Subspace-based 1-bit Wideband Spectrum Sensing Junquan Deng , Yong - - PowerPoint PPT Presentation

1/15

Subspace-based 1-bit Wideband Spectrum Sensing

Junquan Deng∗, Yong Chen

The Sixty-third Research Institute National University of Defence Technology (NUDT) Nanjing, China jqdeng@nudt.edu.cn, cheny63s@nudt.edu.cn

WCSP 2019

Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 1 / 15

2/15

This work focuses on Power-efficient wideband spectrum sensing for cognitive radio sensor networks We consider Spectrum sensing in a wideband cognitive radio system where 1-bit ADCs are adopted at the RF sensors The objective is To detect the occupation states of individual sub-bands simultaneously in a wide frequency range

Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 2 / 15

3/15

High-speed high-resolution ADCs are expensive and power-hungry

The circuit complexity and the power consumption of a ADC grows exponentially with the sampling resolution1

• 1B. Murmann, ADC Performance Survey, http://web.stanford.edu/~murmann/adcsurvey.html.

Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 3 / 15

4/15

1-bit ADCs for wide-band spectrum sensing?

Can be implemented using a single comparator Ultra-low driving power and circuit complexity Incurs only a small performance loss compared to high-resolution ADCs in low-SNR regime Have been considered for massive MIMO, low-cost radar

CLK Input Output

Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 4 / 15

5/15

System architecture for 1-bit wideband spectrum sensing

LO 0o 90o 1-bit ADC 1-bit ADC High Speed Buffer Segmentation LPF LPF Clock Fs Fs LNA Covariance estimation Noise floor evaluation Frequency detection algorithm

{+1 -1} {+1 -1}

I Q

Homodyne RF architecture No automatic gain control (AGC) required Size of buffer can be greatly reduced Low signal processing complexity

Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 5 / 15

6/15

1-bit Wideband Quantized Signal Model

fc fm

B NB

Continuous analog signal: y(t) = M

m=1 αm(t)e j2πf′

m(t−τm) + w(t),

(P1) Discrete received signal: y[n] = M

m=1 αm [n] e j2πf′

m

• n

Fs −τm

• + w [n]

(P2) 1-bit quantized signal: q[n] = 1 √ 2 (sign(ℜ{y[n]}) + j sign(ℑ{y[n]})) (P3)

Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 6 / 15

7/15

Problem Formulation

The M signals with frequencies {fm}M

m=1 are assumed to lie in exactly

M sub-bands The objective of the RF sensor is to provide an N-bit digital word representing the states of the spectrum sub-bands We define 2N binary hypotheses {H0,n}N

n=1 and {H1,n}N n=1, in which

H0,n denotes the idle state of the n-th sub-band and H1,n represents the active state For each sub-band, a test statistics χn is formulated based on the 1-bit sampled data, and a test decision is given as follows: Choose H0,n, if χn < θn, Choose H1,n, if χn > θn, for n ∈ {1, 2, . . . , N}, (P4)

Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 7 / 15

8/15

Subspace-based Technique for Wideband Spectrum Sensing

Based on signal covariance, typical methods are MUSIC and ESPRIT Received signals in vector form: y = s + w = [y[0], y[1], · · · , y[N − 1]]T , (P5) Covariance Matrix for y: Ryy = E

• (s + w) (s + w)H

= A∆AH + σ2

wI

(P6) We have eigen-decomposition Ryy = U(Λ + σ2

wI)UH

The signal and noise spaces are orthogonal for Ryy, we have

U = [Us Un]

Un of size N × (N − M) defines the noise subspace

Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 8 / 15

9/15

Subspace-based Technique for Wideband Spectrum Sensing

The core idea is to estimate frequencies using the pseudo-spectrum Ppseu(f) = 1 vH(f)UnUH

n v(f) =

1 UH

n v(f)2 2

. (P7) where v(f) =

• 1, e

j2π Fs f, e j4π Fs f, · · · , e j2(N−1)π Fs

f

T is the frequency-domain steering vector. If f equals one of the carrier frequencies of the spectrum components, the denominator is small, and there will be M largest peaks.

Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 9 / 15

10/15

How to estimate the covariance based 1-bit quantized data?

