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Wideband Spectrum Sensing for
Cognitive Radios
Zhi (Gerry) Tian
ECE Department
Michigan Tech University
ztian@mtu.edu
February 18, 2011
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Spectrum Scarcity Problem
1
fixed spectrum access policies have
useful radio spectrum pre-assigned
US FCC
inefficient utilization
0 1 2 3 4 5 6GHz
PS
D
“Scarcity vs. Underutilization Dilemma”
Source: Spectrum Sharing Inc.
at any time and location,
most spectrum is unused
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Spectrum Sharing under User Hierarchy
2
CRs opportunistically use the spectrum
Cognitive radio network problems
Finding holes in the spectrum: wideband spectrum sensing
Allocating the open spectrum: dynamic resource allocation
Adjusting the transmit waveforms: waveform adaptation
legacy users
frequency
pow
er
cognitive radios
legacy users cognitive radio
Secondary User (SU) Primary User (PU)
Z. Tian, Michigan Tech Sparsity-Aware Sensing
3
Challenge 1: Wideband Signal Acquisition
multiple RF chains, BPFs
number of bands fixed
LO filter range is preset
simple (energy/feature)
detection within each BPF
single RF chain
flexible to dynamic PSD
burden on A/D: fs ~ GHz
complex wideband sensing
Choices for RF Circuits: multiple NB or single WB ?
• Effective SNR (SNReff) for DSP determined by front-end circuits
Freq.
A/D LNA AGC
LO1
A/D LNA AGC
A/D LNA AGC
LO2
LON
Band 1
Band 2
Band N
multiple narrowband (NB) circuits
NB filter SNReff
wideband (WB) circuit
A/D LNA AGC
Fixed LO
Wideband Sensing
WB filter
SNReff
A. Sahai and D. Cabric, IEEE DySpan 2005 Q: How can we alleviate DSP burden on wideband circuit design?
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Challenge 2: User Hierarchy
“IEEE 802.22 requires CRs to sense PU signals as low as -114dBm”
4
Operating Conditions Technical Challenges
Protection of primary
systems
Sensing at low SNR
Modulation classification
Short sensing time
Random sources of
interference and noise
Robustness to noise uncertainty
Interference identification
Q: How can we alleviate noise uncertainty effects at low SNR?
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Challenge 3: Wireless Fading
If no energy detected on a band, can CR assume PU is absent?
Detection performance limited by received signal strength
Wireless: deep fading, shadowing, local interference
missed detection, hidden terminal problem
CR
1
f multiple (random) paths unlikely
to fade simultaneously
Spatial diversity against fading
f PUs f
CR
2
f
Q: How can we collect cooperation gain at affordable overhead? 5
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Road Map for Wideband Sensing
Compressed Sensing with sub-Nyquist-rate sampling
Exploiting the Sparsity in the received signal (in freq. domain)
Making use of Compressive Sampling to reduce sampling rates
Compressed Cyclic Feature based Sensing
Exploiting the Sparsity in both freq. & cyclic-freq. domains
Making use of Cyclic Statistics for robustness to noise
uncertainty and low SNR conditions
Multiple-CR Cooperative Sensing
Local Compression + Network Cooperation
6
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Limits on Sampling Rates
Lower bounds on sampling rates fs
What is the lowest fs for reconstruction without aliasing?
Nyquist rate = 2B
What is the lowest fs for reconstruction of CR signals?
