Which Is Better for Opportunistic Spectrum Access: The ... - IEEE Xplore

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64, NO. 1, JANUARY 2015

Which Is Better for Opportunistic Spectrum Access: The Duration-Fixed or Duration-Variable MAC Frame? Jing Zhang, Member, IEEE, Fu-Chun Zheng, Senior Member, IEEE, Xi-Qi Gao, Senior Member, IEEE, and Hong-Bo Zhu

Abstract—A media access control (MAC) frame for opportunistic spectrum access (OSA), which decides the scheduling of the sensing-then-transmission time slots, has a major effect on the sensing quality, the interference to primary users (PUs) and the achievable throughput of secondary users (SUs). Considering channel handoff of SUs, there are two MAC frame structures for OSA: the duration-variable (DV) frame and the duration-fixed (DF) frame. Finding out which frame structure is better is the focus of this paper. We first formulate an improved frame structure optimization framework, with which the optimal DV and DF frames, each including a sensing slot and a transmission slot, are derived as closed forms, respectively. Then, the DV and DF frames are compared from different perspectives under the same sensing quality constraint and interference constraint (IC). It turns out that the DV frame provides slightly higher time efficiency and larger throughput for SUs than the DF frame. Simulation results confirm this theoretical analysis and show that the performance difference between both frames depends on the IC, the number of channels, and the traffic rates. In addition, the proposed optimization scheme protects PUs better than previous schemes while keeping the throughput of SUs enhanced or just reduced slightly. Index Terms—Channel handoff, frame structure comparison, interference constraint (IC), media access control (MAC) frame structure optimization, opportunistic spectrum access (OSA).

Manuscript received March 2, 2013; revised September 5, 2013 and January 6, 2014; accepted March 16, 2014. Date of publication April 18, 2014; date of current version January 13, 2015. This work was supported in part by the National Basic Research Program of China under Grant 2012CB316004; by the China High-Tech 863 Plan under Grant 2012AA01A506; by the Jiangsu 973 Project under Grant BK2011027; by the Natural Science Foundation Program of Jiangsu Province under Grant BK20130875; by the National Natural Science Foundation of China under Grant 61271236, Grant 61320106003, and Grant 61001077; by the State Postdoctoral Science Foundation Project under Grant 2012M520972; by the Postdoctoral Science Foundation Project of Jiangsu Province under Grant 1201007B and Grant 1201031C; and by the Program for Jiangsu Innovation Team. The review of this paper was coordinated by Prof. J.-M. Chung. J. Zhang is with the National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China, and also with the Key Laboratory of Wireless Communications of Jiangsu Province, Nanjing University of Posts and Telecommunications, Nanjing 210003, China (e-mail: jingzhang@ njupt.edu.cn). F.-C. Zheng and X.-Q. Gao are with the National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China (e-mail: [email protected]; [email protected]). H.-B. Zhu is with the Key Laboratory of Wireless Communications of Jiangsu Province, Nanjing University of Posts and Telecommunications, Nanjing, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2014.2318512

I. I NTRODUCTION

B

ASED on the miracle of cognitive radio, dynamic spectrum access (DSA) has emerged as a key strategy to improve the radio spectrum efficiency over the past decade [1]. Among the proposed DSA schemes, opportunistic spectrum access (OSA) is the most competitive one due to its compatibility with static spectrum allocation [2]; thus, it has become a candidate technology for Long-Term Evolution. OSA adopts a hierarchical access scheme to utilize the radio spectrum, of which the main idea is to allow unlicensed users (secondary users, SUs) to detect and exploit spatial or temporal spectrum holes while protecting licensed users (primary users, PUs) sufficiently. By reusing the licensed bands, OSA is expected to greatly improve radio spectrum efficiency. Spectrum sensing, providing an insight of spectrum occupancy for SUs to guide spectrum access, is the first key step in OSA. A practical scheme for SUs is to execute periodic spectrum sensing [3], [4]. This leads to two issues: 1) how long the sensing time should be and 2) how often spectrum sensing should be performed. From a protocol perspective, the sensing time and sensing period depend on the media access control (MAC) frame. For example, the IEEE 802.22 protocol suggests that wireless-regional-area-network users adopt a sensing-thentransmission MAC frame structure, which consists of a sensing slot and a transmission slot, to opportunistically utilize the spectrum holes in VHF/UHF TV bands [5], [6]. Channel handoff, which is dependent on spectrum sensing, is an effective mechanism for SUs to avoid collisions with PUs. However, channel handoff needs some time overhead out of the MAC frame, which results in two kinds of sensing-thentransmission frame structures: the duration-variable (DV) frame and the duration-fixed (DF) frame. The DV frame consists of a sensing slot and a transmission slot, and the handoff time is added to both slots. Thus, the frame duration depends upon performing handoff or not, as shown in Fig. 1. The DF frame also consists of a sensing slot and a transmission slot, but the handoff time is included in the transmission slot, i.e., handoff and transmission share a fixed transmission duration, as shown in Fig. 2. An immediate question is thus proposed: Which frame structure is better for OSA? This is the main motivation of this paper. As a main component of the DV and DF frames, the sensing time determines the access collisions between PUs and SUs due to imperfect spectrum sensing, namely, missed detection and false alarm. The transmission time, during which PUs cannot

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ZHANG et al.: WHICH IS BETTER FOR OSA

Fig. 1.

