Training Sequence Assisted Channel Estimation For Mimo Ofdm: Sumei Sun, Ingo Wiemer, C. K. Ho, and T. T. Tjhung
Training Sequence Assisted Channel Estimation For Mimo Ofdm: Sumei Sun, Ingo Wiemer, C. K. Ho, and T. T. Tjhung
Training Sequence Assisted Channel Estimation For Mimo Ofdm: Sumei Sun, Ingo Wiemer, C. K. Ho, and T. T. Tjhung
MIMO OFDM
Sumei Sun∗ , Ingo Wiemer† , C. K. Ho∗ , and T. T. Tjhung∗
∗ Institute for Communications Research, 20 Science Park Road, #02-34/37 TeleTech Park,
Science Park II, Singapore 117674
Email: sunsm, hock, tjhungtt@icr.a-star.edu.sg
† Faculty of Electrical Engineering, IEE, Dresden University of Technology,
Abstract--- In this paper we present several results of our study tical Bell Laboratories Layered Space-Time) MIMO architec-
on training sequence assisted channel estimation for Multiple- ture in a quasi-static narrowband indoor radio channel, spectral
Input Multiple-Output (MIMO) Orthogonal Frequency Division efficiency of 20-40 bits/sec/Hz can be achieved at average
Multiplexing (OFDM) systems. After developing a linear matrix
algebraic model for the cyclic prefix based MIMO OFDM SNR’s ranging from 24 to 34 dB. MIMO architecture can
systems, we will define a generalised preamble structure which is also be used to exploit diversity gain from the spatial domain.
a simple extension of the preambles used in single-input single- In this context, space-time trellis coded modulation (STTCM)
output (SISO) OFDM so that its good properties, such as low has been proposed by Tarokh et. al. [8], [9], and space-time
peak to average power ratio, can be maintained. We then derive block code (STBC) by Alamouti [10] and Tarokh et. al. [11].
the least squares (LS) and linear minimum mean squared error
(LMMSE) channel estimation algorithms based on the proposed In the original development of the BLAST system and
preamble design. In order to reduce the preamble length, we the space-time codes (STC), a narrow band quasi-static flat
further propose a switched subcarrier preamble scheme in which fading channel has been assumed. For wideband signals and
the transmit antennas are divided into groups, and preambles frequency selective channels, the multipath interference can
are transmitted in alternative subset of subcarriers in each be easily alleviated by combining OFDM with the MIMO
group. A LMMSE filter-based interpolation scheme and a DFT-
based LS interpolation scheme will then be used to obtain the structure, as suggested by [12].
channel estimates for all the subcarriers of interest. In all the Both coherent detection in BLAST and STC decoding need
proposed schemes in this paper, the filter parameters can be fixed channel information, hence channel estimation is essential in
and robust performance are obtained even when mismatched a MIMO detector. In this paper, we will focus on training
SNR and channel statistics are used in the filter parameter sequence assisted channel estimation for packet-based MIMO
calculations.
OFDM systems in wireless local area networks (LAN). Due
to the low mobility in this network, a quasi-static channel can
I. I NTRODUCTION
be assumed for each packet. Training signals are thus needed
Orthogonal frequency division multiplexing (OFDM) has only at the beginning of the packet, as in IEEE 802.11a [2] and
been adopted in several high speed wireless communciation Hiperlan/2 [3]. We will first develop a linear matrix algebraic
standards due to its capability to effectively combat intersym- model for cyclic prefix based MIMO OFDM systems, in
bol interference (ISI), and its spectral efficiency achieved by Section II. Using this model, we will then define the basic
spectrum overlapping through the adoption of fast Fourier preamble structure in Section III. It is a simple extension
transform (FFT) and inverse fast Fourier transform (IFFT) of the conventional single-input single-output (SISO) OFDM
in the implementation [1]. For example, IEEE 802.11a [2] preambles, hence the properties of low peak to average power
and ETSI Hiperlan/2 [3] have specified to transmit up to 54 ratio (PAPR), easy time and frequency synchronisation, and so
Mbps data rate with a total of 20 MHz bandwidth at 5 GHz on, can be maintained. It also does not require the transmission
by using OFDM, and IEEE 802.16.1 is drafting an OFDM- of training signals in all the subcarriers. Therefore it is very
based standard [4] to transmit up to 155 Mbps data rate for suitable for deployment in practical systems which usually
broadband wireless access (BWA) in the frequency band of allocate guard subcarriers. We then derive the least squares
2∼11 GHz. (LS) and linear minimum mean squared error (LMMSE)
Two recent information theoretic studies have shown that channel estimation algorithms, which compute the channel
rich scattering wireless channels have enormous capacities if estimates by filtering the received frequency domain signal
the multipaths are properly exploited [5], [6]. This can be with fixed parameters. However, one drawback with this
achieved by deploying multi-element antenna arrays at both scheme is that the preamble period has to be at least equal to
the transmitter and the receiver, hence creating a multiple- the number of transmit antennas. The transmission efficiency
input multiple-output (MIMO) communication system. In [7], can thus be severely degraded when a large number of transmit
it has been shown that by applying a simple VBLAST (Ver- antennas are deployed in the system. In order to overcome
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time slot antenna 1 antenna 2
squares (LS) channel estimates. In order to do this, pilot signal 1
k
+1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1
−10 −9 −8 −7 −6 −5 −4 −3 −2 −1 dc 1 2 3 4 5 6 7 8 9 10 k
+1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1
−10 −9 −8 −7 −6 −5 −4 −3 −2 −1 dc 1 2 3 4 5 6 7 8 9 10
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where subscipts m and n denotes the receive and transmit In this paper, we will consider three types of interpolation,
antenna index, respectively, SNR is the signal to noise ratio namely, linear interpolation, LMMSE interpolation, and DFT-
of the training signals, and β is a constant depending on based LS interpolation.