Motivating factor for CR is low spectrum utilization
Landau rate = 2Beff = 2 rnz B < Nyquist rate
Challenge: locations of occupied bands are unknown
CR j
N 1 n
Spectrum occupancy ratio
Wide band of interest: BW = B
f
7
Compressed Sensing (CS)
rnz = Nnz/N � 1
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Basics of Compressed Sensing
Compressive sampling [Chen-Donoho-Saunders’98], [Candès et al’04-06]
Given y and H, unknown s can be found with high probability
Least-absolute shrinkage selection operator (Lasso)
Ex. (scalar case) closed-form solution
Sparse regression [Tibshirani’96], [Tipping’01]
(a1) s is sparse (nonzero entries unknown)
(a2) H can be fat (K N);
satisfies restricted isometry property (RIP)
variable selection + estimation
8
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Received signal
Fine-resolution (Nyquist-rate) representation:
Sparsity in frequency:
Linear sampling
Compression in time (M/N):
Various designs of random samplers [Kirolos etal’06, Hoyos etal’08]
Sub-Nyquist-rate Sampling
9
F-1
rf rt xt Sc
CS
recovery
r(t) f
analog input digital samples
discrete representation
CS-ADC
rf
rf : N × 1
Sc : K × N
Nnz = ‖rf‖0 � N
Nnz ≤ K ≤ N
r(t) : t ∈ [0, NTs]
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Spectrum Hole/Edge Detection
Spectrum reconstruction Spectrum hole detection (edge detection on wavelet basis)
20%
33%
50%
75%
90%
100%
[Tian-Giannakis’07] 10
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Road Map for Wideband Sensing
Compressed Sensing with sub-Nyquist-rate sampling
Exploiting the Sparsity in the received signal (in freq. domain)
Making use of Compressive Sampling to reduce sampling rates
Compressed Cyclic Feature based Sensing
Exploiting the Sparsity in both freq. & cyclic-freq. domains
Making use of Cyclic Statistics for robustness to noise
uncertainty and low SNR conditions
Multiple-CR Cooperative Sensing
Local Compression + Network Cooperation
11
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Cyclostationarity in Modulated Signals
Modulated signals are cyclostationary processes
Cyclic features reveal critical signal parameters:
- carrier frequency
- symbol rate
- modulation type
- timing, phase etc.
Non-cyclic signals (e.g. noise) do not possess cycle frequencies
12
t t t+
t+T0 t+T0+ T0
+T0
t1 t1+
x(t)
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Why Cyclic Statistics (1)
Energy detection vs. feature detection
13
spectrum density ( = 0) spectral correlation density (SCD)
High SNR
Low SNR
Multi-harmonics
peaks at
f
f
no noise components when 0
[Sahai-Cabric’05]
f
f
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Why Cyclic Statistics (1)
Magnitudes of estimated SCD
a) a BPSK signal corrupted by white noise and five AM interferences
b) the BPSK signal alone c) the white noise and five AM interferences
(a) (b)
(c)
overlapping in PSD, separable in SCD
Spectral Correlation Density (SCD)
[Gardner’88]
14
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Cyclic Feature Detection
Cyclic Feature Detection and Classification
using Compressive Sampling
Issues with cyclic feature detection
Cyclostationarity is induced by OVER-sampling
excessive sampling-rate requirements
Cyclic statistics converge slowly with finite samples
long sensing time
15
Cyclostationarity-based approach for detection
insensitive to unknown signal parameters
cyclic statistics robust to multipath
resilient against Gaussian noise
can differentiate modulation types and separate interferences
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Wideband Cyclic Feature Detection
Cyclic feature detection over a wide band
Goal is to perform simultaneous detection of multiple sources
Need to alleviate the sampling rates and sensing time
Exploiting signal sparsity in two dimensions
Sparsity in frequency domain low spectrum utilization
Sparsity in cyclic-freq. domain modulation-dependent cycles
16
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Signal Model
Wide band of interest:
Multiple PU signals:
Received signal:
Cyclic spectrum (SCD):
Folded SCD of sampled signal:
Aliasing-free condition:
17
Cyclic spectrum of digital
samples. The central diamond region
is the non-zero support [Gardner’91]
x(t) =∑I
i=1 xi(t) + w(t)
xi(t), i = 1, . . . , I
[−fmax, fmax]
fs = 1/Ts ≥ 2fmax
S(α, f) nonzero for
cyclic-freq
freq
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Problem Setup
Cyclostationarity in communication signals
time-varying (TV) covariance is period in time
Sparse signal recovery
to reconstruct Sx( ,f) from samples z[n] at sub-Nyquist rate
18
CS-ADC
(sub-Nyquist) compressive
samples
Sx( ,f) sparse
Sparse Signal
Recovery recovered
SCD
Sx( , f)
zt = Axt
rx(n, ν) = E{x(nTs)x(nTs + νTs)} = E{xt(n)xt(n + ν)}rx(n, ν) = rx(n + kP, ν), ∀n, k, ν
2D cyclic spectrum is NOT LINEAR in the time-domain samples
CS framework not immediately applicable
x(t) ↔ xt zt : {z[n]}
M
Nfs
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Defining Cyclic Spectrum
2nd-order Statistics: covariance and spectra
19
Time-varying Covariance
Cyclic Covariance Time-varying Spectrum
Cyclic Spectrum SCD
r(c)x (a, ν)
a ∈ [0, N−1] ←→ α =1
NTsa
s(c)x (a, b)
sx(n, b)
rx(n, ν)
b ∈ [0, N−1] ←→ f =1
NTs(b − N − 1
2) ∈(−fs
2,fs
2)
Cyclic-frequency:
Frequency:
FT in n (shifted)
FT in v
Q: How can we relate sub-Nyquist data and sparse SCD linearly?
