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Blind SOS subspace channel estimation and equalization techniques exploiting spatial diversity in OFDM systems

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Available online at www.sciencedirect.com
Digital Signal Processing 14 (2004) 171–202www.elsevier.com/locate/dsp
Blind SOS subspace channel estimation andequalization techniques exploiting spatial diversityin OFDM systems
Hassan Ali,
a
,
∗
,
1
Arnaud Doucet,
b
and Yingbo Hua
c
a
Communications and Signal Processing Group, School of Electrical and Computer Engineering,Curtin University of Technology, GPO Box U1987, Perth 6845, Australia
b
Signal Processing Group, Department of Engineering, University of Cambridge, Trumpington Street,Cambridge, CB2 1PZ, UK
c
Department of Electrical Engineering, University of California, Riverside, CA 92521, USA
Abstract
In this paper, we present second-order-statistics (SOS) subspace-based blind channel estimationtechniques, which exploit the receive antenna diversity in each of the following situations: cyclicpreﬁx-OFDM (CP-OFDM), zero padded-OFDM (ZP-OFDM), and bandwidth efﬁcient-OFDM(BWE-OFDM) systems. We also propose a number of combinations of pre-FFT equalizer, post-FFT equalizer, zero-forcing (ZF) equalizer, and minimum-mean-square-error (MMSE) equalizer.For any number of receive antennas, the pre-FFT equalizers require only one FFT at the receiver.As a result, a considerable reduction in hardware complexity and power saving may be obtainedespecially for systems with higher number of sub-carriers. In contrast, post-FFT equalizers result inconsiderable reduction in processing complexity at the cost of one FFT for each antenna. Adaptivelinear-complexity implementations of the proposed receivers are considered, along with some modi-ﬁcations inthe presence of null side carriers. The effectiveness of the new techniques isdemonstratedthrough simulations.
©
2003 Elsevier Inc. All rights reserved.
Index terms:
Blind channel estimation and equalization; CP-OFDM; ZP-OFDM; BWE-OFDM; Spatial diversity
*
Corresponding author.
E-mail addresses:
alih@ece.curtin.edu.au (H. Ali), ad2@eng.cam.ac.uk (A. Doucet), yhua@ee.ucr.edu(Y. Hua).
1
Part of this work was done when he was with the ARC Special Research Centre for Ultra-BroadbandInformation Networks (CUBIN), Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville 3010, Victoria, Australia.1051-2004/$ – see front matter
©
2003 Elsevier Inc. All rights reserved.doi:10.1016/S1051-2004(03)00008-3
172
H. Ali et al. / Digital Signal Processing 14 (2004) 171–202
1. Introduction
Orthogonal frequency division multiplexing (OFDM) [1] is now considered an effec-tive technique for digital broadcasting (terrestrial digital audio, video broadcasting: DAB,DVB [2,3])but also for highrate modemsovertwisted pairs.OFDM has a relativelylongersymbol duration which produces greater protection to multi-path interference and impulsenoise.It reducesbit rateofeachcarrieragainstinter-symbol-interference(ISI)problemandalso provides high bit rate transmission by using a number of those low bit rate carriers.Frequency bandwidth is partitioned into several small parallel independent sub-channelsand each of them is handled by these low rate carriers. As shown in Fig. 1a, OFDM canprovide immunity against frequency selective fading environment: bandwidth of the eachsub-carrierisnarrowenoughcomparedwiththatofconventionalsingle-carriermodulation.In an OFDM system, some carriers may be attenuated by frequency selective fading, butother carriers may not be attenuated. Therefore a multi-carrier OFDM system can transmitdata correctly. Also, due to the ability to transmit different data using several orthogo-nal overlapping sub-carriers an OFDM system increases bandwidth efﬁciency and systemcapacity.In standard OFDM systems (i.e., cyclic preﬁx-OFDM (CP-OFDM)), the problem of inter-block-interference(IBI) arising due to channel memoryis taken care by repeatingthelast few samples of each OFDM symbol at its beginning, prior to its transmission. Thisadded guard interval is known as the cyclic preﬁx (CP). The CP converts linear convolu-tion into circular convolution.This allows diagonalizationof the associated channel matrixand thus equalization of the channel distortion in the frequency domain by using a singletap equalizer for each carrier independently.For equalization purposes in OFDM, a knowntraining sequence is sent by the transmitter and a training algorithm is performed by thereceiver of the observed channel output and the known input to estimate the channel [4].This solution increases the overhead of the system and consumes the valuable channelbandwidth. Implementation of blind channel estimation algorithms, on the other hand, ap-pear attractive since they avoid the use of the training sequences, save bandwidth and arecapable of tracking slow channel variations. A variety of techniques are available for blindchannel identiﬁcation (for example, see [5–10]).