DV MAC frame structure.

Fig. 2.

DF MAC frame structure.

be sensed timely, determines the interference caused by the transmissions of SUs to PUs [7]. The transmission time and the sensing time together characterize the achievable throughput of SUs [6]–[8]. Intuitively, given the transmission time, a longer sensing time results in better sensing quality, thus lowering the interference to PUs, but the achievable throughput of SUs becomes smaller. On the other hand, fixing the sensing time, a longer transmission time leads to higher throughput for SUs, but the interference to PUs due to SUs’ transmissions may increase. To impartially compare the DV and DF frames, it is necessary to optimize the frame structure first under the same sensing quality constraint and interference constraint (IC). In previous literature, the optimization of MAC frame structure was usually based on the sensing–throughput tradeoff (STT) [6]–[10]. Aiming at the DF frame but ignoring channel handoff, the STT was first studied in [6], which showed that there is an optimal sensing time to maximize the throughput of SUs. Moreover, focusing on the DF frame [7] jointly optimized the sensing time and the transmission time by maximizing the time efficiency instead of the throughput of SUs under an IC. The first letter addressing the DV frame optimization is [8]. Assuming that each SU can find at least an idle handoff channel with a large probability, it optimized the channel searching time and spectrum sensing time one by one under a false-alarm constraint (FAC). Using a silence mechanism instead of channel handoff, the silence time after sensing the channel being busy and the transmission time after sensing the channel being idle were, respectively, optimized in [9]. These existing results mainly addressed the tradeoff between the sensing quality and the throughput, but they ignored the tradeoff between missed detection and false alarm. Moreover, they either set channel handoff aside or just considered one special handoff case to simplify analysis. To this end, we first analyzed the generalized channel handoff in [10], then optimized the DF frame by balancing both tradeoffs together, and finally discussed the impact of channel handoff on the MAC frame structure. However, the optimal transmission time derived in [10] may be a little too conservative for two reasons: 1) An approximation instead of the actual transmission time was used to model the interference to PUs, and 2) the sensing time was always taken on as the primary variable of the throughput function during optimization of the transmission time. In this paper, we propose a new MAC frame optimization framework for OSA. Based on the analysis of channel handoff in [10], an improved frame structure optimization model is

199

formulated first, where the sensing quality constraint is slightly relaxed, and the interference metric for PUs is more precise than [10]. Then, the sensing time and the transmission time are jointly optimized. Different from optimizing the sensing time first in [10], we first deduce the transmission time in this paper according to the interference and sensing quality constraints and then optimize the sensing time by perfecting the STT, namely, maximizing the throughput of SUs under the sensing quality constraint given the derived transmission time. The improved optimization scheme achieves a longer transmission time, thus yielding a higher throughput for SUs than in [10]. In contrast to [7]–[9], our method provides better protection for PUs while keeping the throughput of SUs unreduced, obviously, or enhanced. The ultimate contribution of this paper is to find a better frame structure for OSA under the channel handoff mechanism. To compare the DV frame and the DF frame fairly, we first optimize both frames under the same sensing quality constraint and IC with the proposed frame optimization scheme. The optimal DV and DF frames, each including a sensing time and a transmission time, are derived as closed forms. Herein, the synchronization overhead is beyond our consideration. Comparing the two derived MAC frames, we find that the DV frame achieves slightly higher time efficiency and larger throughput than the DF frame. The performance difference between them depends on the handoff overhead, the number of channels, and the traffic rates. The remainder of this paper is arranged as follows. In Section II, the OSA system model and the spectrum sensing model are depicted. In Section III, an improved MAC frame optimization scheme is formulated, with which the optimal DV frame is derived. The DF frame is optimized with the same optimization method in Section IV. The DV and DF frames are compared in Section V. Simulation results are presented in Section VI. II. S YSTEM M ODEL A. Opportunistic Spectrum Access Model Consider an OSA scenario where the PUs have the access priority but are not aware of SUs’ actions. There are N licensed channels, each with bandwidth W and indexed by i, Δ i ∈ I = {1, . . . , N }. The PUs arrive at channel i with the rate −1 λp,i s and depart from it with the rate μp,i s−1 . The arrival and departure processes follow independent Poisson distribution.