zt = Axt
E{xt(n)xt(n + ν)}
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Vector-form Relationship (1)
Linking time-varying covariance matrix with cyclic spectrum
TV covariance matrix:
Degree of freedom: N(N + 1)/2
Vectorized cyclic spectrum
20
rx = [rx(0, 0), rx(1, 0), · · · , rx(N − 1, 0), rx(0, 1), rx(1, 1),
· · · , rx(N − 2, 1), · · · · · · , rx(0, N − 1)]T ∈ RN(N+1)
2 .
Rx =
⎡⎢⎢⎢⎢⎢⎣
rx(0, 0) rx(0, 1) rx(0, 2) · · · rx(0, N−1)rx(0, 1) rx(1, 0) rx(1, 1) · · · rx(1, N−2)rx(0, 2) rx(1, 1) rx(2, 0) · · · rx(2, N−3)
.... . .
...rx(0, N−1) · · · · · · · · · rx(N−1, 0)
⎤⎥⎥⎥⎥⎥⎦
Rx = E{xtxTt }
s(c)x = vec{S(c)
x } = (I ⊗ F)∑N−1
ν=0 (DTν ⊗ Gν)BT︸ ︷︷ ︸
:=T
rx
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Vector-form Relationship (2)
Linking time-varying covariance matrices
TV covariance of compressed data
Finite-sample estimate:
Degree of freedom: M(M + 1)/2
Relationship:
Linear representation for compressed covariance
21
rz = [rz(0, 0), rz(1, 0), · · · , rz(M − 1, 0), rx(0, 1), rz(1, 1),
· · · , rz(M − 2, 1), · · · · · · , rz(0, M − 1)]T .
rz = QMvec{ARxAT } = QM (A ⊗ A)vec{Rx} = Φrx
Rz = E{ztzTt } ∈R M×M
zt = Art −→ Rz = ARxAT
N(N + 1)2
× 1M(M + 1)
2× 1
Rz = 1L
∑lzt,lzT
t,l
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Sparse Cyclic Spectrum Recovery
Reformulated linear relationship
under-determined
Prior Information
is highly sparse
is positive semi-definite (psd)
22
rz = Φrx
Φ : M(M+1)2 × N(N+1)
2
s(c)x = Trx
s(c)x
Rx
minrx
‖Trx‖1 + λ ‖rz − Φrx‖22
s.t. Rx is psd, with vec{Rx} = PNrx.Convex !
L1-norm regularized LS (LR-LS)
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Summary of Reconstruction Steps
23
TV Covariance
Estimation Sparse Signal
Recovery
LR-LS
Cyclic SCD
estimation rx
rz
s(c)x = Trx
s(c)x
Rz = 1L
∑lzt,lzT
t,l
{zt,l}l
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Spectrum Occupancy Estimation
Band-by-band estimation
Region of relevance
Relevant SCD vector for band n
24
fs
2−fs
2
−fs
fs
ff (n)
α
(α, f) :
⎧⎪⎨⎪⎩
f +α
2= f (n)
|f | + |α|2
≤ fmax
(ai, bi) :
⎧⎪⎨⎪⎩
bi +ai
2= n
∣∣bi−N−12
∣∣ +|ai|2
≤ fmaxN
fs≤ N
2
f (n) =n − N−1
2
Nfs ∈
[−fs
2,fs
2
]
Is f (n) occupied or not?
c(n) :{
s(c)x (ai, bi)
}i
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Multi-Cycle GLRT
Binary hypothesis test on band n
: unknown true SCD; multiple cyclic freq.
