Yin et al. EURASIP Journal on Wireless Communications and Networking
(2015) 2015:165
Page 2 of 19
recording the complex time-domain signals, and thus not
suitable for investigating the wideband channel charac-
teristics extracted from multipath parameters. For sam-
pling the mm-wave signals, the oscillo scope devices are
required to have sampling rate up to 100 GHz, which
is not easy to achieve. Furthermore, due to the small
storage in the oscilloscope devices, measurement of wide-
band channel be comes very time-consuming. A solution
tackling these problems is to down-sample the received
wideband signals and store the data at a low speed which
allows transferring data in real-time from local memory
to external disk. Then by using a s o-called sliding correla-
tion (SC) technique, a time-dilated approximate channel
impulse response (CIR) can be calculated by low-pass fil-
tering (LPF) the received data if the sounding signals can
be sent repetitively. The LPF in the receiver is applie d to
remove the distortion components which have higher fre-
quencies [7]. It has been shown in [8] that pre-filtering
techniques can als o be applied in the transmitter side to
achieve the same objective. Due to the benefits of low
complexity in the receiver design and acceptable costs,
the SC-based data acquisition has b een widely adopted
[9–12].
However, the SC-based data acquisition has two prob-
lems. First, the higher-frequency components in the SC’s
output considered as distortions still carry information
of channel parameters and, thus, should be exploited to
improve the accuracy of parameter estimation. A draw-
back resulted when higher-frequency components are
considered is that the time-dilated approximation of CIR
is unavailable, and as a consequence, conventional peak-
searching estimation methods adopted in the SC-based
channel estimation are inapplicable. Second, the time-
dilated CIR generated by the conventional SC requires
the sounding signal being sent repetitively. The number
of the repetitions, also c alled as sliding factor, is usu-
ally in the 10
3
order of magnitude or even higher [7].
In the cases where channels are time-vari ant, the CIR
may not be calculated w ithin the channel coherence time.
As a consequence, the mobile to mobile (M2M) channel
measurements cannot be conducted by using the SC-
based solution. Recently, a Space-Alternating Generalized
Expectation-maximization (SAGE) estimation approach
was introduced in [13] which is der ived based on a para-
metric model characterizing the SC’s output, allowing
the estimation of multipath parameters by using higher-
frequency components. However, this s olution still relies
on the SC’s output obtained by sending the sounding
signals many times. No thorough investigation has been
carried out so far for the feasibility of accurate parameter
estimation based on the SC’s outputs without sending the
sounding signals repetitively.
In this contribution, the SAGE algorithm originally
derived in [13] bas ed on a parametric model for both low-
andhigh-frequencycomponentsofSC’soutputiselabo-
rated. Its performances in estimating multipath parame-
ters are investigated extensively by using simulations. It
shows that without discarding the higher-frequency com-
ponents of SC’s output, the estimation accuracy, particu-
larly for delay parameters , can be improved substantially.
In addition, another benefit of this novel estimation algo-
rithm not found previously is discovered; that is, the esti-
mation of path parameters, including Doppler frequency,
can be performed by using only a fraction of the SC’s
output. Hence, the overall observ ation span can be kept
less than channel coherence time in time-variant cases,
and characteriz ing time-variant channels through SC-
based measurements, which cannot be performed before,
be comes feasible. Simulations are c arried out to com-
pare the performance of the proposed algorithm with
the conventional method, and investigate the impact of
selecting different bandwidth of LPF and the length of the
SC’s output on the RMSEEs, resolution capability of the
algorithm.
The rest of the paper is organized as follows. Section 2
descr ibes the parametric signal model. In Section 3, a
SAGE algorithm is presented. Se ction 4 describes the
simulation results for the performance of the proposed
algorithm. Finally, conclusive remarks are addressed in
Se ction 5. To improve the understandings of the math-
ematical notations adopted in this contribution, Table 1
lists all the symbols introduced and corresponding
explanations.
2Signalmodel
As elaborated in [9, 10] and [7], the SC performs a specific
cross-correlation operation, e.g., between a pseudo-noise
(PN) random sequence u(t) with chip rate f
c
and another
sequence u
(t) with chip rate f
c
. According to [7], both
sequences contain exactly the same chips, and the chip
rates are related as f
c
=
γ −1
γ
f
c
,whereγ is called sliding
factor. By sample-wise multiplying these two sequences in
the time domain for multiple cycles which start with lin-
early incre asing time-offsets and summing the pro ducts
over individual cycles of u
(t), a time-dilated approxi-
mate a
u
(τ/γ ) of the autocorrelation function a
u
(τ ) =
E[ u(t)u
∗
(t − τ)] can be calculated by low-pass-filtering
the SC’s output with bandwidth B =
−f
c
/γ , f
c
/γ
.
In the channel sounding cases, the received signal is the
convolution of the transmitted sequence u(t) with the CIR
h(τ ), the output of the SC after the LPF with bandwidth B,
is the time-dilated approximate
ˆ
h
(
τ/γ
)
of the CIR. Here,
ˆ
h
(
τ/γ
)
is a time-dilated version of
ˆ
h
(
τ
)
= h
(
τ
)
∗ a
u
(
τ
)
with ∗ denoting the convolution operation. It is well-
accepted that only
ˆ
h(
τ
γ
) obtained with the LPF bandwidth
B can be used to estimate the channel parameters [7, 14].
Whether the components obtained with larger B, e.g.,
B
n
=[ −nf
c
/γ , nf
c
/γ ], n > 1, are applicable for estimating