A WIDEBAND SPECTRUM SENSING METHOD FOR COGNITIVE RADIO USING SUB-NYQUIST SAMPLING

1. A WIDEBAND SPECTRUM SENSING
METHOD FOR COGNITIVE RADIO
USING SUB-NYQUIST SAMPLING
M. R. Avendi, K. Haghighi, A. Owrang and M. Viberg
Dept. Signal and Systems, Chalmers University of Technology/ SWEDEN
Abstract
Spectrum sensing is a fundamental component in cognitive radio. A
major challenge in this area is the requirement of a high sampling rate
in the sensing of a wideband signal. In this paper a wideband spec-
trum sensing model is presented that utilizes a sub-Nyquist sampling
scheme to bring substantial savings in terms of the sampling rate. The
correlation matrix of a finite number of noisy samples is computed and
used by a subspace estimator to detect the occupied and vacant chan-
nels of the spectrum. In contrast with common methods, the proposed
method does not need the knowledge of signal properties that mitigates
the uncertainty problem. We evaluate the performance of this method
by computing the probability of detecting signal occupancy in terms of
the number of samples and the SNR of randomly generated signals. The
results show a reliable detection even in low SNR and small number of
samples.
Problem Statement
• Complex wideband signal x(t) with Fourier transform X(f).
• Frequency range [0,Bmax] , Bmax = L×B
• Active channel set b = [b1,b2,...,bN],
• Maximum number of active channels Nmax, channel occupancy Ωmax = Nmax
L
• Problem: given Bmax,B,Ωmax find b!
Wideband Spectrum Sensing Model
LL
xix(t)
z−ci
xdi 1
Mxdx∗
d
ˆR ˆb
Multicoset Sampler
Sample Correlation matrix
Subspace Analysis
favg = αBmax
FIGURE 1: Illustration of the proposed wideband spectrum sensing model.
Multicoset Sampler favg = p
L Bmax
xi(m) = x[(mL+ci)/Bmax],m ∈ Z,i = 1,... p
• p > Nmax, ci ∈ {0,1,...,L−1}
Correlation Matrix from fractional shifted samples, xd(m) =




xd1
(m)
xd2
(m)
...
xdp
(m)




ˆR =
1
M
M
∑
m=1
xd(m)x∗
d(m)
Subspace Analysis
Data model after fractional shifting in the frequency domain
y(f) = A(b)z(f)+n(f), f ∈ [0,B]
where A(b)(i,k) = Bexp j2πcibk
L
y(f) known vector of DFT of fractional shifted samples xdi
z(f) unknown vector of signal spectrum z(f) =




X(f +b1B)
X(f +b2B)
...
X(f +bNB)




• Correlation Matrix
R = E[y(f)y∗
(f)] = A(b)QA∗
(b)+σ2
I
where Q = E[z(f)z∗
(f)]
• Eigen- Decomposition
R = EsλsE∗
s +EnλnE∗
n
• Estimating the Number of Active channels: MDL
• Active channel set recovery: Discrete MUSIC
PMU(k) =
1
a∗
k
ˆEn
2
, 0 ≤ k ≤ L−1
where ak is a column of A(b)
Simulation Results
• Parameters p = 10, L = 32, Bmax = 320 MHz, favg = 100 MHz
• Detected active channels
0 5 10 15 20 25 30
0
20
40
60
MU
80 160 290 320
0
200
400
600
800
|X(f)|P(k)
frequency[MHz]
k,channel index
FIGURE 2: Frequency representation, X( f), and the corresponding PMU values of a typical wideband
signal with L = 32 channels. The position of six significant values specify the occupied channels
ˆb = [8,16,17,18,29,30].
• Detection performance:
Pd= fraction of correctly selected occupied frequency bands
Pf = fraction of wrongly selected occupied frequency bands
11 21 31 41 51 61 71 81 91 101 111 121 131 141
0.7
0.8
0.9
1
SNR=−2dB
SNR=−1dB
SNR=0dB
SNR=1dB
11 21 31 41 51 61 71 81 91 101 111 121 131 141
0
0.05
0.1 SNR=−2dB
SNR=−1dB
SNR=0dB
SNR=1dB
Pd
Pf
M
M
FIGURE 3: Detection performance of the proposed model versus M and SNR for the simulated wideband
system.
Chalmers University of Technology.
Background design by Jan-Olof Yxell