Improved Spectrum Utilization in Cognitive Radio Systems

Transcription

1 Improved Spectrum Utilization in Cognitive Radio Systems Lei Cao and Ramanarayanan Viswanathan Department of Electrical Engineering The University of Mississippi Jan. 15, 2014 Lei Cao and Ramanarayanan Viswanathan (Department Improved Spectrum of Electrical Utilization Engineering Cognitive The University Radio Systems of Mississippi) Jan. 15, / 18

2 Outline 1. Cognitive Radio Systems (Brief) 2. Current Work in Ole Miss Divergence-based Soft Decision for Error Resilient Data Fusion 3. Other Existing and Future Research Lei Cao and Ramanarayanan Viswanathan (Department Improved Spectrum of Electrical Utilization Engineering Cognitive The University Radio Systems of Mississippi) Jan. 15, / 18

3 Cognitive Radio Systems CR: key technology for next break-through communications. 70% of allocated spectrum is sitting idle. Need adpative, multi-dimensional aware, autonomous system spectrum sharing! Presidential Memorandum Expanding America s Leadership in Wireless Innovation, June 14, 2013 Unleashing the Wireless Broadband Revolution, June 28, 2010 National Spectrum Consortium 94 Letters of Intent, Webinar today! Many research issues: Spectrum sensing, spectrum management, sharing strategies, hidden nodes, trust and security, architecture... Lei Cao and Ramanarayanan Viswanathan (Department Improved Spectrum of Electrical Utilization Engineering Cognitive The University Radio Systems of Mississippi) Jan. 15, / 18

4 Cognitive Radio Systems Research foci in Ole Miss PU traffic modeling Prediction Advanced sensing Data fusion CRs Optimization Organization QoS quaranteed sharing Relay Cooperation Anti jamming Current work: Spectrum sensing/sharing. Divergence-based Soft Decision for Error Resilient Data Fusion (IEEE TSP 10/14) Support: NASA EPSCoR Raytheon, Inc. Lei Cao and Ramanarayanan Viswanathan (Department Improved Spectrum of Electrical Utilization Engineering Cognitive The University Radio Systems of Mississippi) Jan. 15, / 18

5 Divergence-based Soft Decision for Error Resilient Data Fusion (Model) H 0 PU H 1 SU 1 SU N L1 L N Quan. Quan. su su L L N 1 BSC BSC fc fc LN L 1 FC Two types of noise: Sensing Communication between SUs and DF Channels between SUs and DF are band-limited D-bits in total Need quantizers at SUs and error resilience schemes! Lei Cao and Ramanarayanan Viswanathan (Department Improved Spectrum of Electrical Utilization Engineering Cognitive The University Radio Systems of Mississippi) Jan. 15, / 18

6 Divergence-based Soft Decision for Error Resilient Data Fusion (Objective) Design local quantizers at SUs for both information representation and error resilience t 1 t 2 t W 2 t W 1 c 1 c 2 c W 1 c W L W 2 D, thresholds and codewords. Tradeoff between information representation and error resilience Determine the Bit Error Probability (BEP) Wall BEP wall is the highest bit error rate beyond which a specific final decision performance, in terms of false alarm probability and mis-detection probability cannot be achieved even if the local sensing is ideal. Lei Cao and Ramanarayanan Viswanathan (Department Improved Spectrum of Electrical Utilization Engineering Cognitive The University Radio Systems of Mississippi) Jan. 15, / 18

7 Divergence-based Soft Decision for Error Resilient Data Fusion (PMFs) After W levels quantization P su j = [P su j (1),... P su j (W), 0,..., 0] 1 2 D where j = 1 or 0, corresponding to H 1 or H 0. Channel Transition matrix: P T = { p ij }, i, j = 1,..., 2 D, p ij = P H(v i,v j ) b (1 P b ) D H(v i,v j ) where H(v i, v j ) is the Hamming distance between v i and v j. At the FC: P fc j = [P fc j (i), i = 1,..., 2D ], and P fc j = P su j P T Lei Cao and Ramanarayanan Viswanathan (Department Improved Spectrum of Electrical Utilization Engineering Cognitive The University Radio Systems of Mississippi) Jan. 15, / 18

8 Methodology and Results (Quantization) Goal: Design quantizers (both thresholds and codewords) maximizing divergence between P fc 1 and Pfc 0. Distributional divergence: asymptotically optimal! E[f (φ(x))] where φ(x) = P 1(x) P 0 (x) Kullback-Leibler (KL)-distance: and f ( ) is convex. D(P 0 P 1 ) = i P 0 (i) log P 0(i) P 1 (i) = E 0 Chernoff metric: E 0 [ ( P 1 P 0 ) λ ] [ log P 1 P 0 ]. Lei Cao and Ramanarayanan Viswanathan (Department Improved Spectrum of Electrical Utilization Engineering Cognitive The University Radio Systems of Mississippi) Jan. 15, / 18

9 Methodology and Results (Quantization) Conjugate functions: f ( ) is convex f (v) = log v = sup w (vw f (w)), where f (w) is the conjugate function of f (v). KL-distance: when f (v) = log v f (w) = sup(wv f (v)) = 1 log( w), w < 0. v Chernoff metric: when f (v) = v λ, 0 λ < 1 f (w) = sup(wv g(v)) = v ( w λ ) 1 λ 1 (w w) λ Lei Cao and Ramanarayanan Viswanathan (Department Improved Spectrum of Electrical Utilization Engineering Cognitive The University Radio Systems of Mississippi) Jan. 15, / 18

