transmitters.
Y(k) = X(k)S(0) + N1
X l S(l k) + nk (17)
3.1. I/Q Mismatch Compensation
I/Q mismatch mitigation has been studied extensively both for SISO and MIMOOFDM systems. In [8], the received signal vector for the kth subcarrier is
The first term represents the desired signal without frequency errors and the second term represents ICI interference. S(l) is the FFT of ej(2 n). For MIMO OFDM the ICI is modeled as
N
N
expressed as Yk = CkXk + Vk where Ck is the matrix
Y (k) = NT X k H
k S
0
containing the desired and interference terms for the kth subcarrier and Vk is the AWGN vector at a given
n m=1 m mn m
+ NT I (k) + n
(18)
receiver. A MMSE solution is used for estimating Xk
m=1 mn k
from Yk i.e., Xk = Wk Yk and the weight vector Wk is
where H k is the channel frequency response from
updated using LMS or RLS (Recursive Least Squares) algorithms. It is shown in [9] that as the number of receive antennas increases, the number of observations for a given mirror frequency subcarrier, increases, which separates the desired subcarrier from interfering
mn
the mth transmitter to the nth receiver for the kth
subcarrier. Imn (k) represents the interference on the kth subcarrier for a given m and n transmitterreceiver pair and is given as
n=0,nk
n=0,nk
subcarriers and that the I/Q mismatch can be fully cancelled if the number of receive antennas is twice
Imn (k) = N1
Xm n Hmn n Smn (n k) (19)
the number of transmit antennas. However the performance is still degraded because the signal energy that leaked into the mirror frequencies is lost.
[2] uses a DDLMS (decisiondirected least mean square) adaptive algorithm for a 2tap transversal filter with the received carrier symbol and the complex mirror symbols as inputs to the filter. The system is initially trained with a known phase reference symbols which then swiches to decisiondirected mode of operation which in turn forms the desired response of the adaptive filter. It uses two adjacent subcarriers to compensate for a single symbol. 
ICI
Intercarrier interference arises due to a number of sources. ICI is created when the channel delay spread is larger than the cyclic prefix, when the channel varies during one OFDM symbol (Doppler shift), when the residual timing offset is large, due to asynchronicity between users in a multiuser scenario because of delay differences between users and also due to phase noise[10]. The baseband representatio of the received signal in time domain with ICI is given as
This indicates that for MIMOOFDM systems, there is interference from neighbouring subcarriers of all the transmit antennas.

ICI Compensation
A lot of ICI mitigation techniques have been investigated extensively in literature both for SISO and MIMOOFDM systems which include ICI self cancellation [13][14], frequency domain equalization [11], frequency offset estimation and compensation [7] and timedomain windowing [12]. The basic idea of an ICI selfcancellation scheme is to modulate a single data symbol onto two adjacent subcarriers but with opposite polarity i.e., X(k) = X(k) and X(k+1) = – X(k) so that the ICI coefficients on each data symbol are selfcancelled by addition at the receiver. This scheme is called adjacent data conversion. There are many variants of selfcancellation scheme like adjacent data conjugate method (X(k) = X(k) and X(k+1) = X*(k)), symmetric data conversion method (X(k) = X(k) and X(Nk1) = X(k)), symmetric data conjugate method (X(k) = X(k) and X(Nk1) = – X*(k)) and weighted conjugate transformation (X(k) = X(k) and X(k+1) = ej/2X*(k)) [23]. Timedomain windowing involves using an adaptive Nyquist window to suppress the side lobes extending beyond
the OFDM symbol interval. Frequency domain equalization technique [11] uses a linear and decision feedback equalization. These schemes were proposed for SISOOFDM systems. However the self cancellation scheme was utilised for designing the SpaceTimeFrequency block codes in [18] for MIMO systems. [15] uses a block processing and matched filtering approach for ICI mitigation by assuming perfect knowledge of channel gain and frequency offset. [7] estimates the frequency offset from pilot symbols and the estimated frequency offset is applied to other data subcarriers through a polynomial curve fitting approach. [19] uses a planar Extended Kalman filter for normalized Doppler frequency offset estimation.


Narrowband Interference (NBI)
Narrowband interference arises when two different systems operate on same frequency bands. This kind of interference is found in the unlicensed frequency bands e.g., the ISM band (Industrial Scientific Medical), coming from systems such as Bluetooth devices, microwave ovens which interfere with OFDM based Wireless Local Area Networks. In an OFDM system, unless the frequency of the NBI coincides with a subcarrier frequency, the spectrum of the NBI will span the whole bandwidth of the system. The received timedomain signal is given by
r = d + i + n (20)
where r, d, i and n are (N+Ng) Ã— 1 vector of the received signal, transmitted OFDM symbol, narrowband interference samples and Gaussian noise samples. The components of i are given by

NBI compensation
The NBI suppression techniques for OFDM systems include frequency excision, frequency identification and cancelling, adaptive narrowband filtering[20] and prediction error filtering[17]. In frequency excision technique, the narrowband interference, which manifests as a peak in the spectra of the received signal, is eliminated by comparing it with a threshold value. Drawbacks of this technique is the inability to completely remove NBI from the data subcarriers. In frequency identification and cancelling technique, the amplitude and phase of the NBI is estimated from the maximum amplitude of the received spectra by applying the Maximum Likelihood solution. An adaptive narrowband bandpass filter is also used whose transfer function is given in [20]. The center frequency of this filter is adjusted to match with that of the narrowband interference frequency and the filter weights are updated by applying LMS algorithm. For MIMOOFDM systems, precoding and spaceblock coding schemes are used at the transmitter side to obtain maximum diversity and to suppress NBI. The main idea behind using space block coding is that if the error probability of receiving a message by transmission over a wireless channel is p, then with the simultaneous transmission of n orthogonal copies
of the message over n independent wireless channels, the total error probability is pn. Thus diversity helps in suppressing NBI.


Conclusion
In this review paper, we presented a study of various interference effects in a MIMOOFDM system and their compensation techniques. Among the techniques discussed, most of them use estimation
in =
Ei ej(2nfi Ts + ) (21)
and compensation process using either pilot symbols or preamble. The different forms of interferences have been studied extensively individually but joint
where Ei is the interference power, Ts is the original
symbol period, is the random phase uniformly
distributed in [,]. The frequency of interference fi is defined by
consideration of all interferences has not been studied so far in literature. Hence an efficient algorithm has to be framed which takes into account all the interferences and is a part of our future work.
f = (m + )fs , 0 m < N2 , – 0.5 0.5 (22)
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= 0, the interference is located directly on one of the subcarriers and therefore is orthogonal to the tones. Nonorthogonal interference is accounted for when
= 0.
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