# Voice Service Support over Cognitive Radio Networks

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3 ,, -, -,2 -Ps,T a - - 2, T -P - s a 2,T a + 2,T a +2 3,2T a - 2,2T a - - n-,t i n-,t i + n-,t b -T a n-,t j - n,t j - n,t j+ n,t b - Fig 2 The state transition diagram the channel sensing error exists) Without loss of generality, we assume that one time slot is used to transmit one voice packet Let T s denote the time of one slot For presentation simplicity, we set T s = Denote the voice packet inter-arrival time and the voice packet delay bound as T a and T b (both in the unit of time slot), respectively We arbitrarily choose a secondary voice user as the tagged user Define state (n, t), where n is the number of voice packets in the queue of the tagged user, and t is queueing delay (in the unit of time slot) experienced by the voice packet that is at the head of the queue of the tagged user The initial state is (,), indicating that there is no voice packet at the tagged user As constant rate voice traffic is considered, after a certain time period (no more than the voice packet inter-arrival time T a), the first voice packet will arrive at the tagged user Therefore, the state will move to (,) with probability Since then, after each time slot, the state will evolve, moving to another state The state transition process is modeled by a discretetime Markov chain, shown in Fig 2 To describe this Markov chain, we use state (i, t k ) (i > ) as an example When t k < i T a, its next state is (i, t k + ) if the tagged user does not successfully transmit a voice packet in the current slot, (i, t k T a + ) if the tagged user successfully transmits a voice packet in the current slot Note that since voice traffic has a constant rate, the voice packet inter-arrival time T a is a fixed value For any two consecutive packets in the queue, the difference of their queuing delay (ie, the waiting time in the queue, not including the time in packet transmission) equals to T a When t k = i T a, its next state is (i +, t k + ) if the tagged user does not successfully transmit a voice packet in the current slot, (i, t k T a +) if the tagged user successfully transmits a voice packet in the current slot This is because when the delay of the packet at the head of queue equals to i T a, a new voice packet will arrive after one time slot Let denote the probability that the tagged secondary user - successfully transmits a voice packet in a randomly chosen time slot, given that the tagged user has packets to send, and P(n, t n, t ) denote the transition probability from state (n, t ) to state (n, t ) In the Markov chain, the one-step transition probabilities are P(,, ) = P(, t j +, t j ) =, t j < T a P(,, t j ) =, t j < T a P(2, t j +, t j ) =, t j = T a P(,, t j ) =, t j = T a P(i, t j + i, t j ) =, t j < it a, i 2 () P(i, t j + T a i, t j ) =, t j < it a, i 2 P(i +, t j + i, t j ) =, t j = it a, i 2 P(i, t j + T a i, t j ) =, t j = it a, i 2 P(i, T b T a i, T b ) =, if T b < it a P(i, T b T a i, T b ) =, if T b = it a Given all the one-step transition probabilities of the Markov chain listed in (), the steady state probability vector of the Markov chain can be obtained Denote π(i, t j ) as the steady state probability of state (i, t j ) Next, we derive for the two proposed cognitive medium access schemes The voice packet arrival rate of each secondary user is T a packets per slot The voice packet service rate of each secondary user is denoted as µ packets per slot Thus, the queue utilization of the secondary user is given by ρ = T a µ As aforementioned in Section II, at each time slot, a primary user will not use the channel with probability P i Thus, the probability that the channel is available for the secondary user to access P p idle = (P i) Np, where N p is the total number of primary users For the contention-based medium access, is given by = P p idle ( k )ρ (Ns ) (2) k= where N s is the total number of secondary users, and is the contention window size of the secondary users The term in the summation indicates the probability that the tagged user chooses a backoff timer value k, and other active secondary users (ie, the users whose queues are not empty) choose backoff timer values larger than k For the contention-free medium access, is given by N s = P p idle ( ρ) i (3) N s i= where the term in the summation indicates the probability that for a randomly chosen slot, the tagged user has mini-slot index i, and all other secondary users with mini-slot index smaller than i have no packet to transmit To determine ρ, we need to characterize the average service time of a voice packet Given that the voice packet at the µ head of the queue has already waited t j slots, the average time (in the unit of slot) needed to serve this packet T s(t j ), ie, the

