An NLLS Based Sub-Nyquist Rate Spectrum Sensing for Wideband Cognitive Radio

An NLLS Based Sub-Nyquist Rate Spectrum Sensing for

Wideband Cognitive Radio

M. R. Avendi, K. Haghighi, A. Panahi, M. Viberg

Department of Signal and SystemsChalmers University of Thechnology

May 2011

M. R. Avendi, K. Haghighi, A. Panahi, M. Viberg Wideband Spectrum Sensing May 2011 1 / 21

Outline

Introduction

Problem Statement

Proposed Model

Comparison and Simulation

Summary


Introduction

Spectrum Sensing


Introduction

Spectrum Sensing

Narrowband

Energy Detection (ED), ...


Introduction

Spectrum Sensing

Narrowband

Energy Detection (ED), ...

Wideband

Challenge: High Sample Rate ADC


Problem Statement

Signal

Complex signal x(t)

Fourier X (f ), f ∈ [0,Bmax ]

Nyquist rate: Bmax = L× B

frequency[MHz]

Sp

ectr

um

0 Bmax

index L = 0, 1, ..., L − 1


Problem Statement Cont.

Active channel set b = [b1, b2, ..., bN ]

Example: b = [8, 16, 17, 18, 29, 30]

frequency[MHz]

Sp

ectr

um

0 8 16 24 32

Given B ,Bmax ,Ωmax = Nmax

Land x(t)

Find b and N ?at fsample < Bmax


Proposed Model

LLxi (m)x(t) Delayxdi 1

MΣxdx

∗d

R b

y(f )

Multicoset SamplerSample Correlation matrix

NLLS Estimator

favg = αBmax


Multicoset Sampler

Non-uniform sampling: xi (m) = x [(mL + ci )/Bmax ];m ∈ Z

0 5 10 15 20 25 30 35 40−3

−2

−1

0

1

2

3

time

x(t)


Multicoset Sampler

Sampling frequency: favg =(

pL

)

Bmax

Landau’s lower bound: Nmax < p ≪ L

Random sample pattern: ci ∈ L

x1(m)

x(t) x2(m)

xp(m)

t = (mL+ c1)/Bmax

t = (mL+ cp)/Bmax


Recall Model


MΣxdx

∗d

R b

y(f )


NLLS Estimator

favg = αBmax


Configuration

Upsampling: factor L

Low pass filtering: [0,B ]

Delaying: with ci samples

Lxi (m)

Delayxci , y(f )


Frequency domain Model

Matrix form:

y(f ) = A(b)x(f ) + n(f ), f ∈ [0,B ]


Frequency domain Model

Matrix form:

y(f ) = A(b)x(f ) + n(f ), f ∈ [0,B ]

y(f ): Known vector of DFT of configured sequences

x(f ): Unknown vector of signal spectrum in the active channels

n(f ): Gaussian complex noise, N (0, σ2I)

A(b)(i , k) = B exp(

j2πcibkL

)


Recall Model


MΣxdx

∗d

R b

y(f )


NLLS Estimator

favg = αBmax


Correlation Matrix

True matrix: R = E [y(f )y∗(f )]

Estimated in time domain using Parseval’s identity

R =

B∫

0

y(f )y∗(f )df =+∞∑

m=−∞

xci [m]x∗ci [m]

Reduce complexity, downsampling xdi (m) = xci [mL]

R =1

M

M∑

m=1

xd (m)x∗d (m)

Lxcixdi 1

MΣxdx

∗d

R


NLLS Based Method

Recall model y(f ) = A(b)x(f ) + n(f ) ⇒ b ?

Minimizing the least square error J(b) = tr(Ip − A(b)A†(b))R

Detection threshold


NLLS Based Method

Recall model y(f ) = A(b)x(f ) + n(f ) ⇒ b ?

Minimizing the least square error J(b) = tr(Ip − A(b)A†(b))R

Detection thresholdJmin = σ2(p − N)


NLLS method

Sequential Forward NLLS Algorithm

Typical Example: p = 10,N = 6, σ2 = 1

1 2 3 4 5 64

6

8

10

12

14

16

18

J(bi )LSE

i

Jmin

(p − i)σ2


Comparison and Simulation

Signal: Bmax = 320MHz ,B = 10MHz ,Ωmax = 0.25

Multicoset sampler: L = 32, p = 10,M = 64favg =

(

pL

)

Bmax = 100MHz!!

0 80 160 240 320frequency[MHz]

Sp

ectr

um


Energy Detection Model

Conventional ED model

x(t) x(nT )

Uniform Sampler

fs = Bmax

Filter Bank

1M

∑

|.|2

1M

∑

|.|2

≷10 η

≷10 η

H0

H0

H1

H1


Numerical Results

Probability of detection

−5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

α=0.3, NLLS

α=0.5, NLLSEDMUSIC

Pd

SNR, [dB ]


Numerical Results

Probability of false alarm

−5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 100

0.005

0.01

0.015

0.02

0.025

α=0.3, NLLS

α=0.5, NLLSEDMUSIC

Pf

SNR, [dB ]


Summary

Wideband Spectrum Sensing

MulticosetSampler

NLLS method

Comparison


Thank you for your attention


An NLLS Based Sub-Nyquist Rate Spectrum Sensing for Wideband Cognitive Radio

Engineering

Transcript of An NLLS Based Sub-Nyquist Rate Spectrum Sensing for Wideband Cognitive Radio