Overlay Systems. Results around Improved Scheme Transmission for Achievable Rates. Outer Bound. Transmission Strategy Pieces

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1 Cooperation at T EE36: Lecture 3 Outline Capacity of Cognitive adios Announcements Progress reports due Feb. 9 at midnight Overview Achievable rates in Cognitive adios Better achievable scheme and upper bounds MIMO cognitive radio capacity BC with cognitive relays Summary Overlay Systems Cognitive user has knowledge of other user s message and/or encoding strategy Used to help noncognitive transmission Used to presubtract noncognitive Transmission Strategy Pieces esults around 7 Cooperation at T ate splitting Precoding against at T Precoding against at T To allow each receiver to decode part of the other node s message reduces emoves the at the To help in sending s message to its Must optimally combine these approaches Achievable ates in Cognitive adios by Devroye, Mitran, Tarokh 4 a Wu et.al. Joviċić et.al. weak strong For Gaussian channel with P =P b M.,Y.,K ew encoding scheme uses same techniques as previous work: rate splitting, G-P precoding against and cooperation Differences: More general scheme than the one that suffices in weak Different binning than the one proposed by [Devroye et.al] and [Jiang et.al.] Improved Scheme Transmission for Achievable ates The uses single-user encoder W W ate split W The uses Wc W a (. P - ate-splitting to allow receiver to decode part of cognitive user s message and thus reduce at that receiver - Precoding while treating the codebook for user as to improve rate to its own receiver - Cooperation to increase rate to receiver (. P Uc U c P (. u Ua Uc c U, U c a Outer Bound The set of rate triples (,, satisfying V; Y U ; Y U, V U ; Y U, V for input distributions that factor as p u u v u, u x v, u x v, u, u, ( x For =, U =Ø, and by redefining as : outer bound for the IC with full cooperation

2 s Outer Bound: Full Cooperation The set of rate triples (,, satisfying V, U ; Y min I ( V, U; Y U ; Y U, V I( U ; Y U, V for input distributions that factor as u u v u, u x u x u, u The exact same form as the air-el Gamal outer bound on the broadcast channel capacity The difference is in the factorization of the input distribution reflecting the fact that only one-way cooperation is possible Summary of new technique Outer bound Follows from standard approach: invoke Fano s inequality educes to outer bound for full cooperation for = Has to be evaluated for specific channels Achievable rates: combine rate splitting precoding against at encoder cooperation at encoder How far are the achievable rates from the outer bound? Capacity for other regimes? Performance Gains from Cognitive Encoding Cognitive MIMO etworks C T C C broadcast bound outer bound this scheme DMT schemes Coexistence conditions: oncognitive user unaware of secondary users Cognitive user doesn t impact rate of noncognitive user Encoding rule for the cognitive encoder: Generates codeword for primary user message Generates codeword for its message using dirty paper coding Two codewords superimposed to form final codeword C T C C Achievable rates ( users For MISO secondary users, beamforming is optimal Maximum achievable rate obtained by solving MIMO cognitive users ( Users Propose two (suboptimal cognitive strategies D-SVD Precode based on SVD of cognitive user s channel Closed-form relationship between primary/secondary user rates P-SVD Project cognitive user s channel onto null space between C T and C, then perform SVD on projection 5, g.374 5, g p 5, g.77 5, g.77

3 Multi-user Cognitive MIMO etworks Other Overlay Systems Extend analysis to multiple primary users Assume each transmitter broadcasts to multiple users Primary receivers have one antenna Secondary users are MISO. Main esult: With appropriate power allocation among primary receivers, the secondary users achieve their maximum possible rate. Cognitive relays Cognitive elay Cognitive BSs Cognitive elay Cognitive MIMO network with multiple primary users Achievable rates with two primary users Broadcast Channel with Cognitive elays (BC Channel Model Cognitive elay data Source Cognitive elay Enhance capacity via cognitive relays Cognitive relays overhear the source messages Cognitive relays then cooperate with the transmitter in the transmission of the source messages Sender (Base Station wishes to send two independent messages to two receivers Messages uniformly generated Each cognitive relay knows only one of the messages to send Coding Scheme for the BC Achievable ate egion Joint probability distribution u u v u v u w, w v, v, u, u x v, u x v, u x w, w, v, v, u, u Achievable rate region: all rates ( +, + s.t. Each message split into two parts: common and private Cognitive relays cooperate with the base station to transmit the respective common messages Each private message encoded with two layers Inner layer exposed to the respective relay Outer layer pre-codes for (GGP coding L I(W ; V V,U,U, L U, V,W ; Y U, L V,W,U ; Y U, L I(W ; V V,U,U, L U, V,W ; Y U, L V,W,U ; Y U, L V,W ; Y U,U, L V,W ; Y U,U, L U, V,W,U ; Y, L U, V,W,U ; Y. L L (I(W ; V V,U,U W ; V V,U,U W ;W V, V,U,U, 3

4 Generality of the esult Without the cognitive relays BC reduces to a generic BC Correspondingly, rate region reduces to Marton s region for the BC (best region to date for the BCs Without the base station BC reduces to an IC Correspondingly, rate region reduces to the Han- Kobayashi egion for the IC (best region for ICs Improved obustness Without cognitive relays When base station is gone, the entire transmission is dead With cognitive relays When base station is gone, cognitive relays can pick up the role of base station, and the ongoing transmission continues Cognitive relays and the receivers form an channel Source data A umerical Example Special Gaussian configuration with a single cognitive relay, A umerical Example o existing rate region can be specialized to this region for the example except [Sridharan et al 8] This rate region also demonstrates strict improvement over one of the best known region for the cognitive radio channel ([Jiang-in 8] and [Maric et al 8] ate region for this special case (obtained from region for BC log ( P log ( ( b P, P log (. ( P Channel parameters: a =.5, b =.5; P = 6, P = 6; Overlay Challenges Complexity of transmission and detection Obtaining information about channel, other user s messages, etc. Full-duplex vs. half duplex Synchronization And many more Summary Cognition can substantially increase capacity Can be applied to many types of systems Capacity of cognitive channels uses all tricks from broadcast, MAC, channels Many idealized assumptions used in obtaining capacity Very interesting to reduce these ideas to practice 4

5 Decentralized Cognitive MAC for Opportunistic Spectrum Access in Ad- Hoc etworks: A POMDP Framework Authors: Qing Zhao, Lang Tong, Anathram Swami, and Yunxia Chen Presented by: Kun Yi 5