: noise statistics determined by
finite-sample effects, not ambient noise
GLRT formulation
Test statistics:
Binary decisions by thresholding
25
{H1 : c(n) = c(n) + εH0 : c(n) = ε
T (n) = (c(n))HΣε−1c(n)
c(n):{s(c)
x (ai, bi)}
i
ε : N (0,Σε)
Fast algorithms possible based on
modulation type, say, for BPSK
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Simulation: Robustness to Rate Reduction
26
Probability of Detection vs. Compression Ratio (CFAR PFA= 0.1)
0 0.2 0.4 0.6 0.8 10.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Compression Ratio
Pro
b o
f D
ete
ctio
n (
Pf =
0.1
)
Monitored band |fmax| < 300 MHz
2 sources: PU1 - BPSK at 100MHz;
PU2 - QPSK at 200MHz; Ts=0.04μs
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
M/N
Pro
babili
ty o
f dete
ctio
n
Cisco 802.11 DSSS
Spread spectrum
50% compression 50% compression
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Simulation: Robustness to Noise Uncertainty
outperforms energy detection (ED)
27
Receiver Operating Characteristic (ROC): PD vs PFA (SNR=5dB, 66% compression)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
PFA
PD
Cyclo, 0dB uncertainityCyclo 1dB uncertainityCyclo 2dB uncertainityED 0dB uncertainityED 1dB uncertainityED 2dB uncertainity
insensitive to noise uncertainty
ED
(noise uncertainty = 0, 1, 2dB)
cyclic
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Simulation: Occupancy Estimation Techniques
28
ROC (SNR = 5dB, 50% compression)
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Classification using Cyclic Statistics
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 0
.1 0.2
0
.3 0.4
0.5
0.6
0.7
0.8
0.9
1
Ma
x. a
mp
litu
de
of
Sp
ectr
al
Co
her
ence
I(
)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 0
.1 0.2
0
.3 0.4
0.5
0.6
0.7
0.8
0.9
1
Cycle frequency /Fs
Ma
x. a
mp
litu
de
of
Sp
ectr
al
Co
her
ence
I(
)
Cycle frequency /Fs
1D: cyclic-frequency domain profile (CDP)
2D: Spectral Correlation Density (SCD)
[Kim etal. 2007]
BPSK QPSK
BPSK QPSK
29
Cycle frequency
/Fs
Spectral frequency
f/Fs
Spectral frequency
f/Fs
Cycle frequency
/Fs
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Simulations: Classification
30
Confusion Matrix (SVM Classifier)
When compression ratio is adequate for detection,
classification accuracy is comparable to non-compression
Good separation of narrowband from spread spectrum
Considerable confusion among spread spectrum signals
BPSK QPSK DS-BPSK DS-QPSK
BPSK 95.45% 0% 4.55% 0%
QPSK 0% 90.9% 9.09% 0%
DS-BPSK 9.09% 0% 59.09% 31.82%
DS-QPSK 4.5% 4.5% 36.46% 54.54%
Z. Tian, Michigan Tech Sparsity-Aware Sensing
Summary and Future Work
Exploitation of signal sparsity in 2D cyclic spectrum domain
reformulated linear relationship between spectrum and covariance
robustness to noise uncertainty
capability in signal separation and classification
31
Direct reconstruction of test statistics from compressive samples
bypass the recovery of the entire cyclic spectrum
reduce sensing time and responsiveness
Sensing techniques for spread spectrum signals
utilize fusion techniques to take advantage of all features in the
wide spectrum of DSSS signals