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

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 1/15 Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 1 / 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 2/15 Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 2 / 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 resolution 1 1B. Murmann, ADC Performance Survey, http://web.stanford.edu/~murmann/adcsurvey.html . 3/15 Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 3 / 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 4/15 Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 4 / 15

System architecture for 1-bit wideband spectrum sensing 1-bit Covariance ADC {+1 -1} estimation I LPF Fs Segmentation 0 o Frequency High LNA LO Clock detection Speed algorithm Buffer 90 o Fs LPF Q Noise floor {+1 -1} 1-bit evaluation ADC Homodyne RF architecture No automatic gain control (AGC) required Size of buffer can be greatly reduced Low signal processing complexity 5/15 Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 5 / 15

1-bit Wideband Quantized Signal Model f m f c B NB Continuous analog signal: � M m ( t − τ m ) + w ( t ) , m =1 α m ( t ) e j 2 πf ′ (P1) y ( t ) = Discrete received signal: � � � M n m =1 α m [ n ] e j 2 πf ′ Fs − τ m (P2) y [ n ] = m + w [ n ] 1-bit quantized signal: 1 √ q [ n ] = 2 ( sign ( ℜ{ y [ n ] } ) + j sign ( ℑ{ y [ n ] } )) (P3) 6/15 Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 6 / 15

Problem Formulation The M signals with frequencies { f m } 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 2 N binary hypotheses {H 0 ,n } N n =1 and {H 1 ,n } N n =1 , in which H 0 ,n denotes the idle state of the n -th sub-band and H 1 ,n represents the active state For each sub-band, a test statistics χ n is formulated based on the 1-bit sampled data, and a test decision is given as follows: � Choose H 0 ,n , if χ n < θ n , if χ n > θ n , for n ∈ { 1 , 2 , . . . , N } , (P4) Choose H 1 ,n , 7/15 Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 7 / 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 : = A∆A H + σ 2 � ( s + w ) ( s + w ) H � R yy = E w I (P6) We have eigen-decomposition R yy = U ( Λ + σ 2 w I ) U H The signal and noise spaces are orthogonal for R yy , we have U = [ U s U n ] U n of size N × ( N − M ) defines the noise subspace 8/15 Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 8 / 15

Subspace-based Technique for Wideband Spectrum Sensing The core idea is to estimate frequencies using the pseudo-spectrum 1 1 P pseu ( f ) = n v ( f ) = (P7) . v H ( f ) U n U H � U H n v ( f ) � 2 2 � T � j 2 π j 4 π j 2( N − 1) π Fs f , e Fs f , · · · , e f where v ( f ) = 1 , e is the frequency-domain Fs 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. 9/15 Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 9 / 15

How to estimate the covariance based 1-bit quantized data? With 1-bit ADC, we only have R qq = E { qq H } According to Bussgang theorem and Vleck’s arcsine law, we have R qq = 2 � � �� − 1 − 1 arcsin 2 2 (P8) Σ y R yy Σ , y π where Σ y = diag ( R yy ) and arcsin( · ) is element-wise. The normalized covariance for unquantized y can be approximated as = π 1 − π . � � ¯ R yy 2 R qq + I (P9) 2 For the an eigenvector v of R yy with R yy v = λ v , we have � λ � π p − 1 + π 2 R qq v . = v , (P10) 2 which implies that R qq and R yy have identical signal and noise spaces 10/15 Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 10 / 15

Subspace-based 1-bit wideband spectrum sensing algorithm 1. Acquire L snapshots of 1-bit quantized data { q 1 , q 2 , . . . , q L } 2. ˆ � L l , ˆ 2 ˆ R qq ← 1 l =1 q l q H R yy ← π 1 − π � � R qq + I L 2 3. ˆ R yy = ˆ U ˆ Λ ˆ U H , where ˆ U = [ u 1 , u 2 , . . . , u N ] , and ˆ Λ = diag { λ 1 , λ 2 , . . . , λ N } with λ i ≥ λ j for i < j 4. Estimate the number of spectrum components using a Minimum Description Length(MDL) estimator 5. Partition ˆ U into [ U s U n ] 1 6. Compute pseudo-spectrum 2 for f ∈ { f 1 , f 2 , . . . , f N } n v ( f ) � 2 � U H 7. Find the N − M smallest elements in pseudo-spectrum, estimate the noise floor P noise as the mean of the N − M smallest elements γ 10 P noise ( γ = 3 dB), mark the n -th sub-band as occupied 8. If p s ( n ) > 10 11/15 Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 11 / 15

Performance Evaluation 1 0.5 0 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 ����������������������������������� 1 0.5 0 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 ���������������������������� 1 0.5 0 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 �������������������������������������� Subspace-based method has a more distinguishable floor compared to FFT-based and correlation-based method 12/15 Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 12 / 15

Time Resolution vs Detection Performances 1 0.3 3 3 0.8 0.25 3 0.2 3 0.6 0.15 0.4 0.1 0.2 0.05 0 0 10 15 20 25 30 35 40 45 50 55 60 10 15 20 25 30 35 40 45 50 55 60 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 13/15 Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 13 / 15

Performance Comparisons under Different SNR Conditions 0.3 1 0.25 False alarm probability Detection probability 0.8 0.2 0.6 0.15 0.1 0.4 0.05 0.2 0 0 -0.05 -20 -15 -10 -5 0 5 10 -20 -15 -10 -5 0 5 10 SNR in dB SNR in dB 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 14/15 Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 14 / 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 other typical sensing methods. 15/15 Junquan Deng (NUDT) 1-bit wideband spectrum sensing WCSP 2019 15 / 15