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...e objective function and its constraint are convex, we show that the optimization problem is a standard convex optimization problem which can be solved by numerous methods (e.g. interior point method =-=[19]-=-) using computer optimization tools (e.g. CVX [20]) efficiently. D. Discussion: Traffic Estimation and The Sensing Order Algorithm in Non-Stationary Traffic We assume stationary PU traffic in our syst...

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...y secondary (unlicensed) users (SUs) in both time and the frequency domains on a Dynamic Spectrum Access (DSA) basis. Thus, finding the unused PU channels becomes an important problem in DSA networks =-=[1]-=-. Vacant spectrum can be found by sensing licensed channels to determine whether PU is present or not. If the PU is present, the SU should switch, within a short time, to another PU channel and sense ...

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..., we show that the optimization problem is a standard convex optimization problem which can be solved by numerous methods (e.g. interior point method [19]) using computer optimization tools (e.g. CVX =-=[20]-=-) efficiently. D. Discussion: Traffic Estimation and The Sensing Order Algorithm in Non-Stationary Traffic We assume stationary PU traffic in our system model, which means the traffic of all channels ...

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...sign such algorithm, i.e., a sequential sensing order A for SUs to sense all PU channels, which maximizes the overall DSA network throughput on a slot basis. PU traffic is modeled as a Markov process =-=[14]-=-, [15], where s represents the current state of the PU. States s = 0 and s = 1 indicate the PU absence and presence, respectively. This traffic is characterized by the steady-state distribution and th...

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...one slot time [10], [11]. To enhance the detectability of the PU channels and to minimize the time spent on sensing, the SUs jointly sense one channel at a time via a cooperative sensing scheme [12], =-=[13]-=-. In turn, the sensing results are forwarded to a DSA base station which makes a collective decision on whether or not there is a PU present on a channel. To simplify analysis, this paper considers th...

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...echniques of estimating the PU traffic parameters were studied in, e.g., [3], [4] (and the references therein), in isolation from the channel sensing order problem. Considering channel sensing order, =-=[5]-=- was the first work to investigate this aspect (to the best of the authors’ knowledge) and introduced the concept of semi-Markov chain to model the availability of PUs (assuming perfect knowledge of t...

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...uch algorithm, i.e., a sequential sensing order A for SUs to sense all PU channels, which maximizes the overall DSA network throughput on a slot basis. PU traffic is modeled as a Markov process [14], =-=[15]-=-, where s represents the current state of the PU. States s = 0 and s = 1 indicate the PU absence and presence, respectively. This traffic is characterized by the steady-state distribution and the tran...

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...uring one slot time [10], [11]. To enhance the detectability of the PU channels and to minimize the time spent on sensing, the SUs jointly sense one channel at a time via a cooperative sensing scheme =-=[12]-=-, [13]. In turn, the sensing results are forwarded to a DSA base station which makes a collective decision on whether or not there is a PU present on a channel. To simplify analysis, this paper consid...

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...mit in their respective queues. We define the effective rate for data transmission for all channels in one slot given the next state information after sensing as the system throughput R(A) [7], [16], =-=[17]-=- R(A) = M∑ i=1 ( T −∑ij=1 T (aj)I T ) CaiI(ŝai), (1) whereas I(x) is the indicator function defined as I(x) = 1 for x = 0, and I(x) = 0, otherwise. The expected throughput E{R(A)} is defined as the a...

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... channel physical layer parameters. The problem of PU traffic parameter estimations was not considered in this work. 2 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. X, NO. X, X 201X Finally, =-=[9]-=- considered finding an optimal channel sensing order (through a constrained Markov decision process) taking collision probability between PU and DSA network into consideration. As in all above referre...

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...ri knowledge of PU traffic. This work considered maximization of the throughput for one SU to transmit in one channel while neglecting the transmission opportunities in other channels. The authors of =-=[8]-=- investigated the optimal sensing order with opportunistic transmissions by considering both adaptive and non-adaptive modulations for SUs to exploit changes in PU channel physical layer parameters. T...

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...nnel at a time [5]–[7]. The transmission structure for each PU is assumed to follow a synchronous, slotted frame within slot time T , implying the activity for the PU is constant during one slot time =-=[10]-=-, [11]. To enhance the detectability of the PU channels and to minimize the time spent on sensing, the SUs jointly sense one channel at a time via a cooperative sensing scheme [12], [13]. In turn, the...

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...t a time [5]–[7]. The transmission structure for each PU is assumed to follow a synchronous, slotted frame within slot time T , implying the activity for the PU is constant during one slot time [10], =-=[11]-=-. To enhance the detectability of the PU channels and to minimize the time spent on sensing, the SUs jointly sense one channel at a time via a cooperative sensing scheme [12], [13]. In turn, the sensi...

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...ssions accordingly when a channel is sensed to be vacant. In order to acquire the PU traffic statistics of each channel (which vary over time, making exact a priori knowledge of PU traffic impossible =-=[3]-=-), a highly accurate PU traffic estimation algorithm is needed. A. Related Work Techniques of estimating the PU traffic parameters were studied in, e.g., [3], [4] (and the references therein), in isol...

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...P̂00, which results in more accurate estimation. In addition, the RMS error achieves the CR bound as long as the number of samples is large enough, which verifies the ML estimation property stated in =-=[18]-=-. Fig. 4(b) plots the RMS error with respect to u. Note that CR bound remains a lower bound for the PU estimators. But for the estimator P̂00, the RMS error 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 2...

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...ri knowledge of PU traffic impossible [3]), a highly accurate PU traffic estimation algorithm is needed. A. Related Work Techniques of estimating the PU traffic parameters were studied in, e.g., [3], =-=[4]-=- (and the references therein), in isolation from the channel sensing order problem. Considering channel sensing order, [5] was the first work to investigate this aspect (to the best of the authors’ kn...

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...esigned PU channel selection protocol and channel sensing order scheme, i.e. the process of ordering PU channels to sense to optimize a predefined objective (throughput, delay, etc.) of a DSA network =-=[2]-=-. For instance, in a centralized DSA network, PU channel selection and sensing order scheduling can be done by the base station (or a coordinator). The DSA base station would then decide on the best s...

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...elements Ci and T (i) I , respectively, for the i-th channel ∀i ∈M. T (i)I is chosen to be less than or equal to 50 ms and Ci is less than or equal to 10 bits/s, which are reasonable values following =-=[6]-=-. Each simulation result is calculated by averaging over 104 realizations. Under perfect sensing for the current PU states, Fig. 2(a) demonstrates that as the PU slot time T increases, the DSA through...

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... transmit in their respective queues. We define the effective rate for data transmission for all channels in one slot given the next state information after sensing as the system throughput R(A) [7], =-=[16]-=-, [17] R(A) = M∑ i=1 ( T −∑ij=1 T (aj)I T ) CaiI(ŝai), (1) whereas I(x) is the indicator function defined as I(x) = 1 for x = 0, and I(x) = 0, otherwise. The expected throughput E{R(A)} is defined as...