Báo cáo hóa học: " Research Article Distributed Cooperation among Cognitive Radios with Complete and Incomplete Information"

Báo cáo hóa học: " Research Article Distributed Cooperation among Cognitive Radios with Complete and Incomplete Information"

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This paper proposes that secondary users are allowed to use the radio spectrum allocated to licensed users, as long as they agree on the primary user by with is by since the option is and knowledge of channel state In we consider two where the users in the scenario have complete or (CCC) where users share this games. We analyze the of the proposed games, and we evaluate the outputs in terms of quality perceived by both primary and secondary users, showing that for cognitive radios is a promising defined as a radio able to utilize available side or its signals with those of the which can be exploited by secondary users (SUs) to the receivers of the primary users in the same frequency channel as long as the SUs somehow aid the PUs, for example, by means of a scenario the SUs may decide to assign part of their power to their own secondary and power to relay the PUs at the PUs receivers that is has often been realized by making use of game where SUs are modeled as the players of a in the (e.g. power, frequency channel, etc.) represent that can be taken by the players, and a function of, SINR or the is the utility of the game [3, 4]. the game utility function an incentive to at the PUs receiver, but not a PUs receivers are passive or where SUs and PUs (overlay approach) can reduce at the PUs as long as the SUs cooperate with the PUs by the proposed system, decisions about the other SUs, since the PUs are we define two games to model channel and power for cognitive radios, underlay and can be as exact potential games compare the overlay to the underlay scheme to among SUs; that is, the wireless channel channel (CCC) where the SUs can share the about their wireless channel gains. we propose a Bayesian Potential Game (BPG), power and channel for SUs reduces of PUs and SUs, and among SUs improves both PUs and SUs and that the primary receivers with nearby SUs. The outline of 3 presents the game theoretic model for and overlay games with complete (Section 3.1) and M PUs pairs, and N SUs pairs (Figure 1). the power levels of the PUs’ the SUs’ as pSj , j = 1, . SUs, both and are randomly and The of the PUs. In this paper we consider and SU selects the frequency channel and the PUs. On the other hand, based on the overlay selecting the power and the the SUs devote part of their power for relaying the primary power level pS′′j , j = 1, . j scheme used by the SUs is shown in Figure 2. Figure 2: relaying scheme for secondary of the SUs. In addition, we consider two the D&F case the user) decodes the primary signal, it, PUs to be aware of the presence and identity of SUs. It and outage of both PUs and SUs. As for PU’s i and a PU’s receiver j, with hPSi j the link a PU’s i and an SU’s receiver j, with hSPi j the link gain between a SU’s i and a PU’s an SU’s receiver so that only one PU is active per frequency in a frequency channel ci is given by j the SINR for the SUs is given by j h In the first case, the of the primary signal f ′ decode the primary signal to relay it. SINR of the primary signal, from PU j at SU i, we use ĥ ji and ĥki to denote the channel gains to the SU If γPSi > ρ, then the SU may relay the primary PU and SUs may transmit (i.e., to j h j h the underlay approach, part of the SU power to at the receiver power). j h signal at SU j is given by k j f i j i j + k j f I j = k j f i j + k j f As for the D&F case, the SINR of the PU will the SINR of the SUs is given by power relay and terms are not supposed to add paper we model joint channel and in a cognitive radio scenario as the output of a the players are the N SUs, the are the choice of the power and of the frequency causes to the PUs and SUs in the same frequency channel, (2) the SU receives from the SUs the PUs and SUs, they need in the scenario share their that the decisions of the SUs are made with and assuming that the decisions of the SUs are made two games modeling the underlay and the overlay games, for An Exact Potential Game Underlay Games with Complete the finite set of players (i.e., the N SUs), and Si is the set of si with player i. set of utility functions that the players associate with their For each player i in game Γ, the utility is a function of si, the strategy selected by player i and power and channel selection problem of the SUs from and overlay and we formulate them as Exact Potential Game. The underlay game is defined as (i) N is the finite set of players, that is, the SUs. (ii) The for player i ∈ N are (b) a channel ci in the set of channels C = (iii) The utility of each player i is defined as j f i j f is causing to the PUs and SUs operating in received by player i from the SUs term only depends on the strategy selected by Game. The overlay game is defined as N is the finite set of players, that is, the SUs. (ii) The for player i ∈ N are its own in the set of power the power level pS (d) a channel ci in the set of channels C si = (pSi , pS′i , pS′′i , ci, sli) ∈ Si. We define S = (iii) The utility of each player i is defined as j f j h i j f j=1 i j by the PUs and by the other SUs in ci from player In case of