Cognitive Multi-Channel MAC Protocols with ... - Semantic Scholar

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2011 proceedings

Cognitive Multi-Channel MAC Protocols with Perfect and Imperfect Sensing David Tung Chong Wong, Shoukang Zheng and Ying-Chang Liang Institute for Infocomm Research, A*STAR, Singapore 1 Fusionopolis Way, #21-01 Connexis, Singapore, 138632 Email: {wongtc, skzheng, ycliang}@i2r.a-star.edu.sg

Abstract—Analytical formulations of the throughput of cognitive multi-channel MACs with perfect and imperfect sensing are presented. Both imperfect concurrent sensing and imperfect sequential sensing schemes are considered. A discrete time Markov chain is used to model the number of communicating node pairs in the MAC protocols. The throughput of the MAC protocol with perfect sensing is expressed as a function of the number of available data channels, the channel transmission rate, the average utilization per channel, the steady state probability of having a number of available data channels, while the throughput of the MAC protocol with imperfect sensing is expressed as a function of the number of available data channels, the channel transmission rate, the average utilization per channel, the steady state probability of having a number of available data channels, probability of false alarm and probability of misdetection. The results also clearly demonstrate the advantage of our proposed MAC protocol with imperfect concurrent sensing having low probability of misdetection but high probability of false alarm. Index Terms—MAC protocols, perfect sensing, imperfect sensing, probability of misdetection, probability of false alarm.

I. I NTRODUCTION Cognitive radio is a hot research area in recent years. IEEE 802.22 draft standard is using cognitive radio in wireless regional area network (WRAN), while IEEE 802.11af draft standard is looking at operating WiFi in TV white space. Medium access control (MAC) protocols with cognitive radio capabilities are also proposed [1],[2]. Reference [1] considers a cognitive IEEE 802.11 MAC, while reference [2] considers multiple cognitive CSMA/CA networks that can coexist together. Comparison of multi-channel MAC protocols is also studied in [3]. Reference [3] compares the throughput performance of a number of multi-channel MAC protocols, including Dedicated Control Channel, Common Hopping, Split Phase and Parallel Rendezvous protocols. However, cognitive radio is not considered. Reference [4] considers a popular scenario of a primary network and a secondary network where the primary network has priority for the usage of the spectrum band over the secondary network. Reference [5] extends multi-channel MAC protocols for opportunistic spectrum access (OSA). The design of multi-channel MAC protocols for OSA in ad hoc networks is considered in [6]. The modeling in [6] embeds the probability of detection and probability of false alarm in their transition probability, modeled by a discrete time Markov chain. These probabilities are not expressed explicitly in the analytical throughput expression. In our paper, we consider cognitive multi-channel MAC protocols using Dedicated Control Channel with perfect and

imperfect sensing. One of the channels is used as the control channel with request-to-send (RTS) and clear-to-send (CTS) messages, while the rest of the channels are used for data packet transmissions if the channel is not occupied by a primary user (PU). The activity of a PU is modeled by a two-state discrete time Markov chain. The contribution of this paper is as follows. First, a discrete time Markov chain is used to model the number of communicating node pairs in the MAC protocols with the probability that at least one channel is detected as available out of the remaining channels or remaining number of pairs of communicating nodes explicitly embedded in the transition probability. Second, the throughput of the MAC protocol with perfect sensing is expressed as a function of the number of available data channels, the channel transmission rate, the average utilization per channel, the steady state probability of having a number of available data channels, while the throughput of the MAC protocol with imperfect sensing is expressed as a function of the number of available data channels, the channel transmission rate, the average utilization per channel, the steady state probability of having a number of available data channels, probability of false alarm and probability of misdetection. Finally, the results in the numerical section demonstrated the advantage of our proposed MAC protocol with imperfect concurrent sensing having low probability of misdetection but high probability of false alarm. The rest of the paper is organized as follows. Section II describes our cognitive multi-channel MAC protocols. In Section III, we present analytical models for our proposed MAC protocols. Numerical results are presented in Section IV. Both analytical and simulation results are presented. Finally, concluding remarks are made in Section V. II. MAC PROTOCOLS We present MAC protocols with perfect and imperfect sensing. Let M denote the number of channels and MD the number of data channels available, excluding the channels used by the communicating secondary nodes and the channels detected as active. A. Perfect Sensing Multi-channel MAC transmits in a number of channels at the same time, resulting in increase in throughput. We consider a multi-channel MAC using a dedicated control channel and M − 1 data channels with a PU in each of the data channels.

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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2011 proceedings

The devices constantly monitor the control channel and keep track of idle devices, data channels and the activities of the PUs. When a device has packets to send to an idle device, it sends an RTS message for that idle device on the control channel. If the idle device hears the request-to-send (RTS) message, it replies with a clear-to-send (CTS) message. Then both sender and the receiver tune to the agreed channel to start transmission of its data message. A data message consists of a geometric number of packets. We assume that there is a genie to inform the devices on the activities of the PUs and this information is obtained instantaneously without any cost in time. Packets will not be sent in slot times occupied by PUs. Packets interrupted by an active PU will be transmitted in the same channel when the PU is inactive.

Total sensing period Reporting Period

Slot time for transmitting a data packet

Superframe of a cognitive multi-channel MAC with imperfect sensing

Fig. 1. Superframe format of a multi-channel cognitive MAC with imperfect sensing

D

0

1D

1 E

Fig. 2.