200


The primary network adopts centralized access management where a central access point (e.g., base station) assigns channels to PUs. Each channel can be used by only one PU at any time, i.e., at most N active PUs can coexist in the network. When no idle channel is available, new primary arrivals are refused directly. The SUs explore and utilize spectrum opportunities with periodic spectrum sensing and employ channel handoff to avoid collisions with PUs. Distributed sensing and access management is adopted by SUs, for which two kinds of MAC frames are optional, i.e., the DV frame and the DF frame, as shown in Figs. 1 and 2. Both frames consist of a sensing slot and a transmission slot. However, the handoff time is outside of the transmission slot in the DV frame, whereas it is inside of the transmission slot in the DF frame. Thus, the DV frame has two frame periods, i.e., T1 = τ + Td and T2 = τ + Th + Td , whereas the DF frame just has one frame period, i.e., T = τ + Tt . Assume that all SUs are equipped with the same timing synchronization system but that the timing overhead is ignored. Each SU senses all channels simultaneously with a wideband transceiver [7] or multiple sensors during the sensing slot. If the current channel is sensed idle, the SU stays at it for continued transmission during the transmission slot. Otherwise, it executes channel handoff, i.e., switches to an idle channel to transmit. If no channel is idle, the SU is blocked and waits in a buffer for the next sensing slot. The arrival and departure of SUs also follow Poisson processes, and the arrival rate and departure rate of SUs are λs,i s−1 and μs,i s−1 , respectively. To simplify the analysis, we assume that all the channels are equivalent and handle the same traffic loads, i.e., λp,i = λp,1 , μp,i = μp,1 , λs,i = λs,1 , and μs,i = μs,1 ; thus, the occupancy of each channel satisfies the identical Markov process [11]–[13].

B. Spectrum Sensing Model Denote a PU’s absence by hypothesis H0 and its presence by hypothesis H1 . Using an energy detection scheme, the detection outcome for channel i can be expressed as [8], [14] Di =

ˆ 0 : Ui = H ˆ 1 : Ui = H

2 N0 2 N0

τ 2 x (t) dt < εi 0τ i2 0 xi (t) dt ≥ εi

(1)

where Ui denotes the normalized output of the integrator in the detector, and xi (t) denotes the sensed signal. N0 is the singlesided power spectrum density of channel noise, and εi denotes the decision threshold. Assuming that x1 (t), . . . , xN (t) follows the same distribution and has the same average power under identical hypothesis, we can infer that all spectrum detectors share the same sensing quality given an identical decision threshold εi = ε. The detection probability Pd is given by [8], [14], [15] ˆ 1 | H1 ) = 1 erfc Pd = Pr(H 2

1 ε − 2m(γ + 1) √ 2 4m(2γ + 1)

.

(2)

The missed detection probability and false alarm probability are accordingly expressed as 1 ε − 2m 1 ˆ Pf = Pr(H1 | H0 ) = erfc √ √ 2 4m 2 m 1 γ (3) = erfc α + 2 2 ˆ 0 | H1 ) = 1 − P d Pm = Pr(H 1 ε − 2m(γ + 1) 1 (4) = 1 − erfc √ 2 2 4m(2γ + 1) √ √ +∞ 2 where erfc(z) = (2/ π) z e−u du, α = erfc−1 (2Pd) 2γ +1, and m = τ W is the time–bandwidth product (a sufficiently large integer). W denotes the detection bandwidth, and γ denotes the SNR sensed by SUs. A certain detection probability should be ensured even at an SNR level as low as γmin , i.e., Pd |γ=γmin ≥ P¯d , where P¯d is the detection probability threshold (DPT), and γmin is the detector sensitivity. III. D URATION -VARIABLE M EDIUM -ACCESS C ONTROL F RAME S TRUCTURE O PTIMIZATION According to the sensing outcome, the SUs may execute three operations, i.e., nonhandoff, successful handoff, and blocking, which lead to three scheduling scenarios of the DV frame, as shown in Fig. 1. The throughput achieved by each SU in three scenarios can be analyzed as follows. • PU absent: When an SU does not sense a PU present at its operational channel, it does not perform channel handoff. Now, the achievable throughput of the SU is (Td /T1 )r, T1 = τ + Td . • PU present and handoff possible: When an SU senses a PU present at its operational channel and at least one idle channel is available for handoff, it switches to an idle channel for continued transmission. Now, the achievable throughput of the SU is (Td /T2 )r, T2 = τ + Th + Td . • PU present and handoff impossible: When an SU senses a PU present at its operational channel but no idle channel is available for handoff, it is blocked. Now, the throughput of the SU is zero. Herein, r = C0 P0 (1 − Pf ) + C1 P1 Pm denotes the average channel capacity for SU: The first item represents accessing to an idle channel, and the second item represents accessing to a busy channel mistaken for idle due to missed detection. C0 = log2 (1 + SNRs ) denotes the channel capacity under the hypothesis H0 , and C1 = log2 (1 + SNRs /(1 + SNRp )) denotes the channel capacity under the hypothesis H1 , where SNRs is the target SNR of the SU, and SNRp is the interference-tonoise ratio due to PU’s transmission [16]. P0 and P1 denote the probabilities of hypotheses H0 and H1 , respectively, with P0 = μp,1 /(λp,1 + μp,1 ), and P1 = λp,1 /(λp,1 + μp,1 ) [17]. Denote the successful handoff probability and nonhandoff probability of SUs by Ph and Pn , respectively (for detailed formulas, see [10]). The average throughput of SUs using the DV frame can be thus derived as RV (τ, Td ) =

