Joint Design for Opportunistic Spectrum Access with Multi-Channel Sensing

Consider a spectrum of N orthogonal channels licensed to a slotted primary network. Let Sn(t) ∈ {0 (busy), 1 (idle)} denote the occupancy of channel n in slot t. We assume that the spectrum occupancy S(t) ∆ = [S1(t), . . . , SN(t)] follows a discrete-time homogeneous Markov process with finite state space S ∆ = {0, 1} and known transition probabilities {Ps,s′}s,s′∈S, where Ps,s′ ∆ = Pr{S(t+ 1) = s |S(t) = s} is the probability that the spectrum occupancy state transits from s ∈ S to s ∈ S. We assume that the transition probabilities remain unchanged for T slots. We consider a secondary ad hoc network whose users independently and selfishly search for and exploit instantaneous spectrum opportunities in these N channels. Specifically, at the beginning of slot t, a secondary user with data to transmit 1) chooses a set A(t) ∈ A s ∆ = {A : A ⊂ {1, . . . , N}, |A| = L} of channels to sense; 2) chooses an operating point E(t) ∈ A δ (A(t)) for the spectrum sensor 1, which is used to detect the occupancy states SA(t) = {Sn(t)}n∈A(t) of the chosen channels A(t); 3) based on the sensing outcomes ΘA(t) ∆ = {Θn(t)}n∈A(t) ∈ {0 (busy), 1 (idle)}, decides whether to access each sensed channel ΦA(t) ∆ = {Φn(t)}n∈A(t) ∈ {0 (no access), 1 (access)}. At the end of the slot, every successful transmission is acknowledged: KA(t) ∆ = {Kn(t)}n∈A(t) ∈ {0 (not successful), 1 (successful)}. We assume that the acknowledgement is error-free and that secondary users do not collide with each other. That is, acknowledgement Kn(t) = 1 is received if and only if the secondary user accesses an idle channel, i.e., Kn(t) = Sn(t)Φn(t). Our goal is to design an OSA strategy for secondary users, which sequentially specifies which channels in the spectrum to sense, which spectrum sensor to use, and which sensed channels to access.