the training signal’s constellation. For MPSK training signals, 1) Linear Interpolation: Assuming that the transmit anten-
β = 1. RHH = E(Hmn HH mn ) is the channel autocorrelation nas are divided into two groups, Ĥm,n,k−1 and Ĥm,n,k+1 are
matrix. When same statistical properties are assumed for each the LS estimates obtained from Equation (6), then channel
SISO channel, RHH is independent of m and n and can be estimate at the kth subcarrier can be obtained through linear
computed off-line. It has been given in [15] that its diagonal interpolation as follows:
element rk,k = 1, and the off-diagonal element rk1 ,k2 (k1 =
k2 ) is: Ĥm,n,k−1 + Ĥm,n,k+1
H̃m,n,k = , (12)
1 2πj(k1 −k2 )
2
−L( τrms + )
1−e N
rk1 ,k2 = L
, which is a linear matrix filtering operation as follows:
1
τrms 1 − e− τrms τrms + j2π k1N
−k2
H̃m,n,k−1 1 0 0 Ĥm,n,k−1
for an exponentially decaying power delay profile with root- H̃m,n,k = 1 1 0 ,
2 2
mean squared delay of τrms and maximum excess delay of L. H̃m,n,k+1 0 0 1 Ĥm,n,k+1
Here N is the FFT size, and the multipath delays are assumed
to be uniformly distributed over [0, L − 1]. where represents any complex number as it does not affect
the results.
The LMMSE channel estimator in Equation (11) is robust to
power delay profile mismatch if RHH for the least correlated 2) LMMSE Interpolation: Linear interpolation expressed
channel is used, as indicated in [15]. As for the SNR mismatch, in (12) assumes a channel correlation matrix RHH with its
[15] showed that a design for a high SNR will be preferable elements defined as:
as channel estimation errors will be concealed in noise for α when |i − j| = 1
low SNR, and they will tend to dominate for high SNR Ri,j = 1 when i = j ,
where the noise is low. Therefore, the LMMSE matrix filter
−1
0 otherwise
β
RHH RHH + SNR I can be calculated off-line. This
where α is a real number and α ∈ (0, 1). This suggests
will greatly reduce the computation load in the receiver.
that more accurate estimates could be obtained if the real
channel correlation information is applied in the interpolation.
C. Interpolation-based Channel Estimation
In this case, not only the neighbouring subcarriers, but all
As discussed in Section III-A and III-B, LS and LMMSE the available subcarriers’ channel estimates will be used to
channel estimations can be obtained if training signals with calculate the missing subcarriers’ channel parameters, and the
nT OFDM symbols are sent and each subcarrier’s training contribution from different subcarriers isdetermined by their
signal matrix S k = Tk M is a non-singular matrix. When the correlation. In our study, we use WRHH RHH + SNR β
I
−1
41
where P represents a permutation matrix of size N × N . As
LS Channel Estimation with N transmit and M receive antennas
0
N=2, M=2, channel A
L multipaths are assumed in the time domain channel, we N=2, M=2, channel E
N=2, M=8, channel A
therefore have the following relation: −5 N=4, M=2, channel A
N=4, M=2, channel A
N=8, M=2, channel A
Ĥm,n,pilot
GH Ĥm,n = GH P = 0N −L , (13) −10
Ĥm,n,missing
−15
where G is the last (N − L) columns of the Fourier transform
MSE in dB
matrix F. Letting GH P = [GT GM ] so as to re-write (13) −20
as:
Ĥm,n,pilot
[GT GM ] = 0N −L . (14) −25
Ĥm,n,missing
−30
we will have the following relation:
GT Ĥm,n,pilot = −GM Ĥm,n,missing , (15) −35
42
LMMSE Channel Estimation with 2 transmit and 2 receive antennas designed for SNR=20dB
0 which needs fewer OFDM symbols in the training sequence
LSE, channel A
LMMSE, R_A, channel A and therefore the transmission efficiency is improved. Three
LMMSE, R_E, channel A
−5 LMMSE, R_A, channel E interpolation schemes, namely, linear interpolation, LMMSE
LMMSE, R_E, channel E
interpolation and DFT-based LS interpolation are proposed,
−10
among which the LMMSE interpolation scheme demonstrates
the best performance, even in the mismatch case. As both
−15
LMMSE channel estimation and LMMSE interpolation can be
MSE in dB
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