Td Td Pn r + Ph r. τ + Td τ + Th + Td

(5)


201

The average interference factor, defined as the expected fraction of the transmission time of PUs disturbed by the transmissions of SUs [7], is calculated as (see Appendix A)

I¯V = P0 e−νTd Pm + (1 − e−νTd )(1 − Pf ) + P1 Pm (6) where ν = max{λp,1 , μp,1 }. It can be inferred that Pm ≤ I¯V ≤ P0 (1 − Pf ) + P1 Pm given Pf ≤ Pd . Fixing the transmission time, the longer the sensing time is, the higher the detection probability is; thus, the interference to PUs becomes smaller. However, the achievable throughput of SUs becomes smaller as well. Fixing the sensing time, a longer transmission time brings higher throughput for SUs, but the interference to PUs becomes larger. Thus, optimizing the MAC frame structure can be turned into balancing the STT. Aiming at maximizing the throughput of SUs while protecting PUs sufficiently, we can therefore model the DV frame structure optimization problem as max τ,Td

s.t.

RV (τ, Td ) r = C0 P0 (1 − Pf ) + C1 P1 (1 − Pd ) Pm (ε, τ ) ≤ Pf (τ, ε) Pd (ε, τ ) ≥ P¯d I¯V ≤ Imax

(7)

where T˜d = ∞ when Imax ≥ P0 Pd + P1 Pm . Equation (8) shows that T˜d is an increasing function of Pd when Imax ≥ Pm . Under the constraint of Pd ≥ P¯d , the maximum transmission time satisfying I¯V ≤ Imax is thus derived as

1 P0 (2P¯d −1)

. (9) Tˆd = T˜d = 1[Imax ≥1−P¯d ] ln P¯d ν P P¯ +P (1− P¯ )−I 1

d

max

Herein, Tˆd = ∞ when Imax ≥ P0 P¯d + P1 (1 − P¯d ). From another perspective, by fixing the sensing time τ , the throughput RV (τ, Td ) is an increasing function of Td , which means the throughput reaches maximum when Td = Tˆd . Thus, (7) reduces to max τ

s.t.

RV (τ, Tˆd ) r = C0 P0 (1 − Pf ) + C1 P1 (1 − Pd ) 1 − Pd (ε, τ ) = Pf (ε, τ ) Pd (ε, τ ) ≥ P¯d .

Pn T1∗ + Ph T2∗ = τ ∗ + Td∗ + T¯h T¯ = Pn + Ph

(13)

which is also termed the average sensing period. IV. D URATION -F IXED M EDIUM ACCESS C ONTROL F RAME S TRUCTURE O PTIMIZATION

where P¯d is the DPT, and Imax is the IC, with Imax ∈ [0, 1]. As regards spectrum sensing, the higher the false-alarm probability is, the fewer the spectrum opportunities for SUs are; thus, the achievable throughput of SUs becomes smaller. As a result, under the constraint of Pm (ε, τ ) ≤ Pf (ε, τ ), when we adjust the decision threshold ε of the spectrum detector to make Pf (ε, τ ) = Pm (ε, τ ), the throughput of SUs reaches maximum. Letting Pf = Pm and consideringPm = 1 − Pd , we can deduce from I¯V ≤ Imax that (see Appendix A) P0 (2Pd −1) 1 Td ≤ T˜d = ν ln P0 Pd +P1 (1−Pd )−Imax , Imax ≥ Pm (8) 0, Imax < Pm

0 d

Theorem 1: Given P¯d and γ, the optimal DV MAC frame structure {τ ∗ , Td∗ } to maximize the throughput of SUs under the sensing quality constraint and IC is given by 2 2 erfc−1 (2 − 2P¯d ) − α0 (11) τ∗ = 2 γ W Td∗ = Tˆd (12) √ where α0 = erfc−1 (2P¯d ) 2γ + 1, and Tˆd is given by (9). Proof: See Appendix B. According to Theorem 1, the DV frame duration can be calculated as T1∗ = τ ∗ + Td∗ and T2∗ = τ ∗ + Td∗ + Th . Define the effective transmission frame as one with a nonzero transmission time. The average frame duration of an effective DV frame can be thus derived as

