For Review Only
2
covariance-based techniques. Since the algorithms reviewed in [2], such as [3], were not specifically designed
for OFDM systems, they did not exploit the special signal structure of OFDM systems. On the other hand, most
algorithms designed for OFDM systems are covariance-based. [4] determined the maximum Doppler spread through
estimating the smallest positive zero crossing point. Cai [5] proposed to obtain the time correlation function (TCF)
by exploiting the cyclic prefix (CP) and its counterpart. However, Yucek [6] pointed out that for scalable OFDM
systems whose CP sizes were varying over time, [5] was difficult to offer a sufficient estimation of TCF, therefore
the accuracy is degraded significantly. In stead, Yucek proposed to estimate the maximum Doppler spread through
the channel impulse responses (CIR’s) estimated from the periodic training symbols. However, in order to reduce
overheads, training symbols are sparse and typically transmitted as preambles to facilitate the frame timing and
carrier frequency synchronization, which would cause [6] to converge slowly or even fail.
In this paper, we propose to estimate TCF by exploiting the comb-type pilot tones [7] which are widely adopted
in wireless standards. In order to reduce noise perturbation, the estimated channel frequency responses (CFR’s) are
projected onto the delay-subspace [8] to obtain CIR’s, and the subspace tracking algorithm [9] is adopted as well to
track the drifting delay-subspace. Then, with a careful derivation of the expression of TCF under a rigorous channel
model, a nonlinear high-order polynomial equation is builded, and by solving which, the maximum Doppler spread
is obtained.
This paper is organized as follows. In Section II, the OFDM system and channel model are introduced. Then,
the maximum Doppler spread estimation algorithm is presented in Section III. Simulation results and analyses are
provided in Section IV. Finally, Section V concludes the paper.
A. Basic Notation
In this paper, uppercase and lowercase boldface letters denote matrices and column vectors, respectively. (·)
∗
,
(·)
H
and || · ||
F
denote conjugate, conjugate transposition, and Frobenius norm, respectively. E(·) represents the
expectation of a stochastic process. [·]
i
and [·]
i,j
denote the i-th and (i, j)-th elements of a vector and a matrix,
respectively.
II. SYSTEM MODEL
Consider an OFDM system with a bandwidth of BW = 1/T Hz (T is the sampling period). N denotes the
total number of tones, and a CP of length L
cp
is inserted before each symbol to eliminate inter-block interference.
Thus the whole symbol duration is T
s
= (1 + r
cp
)NT , where r
cp
=
L
cp
N
. In each OFDM symbol, P tones are
used as pilots to assist channel estimation. In addition, optimal pilot pattern, i.e., equipowerd and equispaced [10],
is assumed.
The complex baseband model of a linear time-variant mobile channel with L paths can be described by [11]
h(t, τ) =
L−1
X
l=0
h
l
(t)δ (τ − τ
l
) (1)
September 3, 2008 DRAFT
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