Continuous Power Allocation for Sensing-based Spectrum Sharing. Xiaodong Wang

Transcription

1 Continuous Power Allocation for Sensing-based Spectrum Sharing Xiaodong Wang Electrical Engineering Department Columbia University, New York joint work with Z. Chen X. Zhang Y. Yılmaz Z. Guo EUSIPCO 13 Columbia University 1

2 Background - Sensing-based spectrum access Sensing slot: SU-Tx listens to all M narrowbands PU-Tx PU-Rx Transmitting slot: SU-Tx accesses the multiband w/ optimal powers 1,j 2,j h j SU-Tx g j SU-Rx Frame m T! Frame m+1 T! Sensing Data Transmission Sensing Data Transmission Columbia University 2

3 Background - Signal model The ith received signal sample by SU-Tx at channel j r i,j = { ni,j, ch. j idle, γ1,j s i,j + n i,j, ch. j busy. PU-Tx PU-Rx 2,j h j 1,j SU-Tx g j SU-Rx Columbia University 3

4 Background - Existing spectrum access methods Underlay: no sensing (τ = 0), SU-Tx has a single power level P j Opportunistic spectrum access: P 1 j = 0 PU-Tx PU-Rx Sensing-based spectrum access: SU-Tx has two power g j levels: Pj 0 > P j 1 > 0 SU-Tx SU-Rx 1,j Frame m T! 2,j h j Frame m+1 T! Sensing Data Transmission Sensing Data Transmission Columbia University 4

5 Background - Optimization max τ,θ j,{p 0 j,p 1 j } Ϝ avg. rate of SU-Tx s.t. 0 τ T, θ j 0, P 0 j 0, P 1 j 0, j, Ϝ : a feasible set of power constraints to satisfy the QoS of PU-Tx. PU-Tx PU-Rx 2,j h j 1,j Frame m Frame m+1 SU-Tx g j SU-Rx Sensing T! T! Data Transmission Sensing Data Transmission Columbia University 5

6 Continuous power allocation Let SU-Tx power be a continuous function of the sensing statistic, i.e., P (x j ), where x j = τf s i=1 Rate calculation: ( R 0 (x j ) = log P (x ) j)g j, N 0 ( R 1 (x j ) = log P (x j)g j R = T τ T M j=1 r i,j 2. ), N 0 + γ 2,j P s,j 0 [p 0,j R 0 (x j )f 0 (x j ) + p 1,j R 1 (x j )f 1 (x j )]dx j. Columbia University 6

7 SU peak Tx power constraint T τ T SU avg Tx power constraint 0 QoS constraints p 1,j h j P (x j )f 1 (x j )dx j Īj, j. T τ T M j=1 0 P (x j ) [p 0,j f 0 (x j ) + p 1,j f 1 (x j )] dx j P. Peak interference power to PU h j P (x j ) Îj, x j, j, Avg interference power to PU T τ T 0 p 1,j h j P (x j )f 1 (x j )dx j Īj, j. Columbia University 7

8 Continuous power allocation - Optimization max τ,{p (x j )} Ϝ R s.t. P (x j ) 0, 0 τ T, : a feasible set specified by a particular combination of the QoS constraints. Ϝ Lemma 1: The above problem is concave with respect to the transmit power P (x j ) under any combination of the QoS constraints. Columbia University 8

9 Continuous power allocation with quantized CSI PU-Rx employs a quantizer Q h for h, with Q h = Q h. SU-Rx employs a 2D quantizer Q g for (g, γ 2 ), with Q g = Q g. Can design Q h Q g continuous power allocation functions P l,k (x), s.t. for channel values (h, g, γ 2 ), the power is P Qh (h),q g (g,γ 2 )(x). Q h = 1 corresponds to when there is no feedback link between PU-Rx and SU-Tx, and only some statistical information of h is available at SU-Tx. PU-Tx PU-Rx 2,j h j 1,j SU-Tx g j SU-Rx Columbia University 9

10 Simulation Results Power allocation functions under avg transmit and avg interference power constraints Sensing based spectrum sharing Opportunistic spectrum access Underlay Continuous power allocation Power Allocation Received signal energy Columbia University 10

11 Simulation Results Secondary achievable rate vs. P under avg transmit and avg interference power constraints. Average Secondary Achievable Rate (bits/sec/hz) Sensing based spectrum sharing Opportunistic spectrum access Underlay Continuous (quantized CSI, Q = Q g = 4 ) Continuous (quantized CSI, Q = Q g = 8 ) Continuous (perfect CSI) h h P- / db Columbia University 11

12 Simulation Results Secondary achievable rate vs. Ī j under the peak transmit and avg interference power constraints. Average Secondary Achievable Rate (bits/sec/hz) Sensing based spectrum sharing Opportunistic spectrum access Underlay Continuous (quantized CSI, Q = Q = 4 ) Continuous (quantized CSI, Q = Q = 8 ) Continuous (perfect CSI) h g h g I j / db Columbia University 12

13 Sequential power allocation with statistical CSI PU-Tx PU-Rx 2,j h j 1,j SU-Tx g j SU-Rx PU preamble in both ways during t (0, T p ] n t,j if H 0 r t,j =, t = 1,..., T p x p t,j + n t,j if H 1 x = h j N (µ h, σ 2 h), n t,j N (0, σ 2 ) p t,j : random & observed Columbia University 13

14 Sequential Joint Detection & Estimation Sequentially decide H 0 /H 1, and estimate x when H 1 decided Use Sequential Joint Detection & Estimation (SJDE) algorithm which solves a min E[τ] s.t. c 0 P 0 (d τ = 1)+c 1 P 1 (d τ = 0)+c e E 1 [(ˆx τ x) 2 ] C τ,d τ,ˆx τ a Y. Yilmaz, G.V. Moustakides, X. Wang, Sequential Joint Detection and Estimation, SIAM Theory Probab. Appl., to appear Columbia University 14

15 SJDE algorithm Stop at time τ = min{t N : t i=1 p2 i,j γ} γ selected to maximize R satisfying P 1 (d τ = 0) P out and P(τ T p ) = 1 Estimate ˆx τ = t i=1 r i,j p i,j + µ h σ 2 t i=1 p2 i,j + σ2 σ 2 h declare only when H 1 decided Decide d τ = σ 2 h 1 if L τ c 0 c 1 +c e ˆx 2 τ 0 o.w., L τ = f 1({r t,j }) f 0 ({r t,j }) Columbia University 15

16 Power allocation using SJDE Peak Tx & Interference constraints: P j P max, h j P j Îj, j P max if d τ = 0 P j = { } min P max, Ĩj ˆx if d 2 τ = 1 τ Ĩ j selected to satisfy the PU outage probability constraint can be easily extended to cooperative multi-su case Columbia University 16

17 Simulation Results Average SU Achievable Rate (bits/sec/hz) Underlay Opportunistic SJDE Pmax (db) Columbia University 17

18 Simulation Results Average SU Achievable Rate (bits/sec/hz) Underlay Opportunistic SJDE PU Outage Probability Columbia University 18