Discrete time Markov chain model of the activity of a PU a0 K

B. Imperfect concurrent sensing Each superframe consists of a total sensing period, a report period and a slot time for sending a portion of a data packet as shown in Fig. 1. When a device has packets to send to an idle device, it sends an RTS message for that idle device on the control channel, provided that the data channel is detected as available. This available channel is chosen from the first detected available channel out of all detected available channels. If the idle device hears the RTS message, it replies with a CTS message. Then both sender and the receiver tune to the agreed channel to start transmission. The packets of a message are then transmitted until all the packets are transmitted regardless of the channel conditions. Usually, both probability of misdetection and probability of false alarm are set to low values. Misdetection will cause packets to be lost, while false alarm will cause lost opportunity for packets to be sent. A low probability of misdetection is used to protect the PUs. However, a low probability of false alarm, for a fixed probability of detection, will cause the sensing time of a channel to be long. For concurrent sensing, we assume that there is a dedicated device to do sensing on each of data channels concurrently for all the data channels in the total sensing period and report the outcomes of the activities of the PUs to all other devices in the control channel during the reporting period. The total sensing time is just the time to sense one channel. That is, this dedicated device has only M − 1 detectors. On the other hand, a high probability of false alarm, at fixed probability of detection, will give a small sensing time for a channel. Thus overall throughput can be improved significantly as shown later in the numerical section. This is why we allow the packet transmissions regardless of the detected channel conditions, assuming low probability of misdetection and high probability of false alarm, to made full use of the short sensing time for a channel under such conditions. It allows packets to be transmitted when there is high false alarm probability, which will otherwise not be transmitted through missed opportunity. Packets are lost only through misdetection. C. Imperfect sequential sensing The MAC protocol of imperfect sequential sensing is the same as that using imperfect concurrent sensing, except that

1 E

a1K a12

a01

0 a00

…

1 a10

a K 1, K

a21

a K , K 1

a11

K a KK

aK1 aK 0

Fig. 3.

Discrete time Markov chain model of the number of active PUs

sensing is done sequentially for each of the data channels. The total sensing period is the sum of the sensing time in each of the data channels. That is, the dedicated device has one detector. III. ANALYTICAL MODEL A. Probability of the Number of Available Channels The activity of a primary user (PU) in a channel can be modeled by a discrete time Markov chain with the probability of becoming active from an inactive state, β, and the probability of becoming inactive from an active state, α, as shown in Fig. 2. The discrete time is in terms of one superframe time. From balance equations and the total probability equation equal to 1, the probability of a PU being in the inactive state, denoted by B0 , is given by B0 =

β , α+β

(1)

while, the probability of a PU being in the active state, denoted by B1 , is given by α , (2) B1 = α+β respectively. The discrete time Markov chain in Fig. 2 can be extended to consider the number of active PUs as shown in the discrete time Markov chain in Fig. 3. The state transition matrix of this Markov chain, denoted by A, is given by ⎡ ⎤ a00 a01 · · · a0K ⎢ a10 a11 · · · a1K ⎥ ⎢ ⎥ A=⎢ . (3) .. .. .. ⎥ , ⎣ .. . . . ⎦ aK0

aK1

···

aKK

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2011 proceedings

where aij , i,j = 0, 1, · · · , K, K = M − 1, is given by aij

=

i

 i u=0

u

β (1 − β) u

i−u

K −i αj−i+u j−i+u

·(1 − α)K−j−u I(j − i + u), where

and

 I(x) =

1, 0,

if x ≥ 0 if x < 0.

(j)

Tk (4)

(5)

A is a (K + 1) × (K + 1) matrix. From the balance equations of this discrete time Markov chain and solving the balance equations with the total probability equation equal to one, it can be derived that the probability of i active PUs, denoted by Ai , is given by [7]

i

K−i β α K Ai = , i = 0, 1, · · · , K. (6) i α+β α+β Similarly, the probability of MD inactive PUs or available channels, denoted by πCH (MD ), is given by

MD

K−MD

β α K , πCH (MD ) = MD α+β α+β MD = 0, 1, · · · , K. (7)

B. Multi-Channel MAC The following simplifications are made for all protocols. • • • •

Time is divided into small time slots with perfect synchronization at the slot boundaries. For each channel agreement, the devices can transmit only one data message. The data message length is geometrically distributed with parameter q and the mean data message length is 1/q. Every device always has messages to send to all other devices and an idle device attempts to transmit with probability p in each time slot.

These simplifications allow a Markov chain to be formed with state Xt representing the number of communicating node pairs at time t. When Xt = k, 2k devices are involved in data communications while the other (N − 2k) devices are idle, where N is the number of devices. The state space of the Markov chain, denoted by S, is bounded by the minimum of N/2 and MD . A state transition in the Markov chain happens when new agreements are made or when existing (i) (j) transfers end. Let Sk and Tk denote respectively the probability that i new agreements are made and the probability that j transfers terminate in the next slot when the state is k. An agreement is made when exactly one idle device attempts to (i) transmit an RTS message on the control channel. Then Sk (j) and Tk are respectively given by [3] ⎧ N −2k−1 , i=1 ⎨ (N − 2k)p(1 − p) (i) (1) (8) Sk = 1 − Sk , i=0 ⎩ 0, otherwise,

=

P r{j transfers terminate at time t + 1|Xt = k}

k j (9) = q (1 − q)k−j . j

(j)

Tk = 0 when j < 0. For the protocols considered in this (i) section, Sk = 0, ∀i > 1. Let pkl denote the state transition probability from state k at time t to state l at time t + 1. At most one additional pair can meet in the next slot. pkl can be rewritten as ⎧ l >k+1 ⎪ ⎪ 0,(0) (1) ⎪ ⎪ ⎪ l =k+1 ⎨ T k Sk , (k−l) (0) (k−l+1) (1) Tk Sk + T k Sk pkl = (10) ⎪ (0) (1) ⎪ ⎪ +T S 1(l, k), 0