Fig. 1. (a) Robustness to frequency selective fading: single-carrier modulation and multi-carrier OFDM modula-tion. (b) Coded-OFDM (COFDM).
H. Ali et al. / Digital Signal Processing 14 (2004) 171–202
173
Pushed by the recent requirement of tremendous capacity increase for voice, Internetand multimedia trafﬁc along with high speed data handling capabilities in future genera-tion mobile wireless systems, OFDM is newly considered for mobile wireless broadbandsystems (ETSI BRAN, IEEE802.11a[11], MMAC, and HIPERLAN/2 [12]).However,us-ing OFDM in mobile channels is critical because of the impact of the time variant natureof the channel and thus resulting impact of frequency nulls (deep fades). That is if a sub-carrier coincides with the channel null (in other words when the channel has nulls (deepfades) on the FFT grid), then information carried by that sub-carrier is lost.A number of solutions have been proposed to make OFDM more robust to this narrowband fading. The ﬁrst is to employ channel coding together with interleaving and/or fre-quency hopping as in the so called coded-OFDM (COFDM) [13,14] (see Fig. 1b) variant.For example, the conventional trelliscoded modulation (TCM) was used in [13], and turbocodes were used in [14]. However, COFDM techniques often incur high complexity andinvolve large decoding delay [15]. Some of them require channel state information (CSI)at the transmitter [16,17], which may be unrealistic or too costly to acquire in wirelessapplications where the channel changes on constant basis [18]. COFDM techniques fur-thermorecome at the price of bandwidth efﬁciencyreduction which is not compatible withbandwidth expensive mobile and wireless applications. The second way to guaranteeingsymbol detect-ability in presence of bad carriers is zero padded-OFDM (ZP-OFDM): in-stead of introducing the CP, after each IFFT processed block a zero padded guard intervalis inserted. Some channel estimation techniques employing ZP precoding to combat IBIcaused by multi-path channel have also been reported [19]. However, ZP-OFDM imple-mentation involves transmitter modiﬁcation and complicates the equalizer. Another wayof robustifying OFDM against random frequency selective fading is to introduce memoryinto the transmission by linear precoding(LP) [18] across the sub-carriers.LP-OFDM alsocomes at the price of complicatingthe transmitter and receiverand furthermoreat the priceof bandwidth reduction.Our way of robustifying OFDM against faded sub-carriers is to exploit rich spatial di-versity by employing multiple antennas at the receiver. The objective that motivates theuse of spatial diversity is threefold: ﬁrst, the maximization of the mean signal power withrespect to any noise thereby resulting in improving link budget, signal quality, and capac-ity of communication system, second, mitigating the impact of deep fades, and third, noadditionalpoweror bandwidthconsumption.The transceiversystem is essentially a single-input/multiple-output(SIMO) system with a single antennaat the base station and multipleantennas at the mobile terminals or vice versa. Multiple antennas are traditionally used atthe base station in order to achieve high performance and capacity. The use of multipleantennas at the mobiles is now being considered. This enables parallel data transmission,improved signal-to-interference ratio (SIR) and extended coverage [20].Figure2showstheconceptoftheproposedspatial diversitybasedOFDMsystem whosereceiver has multiple antennas with independent fading patterns and whose transmitter hasa single antenna. The use of multiple antennas at the receiver makes fading to becomemore randomized between OFDM tones of each antenna than the conventional system. If two or more antennas are placed at the receiver, each would have a different set of multi-path signals giving effect to different fading for each carrier at each antenna. The effectof each channel would vary from one antenna to the next, therefore, carriers that may be
174
H. Ali et al. / Digital Signal Processing 14 (2004) 171–202
Fig. 2. Concept of randomized fading due to spatial diversity in OFDM systems.
