Simulated Annealing Mechanic Based Noncoherent Signal Detection 2129
the down-Nyquist rate is also feasible, due to the exclusion of parametric CIR estimation.
Accordingly, the received signal y(n) can be expressed as:
y(n) =
h(n) + w(n) H
1
w(n) H
0
(4)
where w(m) is the additive white Gaussian noise (AWGN) with zero mean and variance σ
2
w
.
The decision variable in classical ED is defined as Y
ED
=
n
y
2
(n), and channel E
b
/N
0
is
given by
n
y
2
(n)/(Nσ
2
w
). It should be noteworthy that, the formulation in (4)alsorepresents
the binary-hypothesis target detection, i.e. the presence or absence of a target, and h(n) can
be viewed as the reflected waveform from a specific target [9]. In the noncoherent scheme
above, signal demodulation is to identify whether there is sufficient signal power available in
current time bin. Apparently signal power can characterize the UWB multipath signals only
in a rather coarse way, resulting in uncompetitive detection performance [17,21,35]. In this
paper, we develop a novel noncoherent algorithm that may enhance detection performance
considerably.
3 Noncoherent Signal Detection
Careful observations on nature processes imply that biological activities can solve the prob-
lems encountered in a much efficient way, and the achieved decisions are far superior to what
we can achieve with our current engineering knowledge and methods, especially for the non-
ideal situations in the presence of information limitations and uncertainties [35–37]. Inspired
by the appealing mechanics mentioned above, we deal with noncoherent detection as a state
classification problem by using the powerful SA optimization. We establish a character rep-
resentation of the reflected UWB signals, and further extract certain quantitative features
from it. The received signals are then mapped into different two patterns in a representative
space [38].
3.1 Characteristic Representation
Given the observed signals consists of N samples, y(n) (n = 0, 1, 2,...,N − 1), firstly we
construct a covariance matrix A according to
A = y
T
y (5)
In order to exploit the more profound information of UWB multipath signals, we further
derive a symmetric matrix from A
N×N
.
B = A
T
A (6)
We denote the principal diagonal elements of B
N×N
by
β
N×1
, while the elements imme-
diately below this diagonal by
ρ
(N−1)×1
.
β
N×1
= diag(B) = B
(
i, i
)
, i = 0, 2,...,N − 1(7)
ρ
(
N−1
)
×1
= diag
(
B
)
= B
(
i + 1, i
)
, i = 1, 2,...,N − 1(8)
The characteristic spectrum of UWB signals can be now defined as the linear correlation
function between
β
and
ρ
2
.
c
(2N−2)×1
=
β
ρ
2
(9)
123
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