10 Methodology and Results (Quantization) Through supremum process, we have KL-distance: [ E 0 log P ] 1 P 0 ( = sup z i >0 Where A(z i ) = log z i + 1 and B(z i ) = z i. Chernoff metric: E 0 [ ( P1 P 0 ) λ ] ( = sup z i >0 [ P0 (i)a(z i ) + P 1 (i)b(z i ) ]). (1) i [ P0 (i)c(z i ) + P 1 (i)d(z i ) ]) (2) i where C(z i ) = (λ 1)z λ i and D(z i ) = λz λ 1 i. Lei Cao and Ramanarayanan Viswanathan (Department Improved Spectrum of Electrical Utilization Engineering Cognitive The University Radio Systems of Mississippi) Jan. 15, / 18

11 Methodology and Results (Quantization) Local optimal algorithms can be developed. Two-stage-Algorithm based on KL-distance: For fixed A(z i ) and B(z i ), find P 0 (i) and P 1 (i) that increases E 0 [ log P 1 P 0 ]. For fixed P 0 (i) and P 1 (i), update A(z i ) and B(z i ) with z i = P 1(i) P 0 (i). The algorithm alternates between these two stages while updating P 0 and P 1 in each iteration, until no further improvement in divergence is obtained. Algorithm based on Chernoff metric obtained accordingly. Lei Cao and Ramanarayanan Viswanathan (Department Improved Spectrum of Electrical Utilization Engineering Cognitive The University Radio Systems of Mississippi) Jan. 15, / 18

12 Methodology and Results (Quantization) For KL-distance criterion Quantizer KL, D=3 Quantizer 0, D=3 Quantizer MOE, D=3 Quantizer KL, D=2 Quantizer KL, D=4 Quantization Thresholds KL Divergence Channel Error Probability Channel Error Probability Figure : Quantization thresholds (D = 3) and KL-distance at FC Lei Cao and Ramanarayanan Viswanathan (Department Improved Spectrum of Electrical Utilization Engineering Cognitive The University Radio Systems of Mississippi) Jan. 15, / 18

13 Methodology and Results (Quantization) For Chernoff Metric criterion 1.5 Quantization Thresholds Chernoff exponent Quantizer 0, D=4 Quantizer MOE, D=4 Quantizer Chernoff, D=4 Quantizer Chernoff, D=3 Quantizer Chernoff, D= Channel Error Probability Channel Error Probability Figure : Quantization (D = 4) and negative Chernoff metric at FC Lei Cao and Ramanarayanan Viswanathan (Department Improved Spectrum of Electrical Utilization Engineering Cognitive The University Radio Systems of Mississippi) Jan. 15, / 18

14 Methodology and Results (BEP Wall) Theorem: A quantizer design based on either KL divergence or Chernoff metric has the fundamental property that the two codewords used in the ideal sensing have Hamming distance D if the rate of transmission is limited to D bits. Furthermore, for a given (α, β), the BEP wall, P b,wall, based on this quantizer is { P b,wall = max K min { IK,ND K+1 1 (α), 1 I 1 K,ND K+1 (1 β)}} (3) where N is the number of SUs. I z,w (x) is the Incomplete Beta function defined as 1 x I z,w (x) t z 1 (1 t) w 1 dt B(z, w) 0 where (z 1)!(w 1)! B(z, w) =. (z + w 1)! Lei Cao and Ramanarayanan Viswanathan (Department Improved Spectrum of Electrical Utilization Engineering Cognitive The University Radio Systems of Mississippi) Jan. 15, / 18

15 Methodology and Results (BEP Wall) How to find the wall? Lemma: Define γ = I K,M K+1 (p), then p = IK,M K+1 1 (γ) is a monotonically increasing function with respect to K for given values of M and γ. This Lemma asserts that for a given (α, β) pair and the number of SUs and the rate limit D, the first term inside eqn. (3) increases with K while the second term decreases with K. As a result, there must exist a K 0, 1 < K 0 < ND where the highest P b,wall attains. This K 0 gives both the wall and the optimal counting rule. for α = β, K 0 = M 2 (i.e., not the majority logic rule!) Lei Cao and Ramanarayanan Viswanathan (Department Improved Spectrum of Electrical Utilization Engineering Cognitive The University Radio Systems of Mississippi) Jan. 15, / 18

16 Methodology and Results (BEP Wall) Under optimal counting rule and the majority counting rule alpha=0.05, beta= BEP wall alpha=0.05, beta=0.01 BEP wall optimal counting rule majority logic rule alpha=0.01, optimal alpha=0.1, optimal alpha=0.01, majority alpha=0.1, majority M beta Figure : (L) BEP wall for different M = ND under optimal counting rule and majority logic rule. (R) BEP wall for different (α, β) pairs under optimal counting rule and majority logic rule, M = 99. Lei Cao and Ramanarayanan Viswanathan (Department Improved Spectrum of Electrical Utilization Engineering Cognitive The University Radio Systems of Mississippi) Jan. 15, / 18

17 Conclusion and Other Work Quantizers based on divergence are obtained and BEP Wall is theoretically determined! Existing and Future Work: When observations are correlated. Results unavailable even for simple bivariate Gaussian case (Poster session) Sensing multiple spectrum holes simultaneously through compressed sensing. CS reconstruction criteria for detection purpose (being undertaken) Utilizing multiple holes among multiple SUs with different QoS requirements. Fountain codes eliminate scheduling? Lei Cao and Ramanarayanan Viswanathan (Department Improved Spectrum of Electrical Utilization Engineering Cognitive The University Radio Systems of Mississippi) Jan. 15, / 18

18 Thanks Questions? Lei Cao and Ramanarayanan Viswanathan (Department Improved Spectrum of Electrical Utilization Engineering Cognitive The University Radio Systems of Mississippi) Jan. 15, / 18