According to three handoff cases, i.e., nonhandoff, successful handoff, and blocking, there are three application scenarios of the DF frame, as shown in Fig. 2. Similar to the DV frame, the throughput achieved by each SU with the DF frame can be analyzed in three scenarios as follows, where r has the same definition as in Section III. • PU absent: The achievable throughput of an SU is rTt / (τ + Tt ). • PU present and handoff possible: The achievable throughput of an SU is r(Tt − Th )/(τ + Tt ). • PU present and handoff impossible: The achievable throughput of an SU becomes zero. Still denote the successful handoff probability and nonhandoff probability of SUs by Ph and Pn . The average throughput of SUs using the DF frame can be determined as RF (τ, Tt ) =

1 − Pf − Pm I¯F = P0 (1 − Pf ) + P1 Pm − Pn + Ph ×P0 Pn e−νTt + Ph e−ν(Tt −Th )

(15)

where ν = max{λp,1 , μp,1 }. It is easy to find that Pm ≤ I¯F ≤ P0 (1 − Pf ) + P1 Pm , given Pf ≤ Pd . Aiming at maximizing the throughput of SUs under the sensing quality constraint and IC, we can model the DF frame structure optimization problem as τ,Tt

s.t.

By solving (10), the optimal sensing time can be derived; then, the optimal DV frame structure is obtained as follows.

(14)

The average interference factor to PUs due to the transmissions of SUs is given by (15) (see Appendix C)

max

(10)

Tt Tt − Th Pn r + Ph r. τ + Tt τ + Tt

RF (τ, Tt ) r = C0 P0 (1 − Pf ) + C1 P1 (1 − Pd ) Pm (ε, τ ) ≤ Pf (ε, τ ) Pd (ε, τ ) ≥ P¯d I¯F ≤ Imax

(16)

where P¯d is the DPT, and Imax is the IC, with Imax ∈ [0, 1].

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TABLE I T WO MAC F RAME S TRUCTURES C OMPARISON

Similar to (7), the throughput of SUs with the DF frame, namely RF (τ, Tt ), reaches maximum when Pf (ε, τ ) = Pm (ε, τ ) under the constraint Pm (ε, τ ) ≤ Pf (ε, τ ). Letting Pf = Pm and considering Pm = 1 − Pd , we can derive (17) according to I¯F ≤ Imax as follows (see Appendix C): ⎧ Pn +Ph eνTh 1 ⎪ ⎪ ⎨ ν ln Pn +Ph P0 (2Pd −1) Tt ≤ T˜t = (17) + ln ⎪ P0 Pd +P1 (1−Pd )−Imax , Imax ≥ Pm ⎪ ⎩ 0, Imax < Pm where T˜t = ∞ when Imax ≥ P0 Pd + P1 Pm . Under the constraint of Pd ≥ P¯d , the maximum transmission time satisfying I¯F ≤ Imax is obtained as follows:

1 Pn + Ph eνTh

Tˆt = T˜t = 1[Imax ≥1−P¯d ] ln P¯d ν Pn + Ph P0 (2P¯d − 1) + ln . (18) P0 P¯d + P1 (1 − P¯d ) − Imax Since the throughput of SUs is an increasing function of Tt , as shown in(14), RF (τ, Tt ) reaches maximum when Tt = Tˆt . As a result, (16) reduces to max τ

s.t.

RF (τ, Tˆt ) r = C0 P0 (1 − Pf ) + C1 P1 (1 − Pd ) 1 − Pd (ε, τ ) = Pf (ε, τ ) Pd (ε, τ ) ≥ P¯d .

(19)

By solving (19), the optimal sensing time can be derived. Then, the optimal DF frame is given as follows. Theorem 2: Given P¯d and γ, the optimal DF MAC frame structure {τ ∗ , Tt∗ } to maximize the throughput of SUs under the sensing quality constraint and IC is given by τ∗ =

2 γ2W

Tt∗ = Tˆt

2 erfc−1 (2 − 2P¯d ) − α0

(20) (21)

V. C OMPARISON OF T WO M EDIUM ACCESS C ONTROL F RAME S TRUCTURES According to Theorems 1 and 2, the optimal DV and DF frames are compared in Table I. We can see that both frames share the same optimal sensing time given the identical P¯d and Imax , but the effective transmission time (ETT) and the achievable throughput are different. Next, we research the difference between the two frames. Lemma 1: Given Th > 0 and N > 1, the transmission time gap between the DV frame and DF frame, i.e., Pn + Ph eνTh 1 ΔTd = T¯d − Td∗ = ln ν (Pn + Ph )eν T¯h