SUs, p player i by the SUs active in channel ci and in the same than the other terms of the utility realized by the SUs. This term is defined SUs to cooperate with PUs in exchange for that the term f ′′(γPSi > ρ) For the A&F scheme, the relay always the term f ′′(γPSi > ρ) is always 1. them is the class of Exact Potential Games. A game Γ = {N , {Si}i∈N , {ui}i∈N} is an Exact Potential game if Γ. is an exact potential function of the game Γ, and s∗ ∈ then s∗ is a Nash of the game. the initial condition of the game, as long as only one we can define two exact potential Underlay game Potential j f i j f (ii) Overlay game Potential j f j h i j f j=1 i j f The proof that the underlay and overlay potential functions defined in (17) and (18), are games is given in the Bayesian Potential Game Underlay Games with a CCC where SUs share their model joint channel and power cognitive radios with as of a Bayesian Potential two games of the one of these games is defined as Γ = (i) N is the finite set of players, that is, the SUs, and players (i.e., the for every i ∈ N , Si is the set of in Section 3.1.1 and for the overlay game in (iii) a game of with respect to a game of complete is the player’s utility function, his belief player’s utility and so the wireless channel gains of player i. tion (PDF) on H defining the wireless channel gain (v) for every i ∈ N , ui : S×H → R is the utility utility functions for player i, for the underlay games with are very player i’s chosen strategy si ∈ Si and other (s−i), they are functions of player i’s gains ηi ∈ Hi and other SUs and PUs’ for the underlay game with si, j f i j f and for the overlay game with j f j h i j f j=1 i j f games with utility functions defined in (19) and (20) Potential games, if the following Potential for the underlay (21) and overlay (22) games si, j f i j f si, j f j h i j f j=1 i j channel gain 3: Wireless channel gain PMF derived by channel gain PDF. As for the game with complete we need to In a Bayesian game, is a Nash of a Bayesian game. si, have shown to always converge to a Nash that for the Bayesian Potential game Γ there exists a respect to the strategy space, the set of power levels PS = Each channel M = 4 PUs pairs, one pair for each frequency channel, 4: of SUs power of a PU is In order to define the PDF of the wireless mass function (PMF) of the wireless of the proposed joint power and algorithm for underlay and overlay in game for the case ofN = 8 SUs in the scenario, and D&F relay the overlay game, which is split in two parts, the first one one to relaying the primary action updates of the underlay game is not shown are very similar to those of the overlay with (BPG) to the Game with complete in terms of SINR for both PUs and overlay taking as a reference the D&F mode and the case, since 5: of SUs power devoted to Figure 6: of SUs pairs power and the overlay as a function of the the overlay paradigm the underlay scheme in PU receiver, which are very critical for the underlay the message relayed by the SU is received with a Figure 9 compares SINR results for both PUs and SUs. It can be observed again that the overlay PUs but reduces the SUs which is the both the overlay and underlay games provide the PUs game with and b = 0.001 for the underlay game with user, user, user, 7: SINR results: Bayesian Potential game with versus Exact Potential game with complete for PUs and 8: PUs Outage for overlay and underlay from Figure 10 that even if the PUs results in terms of outage are the SUs are on the PUs, also the SUs are benefited by power levels, as long as they devote a part of it for game. D&F and A&F relay modes, for the overlay game user, user, user, 9: SINR results: overlay versus underlay, for PUs and user, BPG (b = user, BPG (b = 10: SINR results for SUs different values of versus overlay, when the outage of PUs is of the primary message at the SUs’ receivers are D&F relaying approach provides better than the that the SUs are able to cooperate with the PUs. the A&F approach provides 11: of D&F and A&F outage this paper we have potential games to channel and power for and about the wireless channel gains is taken into account and both D&F and A&F relay options of where SUs are allowed to use licensed channels as to a scheme where between SUs and PUs by means of two Potential games, which are of where SUs of the wireless channel gains of the other PUs and the underlay and overlay schemes have been modeled by means of Bayesian potential games to a pure that benefits both PUs and SUs and that the We prove that the game with the utility function defined in (20) and the potential function defined in (22) is a Bayesian potential =W(si, j f Z(S,H) = Z(si, j f X(S,H) = X(si, h i j f Y(S,H) = Y(si, first term W(si, can be rewritten in the si, j f j=1 k j f j=1 i j f j=1 k j f The second term Z(si, can be rewritten as si, j f j=1 k j f j=1 i j f j=1 k j f si, h i j f j h k j f j h i j f j h k j f j h i j f j h k j f si, h i j Y(si, can be rewritten as si, hi j f j=1 i hi j f j h i j f si, = u(si, a result, if player i changes its strategy from si to si, u(si, order to prove that the underlay game is also an game, we define pSi ≡ game matches that of the underlay game in gridlock with cognitive radios: an power control and channel in cognitive Theory in Networks (GameComm ’07), [5] J. [6] with multiple parallel relays,” IEEE on [11] J.