unusable on one antenna due to fading become usable on another. Though receiver an-tenna diversity based beam-forming techniques can be applied in OFDM systems withco-channel interference [21]. However, beam-forming is not always able to fully exploitall the pathgains[22].Furthermore,limitationsof beam-formingtechniquesforbroadbandwireless Internet access arises from implementation [23]. A couple of diversity combiningtechniques [24–26], including Cisco’s vector OFDM (VOFDM) [27] have been reported,however, they use training sequences or pilot tones to estimate the channel coefﬁcients.When viewed as FIR SIMO system, the receiver antenna diversity can be optimally ex-ploited by the blind two-step maximum likelihood (TSML) approach proposed in [28].But in this paper, we consider a suboptimal approach based on the subspace concept.Motivated by aforementioned challenges and convincing advantages of spatial diver-sity, in this paper, we propose blind spatial diversity combining techniques in a commonframework. These techniques can be seen as counterpart to training or pilot symbol baseddiversity combining and above described robust frequency selective techniques. First, weproposeasecondorderstatistical (SOS)basedblindsubspacechannelestimationtechniqueexploitingspatialdiversityintheCP-OFDM.We alsoproposecorrespondingpre-andpost-FFT zero-forcing (ZF) and minimum-mean-square-error (MMSE) equalizers. Second, asZP-OFDM offers a number of advantages over CP-OFDM, we also develop a blind sub-space channel estimator exploiting spatial diversity in ZP-OFDM and corresponding pre-and post-FFT ZF and MMSE equalizers. A number of equalization techniques [29–31]have recently been proposed for spectrally efﬁcient OFDM systems which do not use a CPor ZP guard interval. We thus extend the idea of spatial diversity to bandwidth efﬁcient-OFDM (BWE-OFDM) and propose a spatial diversity exploiting blind channel estimatorand corresponding ZF and MMSE equalizers. Linear adaptive implementation of the pro-posed receivers is considered. It is furthermore shown how the proposed estimators take
H. Ali et al. / Digital Signal Processing 14 (2004) 171–202
175
into accountknownzeros in the input stream for channelidentiﬁcation.These knownzerosin the input stream are referred to as virtual carriers and are sometimes used in practicalOFDM systems to create frequency guard bands [2].The remainderof this paper is organizedas follows. In Section 2, we describe the multi-channel baseband signal model for the CP-OFDM system. The new subspace channelestimator and corresponding equalizers are presented in this section. In this section, wealso propose modiﬁcations as to the proposed estimator in presence of null side carriers.Sections 3 and 4 similarly deal with ZP- and BWE-OFDM, respectively. Section 5 dealswiththelinearadaptiveimplementationoftheproposedreceivers.InSection6,wedescribethe properties of proposed techniques. In Section 7, we present computer simulations andﬁnally, in Section 8, we summarize and draw some conclusions.
2. CP-OFDM spatial diversity exploiting channel estimation and equalization
In standard CP-OFDM systems, a CP equal to or greater than the channel order is usu-ally inserted as the guard interval to prevent IBI and allow one tap equalization.
2.1. Multi-channel baseband data model
The developmentof the multi-channelbasebanddata modelis based uponthe followingassumptions:(1) The transmitted signal
s(n)
goes through
Z
ﬁnite impulse response (FIR) channels(due to over-samplingin spatial domainby a
Z
antennareceiversystem) with complexvaluedimpulseresponsevectors
h
(r)
= [
h
(r)
(
0
),...,h
(r)
(L)
]
T
,
r
=
1
,...,Z
, where
L
denotes the known maximum channel order
L
.(2) Data model satisﬁes
P > M > L
and CP guard interval
P
−
M
L
. Here
M
and
P
denote symbol block length and transmitted data vector length including the CP,respectively.(3) We assume perfect synchronization of carriers and symbol blocks.Figure 3 shows the concept of the proposed CP-OFDM system, whose transmitter hassingle antenna and receiver has
Z
antennas. This wireless communication system withantenna array receiver can be modelled as a SIMO system. To facilitate the developmentof the multi-channel model arising due to antenna array, we ﬁrst visit some basic theoryfrom [5,32], in case of a mono-sensor system (i.e., we have a single antenna at both thetransmitterandreceiver).Let us considerthe CP-OFDM transmitterin Fig. 3a. First, the bitstreamis mappedtothe complexvalueddatastream.Thecomplexvaluedinputdatastream
s(n)
is parsed into blocks of size
M
:
s
(i)
:= [
s(iM),s(iM
+
1
),...,s(iM
+
M
−
1
)
]
T
,where the block index
i
=
n/M
and
.
denotes integer ﬂoor of the argument. For eachsymbolindex
n
, we can write
n
=
iM
+
m
,with
m
∈ [
0
,M
−
1
]
.Theindex
n
thus indicatesthe position of a symbol inside the symbol block
s
(i)
which constitutes the
i
th OFDMsymbol. The symbol block
s
(i)
is then modulated by the IFFT matrix
F
H M
, where
F
M
stands for the size
M
×
M
FFT matrix with entries
(
1
/
√
M)
exp
(
−
j
2
πmn/M)
. The data

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