(23)

is a positive real close to zero, i.e., ΔTd > 0 and ΔTd → 0. When Th = 0, the time gap is ΔTd = 0. Proof: See Appendix E. Based on the Lemma, we further compare the sensing period, the time efficiency and the throughput of both frames as follows. A. Sensing Period Given Th > 0, we can infer that T¯d > Td∗ due to ΔTd > 0, i.e., the DF frame provides slightly longer ETT than the DV frame. We can therefore obtain T ∗ > T¯, which means that the DF frame achieves a longer sensing period than the DV frame. However, the sensing period gap between both frames, which is equal to ΔTd , is very small due to ΔTd → 0. Thus, we can . further conclude T ∗ = T¯. B. Time Efficiency Define the time efficiency as the mean of the transmission time to frame duration ratio. Thus, the time efficiency levels of the DV frame and DF frame are, respectively, deduced as Td∗ Td∗ Pn Td∗ Ph Td∗ P + P = + n h T1∗ T2∗ τ ∗ + Td∗ τ ∗ + Th + Td∗ ∗ ∗ T T − Th (Pn + Ph )T¯d . ηf = t∗ Pn + t ∗ Ph = ∗ ¯ T T τ + Th + T¯d ηv =

(24)

√ where α0 = erfc−1 (2P¯d ) 2γ + 1, and Tˆt is given by (18). Proof: See Appendix D. Since the average handoff time is T¯h = Ph Th /(Pn + Ph )[10], the average transmission time in an effective DF transmission frame is therefore obtained as follows: 1 Pn + Ph eνTh T¯d = Tt∗ − T¯h = 1[Imax ≥1−P¯d ] ln ν (Pn + Ph )eν T¯h P0 (2P¯d − 1) + ln . (22) P0 P¯d + P1 (1 − P¯d ) − Imax

Theorem 3: Given Th > 0 and N > 1, there are ηv > ηf and ηv − ηf → 0, i.e., the DV frame makes slightly higher time efficiency than the DF frame under the same sensing quality constraint and IC. Proof: See Appendix F. Theorem 3 indicates that the DV frame makes a little more effective use of time than the DF frame.

The optimal DF frame duration, namely, the optimal sensing period, is then T ∗ = τ ∗ + T¯h + T¯d .

The achievable maximum throughput of SUs with the DV V F and Rmax , frame and that with the DF frame, denoted by Rmax

(25)

C. Achievable Maximum Throughput


203

TABLE II C OMPARISON OF THE S ENSING T IMES OF T HREE DF F RAMES

respectively, can be determined as Td∗ T∗ Pn r0 + d∗ Ph r0 = ηv r0 ∗ T1 T2 Tt∗ T ∗ − Th = ∗ Pn r0 + t ∗ Ph r0 = ηf r0 T T

V = Rmax

(26)

F Rmax

(27)

where r0 = C0 P0 (P¯d + δ), and δ = C1 P1 /C0 P0 . It is clear V F > Rmax due to ηf > ηv , i.e., the DV frame provides that Rmax a larger throughput for SUs than the DF frame. However, the throughput gap is very small due to ηv − ηf → 0. In conclusion, the DV frame provides slightly higher time efficiency and larger throughput for SUs than the DF frame with nearly equivalent sensing period. However, the performance gap between both frames is small.

Fig. 3. Transmission time of DF frame Td∗ versus IC Imax .

VI. S IMULATION R ESULTS Based on MATLAB, the performance of the DV and DF frames are compared with simulation in this section. As the premise, the proposed frame optimization scheme is compared with previous schemes as well. Note that the traffic rates for simulation correspond to the whole network in this section, e.g., λp = N λp,1 . A. Comparison of the DF Frame Optimization Schemes By letting N = 5, W = 100 kHz, λp = μp = 3 s−1 , λs = 3 s−1 , μs = 5 s−1 , Th = 10 ms, SNRs = 10 dB, and SNRp = γ = −10 dB, the new DF frame optimization scheme is compared with those proposed in [7] and [10] by checking the performance of three derived DF frames, shown in Table II and Figs. 3 and 4. Note that the optimization method in [7] is not subject to the constraint Pd ≥ P¯d directly. Table II shows the sensing times of three DF frames versus ∗ ∗ ∗ , τDF2 , and τDF3 the IC Imax and the DPT P¯d , where τDF1 denote the sensing times derived according to the optimization schemes proposed in this paper, in [10], and in [7], respectively. ∗ ∗ equals to τDF2 , which both are indepenWe can see that τDF1 ¯ dent of Imax but depend on Pd . The higher the DPC is, the ∗ ∗ ∗ and τDF2 will be. However, τDF3 shortens with longer the τDF1 Imax rising, which is because the IC inherently decides the DPC due to the constraint 1 − Pd ≤ Imax . Compared with [7], our proposed frame optimization scheme is more flexible to protect PUs by directly tracking the change of the DPT. With regard to the transmission time, the one derived accord∗ , is increasing with Imax , whereas ing to [7], denoted by Td,DF3 ∗ (namely the one newly derived in this paper, denoted by Td,DF1 T¯d ), remains zero when Imax < 1 − P¯d and then increases with Imax rising when Imax ≥ 1 − P¯d , as shown in Fig. 3.