4 time to let the packet leave the queue (either due to successful transmission or due to packet dropping), is given by T s(t j ) = T b t j k= ( ) k k+( ) T b t j (T b t j ) (4) The average service time of a voice packet µ µ = t j = π(m(t j), t j ) T s(t j ) t j = π(m(t j), t j ) is derived as where m(t j ) is the corresponding number of voice packets in the queue, given that the queueing delay of the voice packet at the head of the queue is t j With a constant voice packet arrival rate T a, it is straightforward to have tj + m(t j ) = T a Given equations (), (4), and (), along with equation (2) or (3), can be solved numerically for the two proposed cognitive medium access schemes The steady state probability vector for the Markov chain can further be obtained Let P drop denote the voice packet dropping probability P drop can be expressed as P drop = () t j = π(m(t j), t j ) ( ) T b t j t j = π(m(t (6) j), t j ) Note that P drop is a function of N s, denoted by P drop (N s) In order to guarantee the QoS of voice traffic, P drop (N s) should not exceed the voice packet dropping rate bound P l Thus, the capacity for voice service of secondary users is the maximum integer N s (denoted by N s ) satisfying P drop (N s) P l B Average overhead In addition to voice service capacity, the other important performance metric of the proposed cognitive medium access is the average overhead, which is measured as the average number of mini-slots needed in each slot before a successful transmission Let O c and O f denote the average overhead of the contention-based and the contention-free medium access schemes, respectively We have N s ( Ns ) ( O c = ρ i ( ρ) Ns i i i ( j ) )i j, i= j= where the term ( N s i ) ρi ( ρ) Ns i indicates the probability that out of N s, i secondary users are active in a random slot, and the term in the second summation indicates that j mini-slots are needed before a successful transmission when an active secondary user chooses a backoff timer value j, and other active secondary users choose backoff timer values larger than j For the contention-free medium access, we have O f = Ns i= ρ ( ρ)i i Ns, i= ρ ( ρ)i where the denominator is the probability of a successful transmission in a randomly chosen slot, and the term in the summation in the numerator indicates that the number of minislots needed before a successful transmission is i when all the The cognitive voice capacity 3 2 Contention, Analysis Contention, Simulation Contention free, Analysis Contention free, Simulation Fig 3 The cognitive voice capacity with P i = 9% secondary users with mini-slot index smaller than i have no packet to send, and the secondary user with mini-slot index i has packet to send V NUMERICAL RESULTS AND DISCUSSIONS We validate our analytical results by simulations using Matlab The simulation for each run consists of time slots Without loss of generality, we choose T a = 4 and T b = 4 The voice packet dropping rate bound P l is set as % We vary the other parameters such as N p, P i, and to investigate their impact on the voice service capacity A Voice Service Capacity First, we fix the value of P i as 9% and the contention window size as 4 mini-slots, and vary the number N p of primary users in the system The cognitive voice service capacity (ie, the maximum number N s of secondary voice users that can be supported with QoS guarantee) is calculated by using the proposed analytical model The analytical results are shown in Fig 3 It can be seen that when the number of primary users increases, the capacity of secondary voice users decreases due to the reduced available channel resources The capacity of the contention-free medium access is larger than that of the contention-based medium access The reason is that the contention-free medium access utilizes the channel more efficiently than the contention-based medium access by eliminating collisions, resulting in a larger capacity The simulation results are also shown in Fig 3 In the simulation, if a voice packet cannot be delivered within the delay bound T b, it will be dropped Voice capacity is obtained as the maximum number of voice users such that the voice packet dropping rate is less than P l As shown in Fig 3, the simulation results match well with the analytical results in all cases Next, we change P i from 9% to 92%, the corresponding capacities of the two proposed medium access schemes are shown in Fig 4 It is obvious that with a lower P i, fewer channel resources are left for the secondary users, leading to a smaller capacity Again, the simulation results conform to the analytical results For the contention-based medium access, the choice of also has impact on the capacity Fig compares the capacity

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