IEEE - Aerospace and Electronic Systems - April 2022 - 49
Wu et al.
Cramer-Rao lower bound (CRLB) of u0 estimation is
given by 3=ðp2MLg0Þ.
We see from Figure 5 that the MSEs of both ^u0 and ^b0
monotonically decrease with the SNR. In particular, the
MSE of ^u0 approaches the CRLB when the SNR exceeds
6 dB, which validates the high accuracy of the estimation
method provided in the section " Estimating Channel
Figure 5.
Illustration of the channel estimation performance using the
method elaborated on in the section " Recent Advances in Channel
Estimation for FH-MIMO DFRC. " The AoD of the LoS path is
set as u0 ¼ p=2; the path gain b0 has unit amplitude but random
angles uniformly taken in ½0; 2p radius; refer to Table 1 for other
parameter settings.
which is illustrated in Node E of Figure 3. We see that the
DFT result on the second discrete frequency bin, denoted
by ~m, has the maximum amplitude. This indicates that the
true u0 is closer to 2p ~m=M compared with 2pm=M for
8mð¼ 0; 1; 2; 3Þ and m 6¼ ~m. To improve the u0 estimation,
interpolating DFT coefficients has been suggested
in [24] and[25]. For completeness of the article, we simply
summarize the steps for u0 estimation based on the q-shift
estimator (QSE), originally designed in [24] and later
improved in [25]. The technical details are suppressed
here (interested readers are referred to [24], [25]).
To refine the estimate of u0, QSE interpolates the
PM1
DFT coefficients around m~ , yielding Z
¼
Y~0 mej
2pmð ~mþz
Þ
M
based on Z
, as given by g ¼ ZþZ
update z by the relation: z ¼ cos 2ðpÞ
m¼0
, where z is an interpolation factor to be
updated iteratively and is an intermediate variable satisfying
minfM1
3; 0:32g[25, Eq. (23)]. Construct a ratio
ZþþZ . Use the ratio g to
1p cotðpÞ
IEEE - Aerospace and Electronic Systems - April 2022
Table of Contents for the Digital Edition of IEEE - Aerospace and Electronic Systems - April 2022
Contents
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