Fig. 4. Normalized throughput Rmax /(C0 P0 ) versus IC Imax .

This is because the SUs can access to transmit just when Imax ≥ 1 − P¯d in our proposed optimization scheme, as proven in Appendix C. The similar result exists in the transmission ∗ . However, time derived according to [10], denoted by Td,DF2 ∗ ∗ dependent Td,DF2 tends to a constant after a certain point Imax ∗ ∗ on Pd , e.g., Imax = 0.11 for P¯d = 0.90 and Imax = 0.085 for P¯d = 0.93. The achievable throughput of SUs with the DF frame derived in [10] follows the same pattern, as shown in Fig. 4. ∗ ∗ = Td,DF2 when In Fig. 3, we also can find that Td,DF1 ∗ ∗ ∗ ∗ , Imax ≤ Imax and that Td,DF1 > Td,DF2 when Imax > Imax which means that the new optimization scheme provides a longer transmission time than [10] in the loose IC region. ∗ ∗ is smaller than Td,DF3 due to the new DF However, Td,DF1 frame scheme directly subject to the constraint Pd ≥ P¯d to enhance the protection for PUs. Although the gap between ∗ ∗ and Td,DF3 is obvious, the throughput gap between our Td,DF1 new scheme and [7] is small and tends to zero when Imax is large enough, as shown in Fig. 4. Compared with [10], the new frame optimization scheme provides obviously higher throughput for SUs.

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As regards the transmission time, the one derived in this ∗ , is independent of W but increasing paper, denoted by Td,DV1 ¯ with Pd , as shown in Table III. The achievable throughput of SUs with the new DV frame scheme ascends with P¯d rising first, then tends to a constant, as shown in Fig. 6. Turning to the DV frame scheme in [8], with P¯d rising, the transmission time ∗ ∗ keeps constant while the sensing time τDV2 increases; Td,DV2 thus, the throughput of SUs is decreasing with P¯d . Fig. 6 also shows that the new frame optimization scheme can provide a larger throughput for SUs than [8] in the high DPT region, e.g., RDV1 > RDV2 when P¯d > 0.94 given W = 200 kHz. Moreover, it makes the throughput and the sensing quality improved together. C. Comparison of the DV Frame and the DF Frame Fig. 5. Sensing time of DV frame τ ∗ versus detection probability constraint Pd .

Fig. 6. Normalized throughput Rmax /(C0 P0 ) versus detection probability constraint Pd .

B. Comparison of the DV Frame Optimization Schemes By letting Imax = 0.1 and varying P¯d within [0.92, 0.97], the new DV frame optimization scheme is compared with that in [8] by checking the performance of two derived DV frames, shown in Figs. 5 and 6, and in Table III. Note that [8] optimized the handoff channel searching time instead of the transmission time subject to an FAC, namely, Pf ≤ P¯f . In the simulation, we let P¯f = 0.05. We can see in Fig. 5 that the sensing time derived with our ∗ , and the one derived with the new scheme, denoted by τDV1 ∗ , are both increasing with P¯d . scheme in [8], denoted by τDV2 ∗ is more The former ascends faster than the latter, i.e., τDV1 ∗ sensitive to the change of P¯d than τDV2 , which means that our DV frame scheme can protect PUs better. Given the DPC, the larger the sensing bandwidth W is, the shorter the sensing ∗ ∗ < τDV2 , time becomes. When P¯d < 0.95, there is always τDV1 i.e., the new proposed frame optimization scheme can achieve a shorter sensing time under the same sensing quality constraint than [8] in the middle-and-low DPC region.