With 1-bit ADC, we only have Rqq = E{qqH} According to Bussgang theorem and Vleck’s arcsine law, we have Rqq = 2 π

• arcsin
• Σ

− 1

2

y RyyΣ − 1

2

y

• ,

(P8) where Σy = diag(Ryy) and arcsin(·) is element-wise. The normalized covariance for unquantized y can be approximated as ¯ Ryy . = π 2 Rqq +

• 1 − π

2

• I

(P9) For the an eigenvector v of Ryy with Ryyv = λv, we have π 2 Rqqv . = λ p − 1 + π 2

• v,

(P10) which implies that Rqq and Ryy have identical signal and noise spaces

Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 10 / 15

11/15

Subspace-based 1-bit wideband spectrum sensing algorithm

• 1. Acquire L snapshots of 1-bit quantized data {q1, q2, . . . , qL}
• 2. ˆ

Rqq ← 1

L

L

l=1 qlqH l , ˆ

Ryy ← π

2 ˆ

Rqq +

• 1 − π

2

• I
• 3. ˆ

Ryy = ˆ U ˆ Λ ˆ UH, where ˆ U = [u1, u2, . . . , uN], and ˆ Λ = diag{λ1, λ2, . . . , λN} with λi ≥ λj for i < j

• 4. Estimate the number of spectrum components using a Minimum

Description Length(MDL) estimator

• 5. Partition ˆ

U into [Us Un]

• 6. Compute pseudo-spectrum

1 UH

n v(f)2 2 for f ∈ {f1, f2, . . . , fN}

• 7. Find the N − M smallest elements in pseudo-spectrum, estimate the

noise floor Pnoise as the mean of the N − M smallest elements

• 8. If ps(n) > 10

γ 10 Pnoise (γ = 3 dB), mark the n-th sub-band as occupied Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 11 / 15

12/15

Performance Evaluation

• 0.5
• 0.4
• 0.3
• 0.2
• 0.1

0.1 0.2 0.3 0.4 0.5

• 0.5
• 0.4
• 0.3
• 0.2
• 0.1

0.1 0.2 0.3 0.4 0.5 1

• 0.5
• 0.4
• 0.3
• 0.2
• 0.1

0.1 0.2 0.3 0.4 0.5 0.5 1 0.5 1 0.5

Subspace-based method has a more distinguishable floor compared to FFT-based and correlation-based method

Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 12 / 15

13/15

Time Resolution vs Detection Performances

10 15 20 25 30 35 40 45 50 55 60 0.2 0.4 0.6 0.8 1 3 3 10 15 20 25 30 35 40 45 50 55 60 0.05 0.1 0.15 0.2 0.25 0.3 3 3

When SNR is 0, the proposed method has perfect performances with 32 snapshots, corresponds to a time-resolution of 3.2 µs When SNR is high, more snapshots of data are needed to attain a zero false alarm rate In high SNR regime, more samples are needed to average out the 1-bit quantization distortion in estimating the empirical covariance matrix 1-bit wideband spectrum sensing has a preferred operational SNR range

Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 13 / 15

14/15

Performance Comparisons under Different SNR Conditions

• 20
• 15
• 10
• 5

5 10 SNR in dB 0.2 0.4 0.6 0.8 1 Detection probability

• 20
• 15
• 10
• 5

5 10 SNR in dB

• 0.05

0.05 0.1 0.15 0.2 0.25 0.3 False alarm probability

Performances with 1-bit ADCs are comparable to those with infinite-resolution ADCs The detection probability of the proposed method is lower than that of DFT-based and higher than correlation-based The proposed method achieves almost zero false alarm and is superior compared to the other two

Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 14 / 15

15/15

Concluding Remarks

We have proposed a subspace-based 1-bit wideband spectrum sensing method, it exhibits ultra-low power consumption, low memory and computation demands, and is suitable for larger-scale RF sensor network deployments. Our results suggest that the superiority of the subspace technique in parameter estimation translates into efficacy in 1-bit wideband spectrum sensing. We show by simulations that the proposed method exhibits near-zero false alarm while achieves similar detection probability as compared to

• ther typical sensing methods.

Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 15 / 15