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

LLxix(t)

z−cixdi 1

Mxdx∗

dR b

Multicoset SamplerSample 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)

R =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)+σ 2I

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∗kEn‖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 25 300

20

40

60

MU

80 160 290 3200

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

b = [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 1410.7

0.8

0.9

1

SNR=−2dBSNR=−1dBSNR=0dBSNR=1dB

11 21 31 41 51 61 71 81 91 101 111 121 131 1410

0.05

0.1

SNR=−2dBSNR=−1dBSNR=0dBSNR=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