Letting W = 100 kHz, λp = 3 s−1 , μp = 5 s−1 , λs = μs = 5 s−1 , P¯d = 0.95, Imax = 0.06, SNRp = γ = −10 dB, SNRs = 10 dB, the differences between the DV frame and the DF frame under our proposed frame optimization scheme, are shown in Figs. 7–12. Herein, we do not compare the sensing times of both frames since they are identical in theory. Fig. 7 shows the ETT gap ΔTd between the DV frame and the DF frame versus the handoff overhead Th and the number of channels N , where ΔTd = T¯d − Td∗ . We can see that ΔTd is positive and increasing with Th given N > 1. However, there is ΔTd |N =5 > ΔTd |N =10 > ΔTd |N =1 , which implies that ΔTd is not a monotonous function of N . Although the DF frame has a slightly larger ETT when N > 1, the throughput provided by the DF frame is slightly smaller than the DV frame, as shown in Fig. 8. The normalized throughput gap, defined as F V F F = (Rmax − Rmax )/Rmax , is increasing with Th . ΔR/Rmax However, it is not a monotonic function of N , as shown in Fig. 9. When N = 1, no handoff can occur; thus, the DV frame and the DF frame provide the same throughput. Letting N = 5 and varying λp , μp within [0, 10] s−1 , the differences between the DV and DF frames versus PUs’ traffic rates are presented in Figs. 10–12. It is shown in Fig. 10 that, with λp rising, the ETT gap ΔTd between the DV and DF frames expands first, then shrinks until λp reaches a certain point λ∗p , after which ΔTd ascends slightly again then tends to a constant. It is interesting that the local valley point seems to be λ∗p = μp . Fixing λp , ΔTd expends with μp rising. The higher the μp is, the quicker the ETT gap ΔTd changes with λp when λp ≤ λ∗p , and the faster ΔTd tends to a constant when λp > λ∗p . However, ΔTd is very small relative to the transmission time, i.e., the DV frame has nearly the same ETT as the DF frame. Although the DV frame has a small disadvantage in ETT, it still provides slightly higher throughput than the DF frame, regardless of how PUs’ traffic rates change, as shown in Fig. 11. The throughput of SUs, provided by either the DV frame or the DF frame, is decreasing with λp . There V V V |μp=2/s > Rmax |μp=5/s > Rmax |μp=8/s when λp < 1s−1 , is Rmax V V V and Rmax |μp=8/s > Rmax |μp=5/s > Rmax |μp=2/s when 3 s−1 < −1 λp < 8 s , i.e., the throughput of SUs is not a monotonic function of μp . As regards the throughput gap, it follows similar going trend as the ETT gap, as shown in Fig. 12. The difference


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TABLE III C OMPARISON OF THE T RANSMISSION T IMES OF T WO DV F RAMES

Fig. 7.

Effective transmission time gap ΔTd versus handoff overhead Th .

F Fig. 9. Throughput gap ΔR/Rmax versus handoff overhead Th .

Fig. 8.

Normalized throughput Rmax /(C0 P0 ) versus handoff overhead Th .

Fig. 10. Effective transmission time gap ΔTd versus PUs’ traffic rates.

is that the throughput gap still descends, whereas the ETT gap keeps stable when λp > λ∗p . Figs. 7–12 indicate that the performance difference between the DV frame and the DF frame depend on the IC, the number of channels, and the traffic rates. VII. C ONCLUSION In the paper, we have studied the optimization of MAC frame structure for OSA under channel handoff mechanism, and compare the DV frame and DF frame to find out which one is better. An improved MAC frame optimization method

is proposed, with which the optimal DV frame and DF frame are respectively derived as closed forms under identical sensing quality constraint and IC. The derived DV frame and DF frame are compared from the perspectives of sensing period, time efficiency, and achievable throughput. Simulation results show that our proposed frame optimization scheme can provide better protection for PUs while keeping the achievable throughput of SUs improved or just reduced slightly. Under the proposed optimization framework, the DV frame achieves slightly higher time efficiency and larger throughput than the DF frame, i.e., the DV frame and DF frame have close performance. Our research provides insight into MAC frame structure versus

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of SUs, is further determined as I1 + I0 I¯V = T d · P1 = Pm (P0 e−μp,1 Td + P1 ) + P0 (1 − Pf )(1 − e−λp,1 Td ) . (30) = P0 (1−Pf )+P1 Pm −P0 (1 − Pf −Pm )e−νTd where ν = max{λp,1 , μp,1 }. It can be inferred that Pm ≤ I¯V ≤ P0 (1 − Pf ) + P1 Pm due to Pf ≤ Pd and Td ≥ 0. Let I¯V ≤ Imax ; then, we have 1 Imax −P1 Pm ˜ Td ≤ Td = ln(Pd −Pf )−ln 1−Pf − (31) ν P0 when Imax < P0 (1 − Pf ) + P1 Pm and Td ≤ T˜d = +∞ when Imax ≥ P0 (1 − Pf ) + P1 Pm . It is easy to find that Td ≤ T˜d < 0 when Imax < Pm , which is contrary to Td ≥ 0. Using T˜d = 0 for Imax < Pm , and Td can be thus expressed as 1 P0 (Pd −Pf ) ln , Imax ≥ Pm ˜ Td ≤ Td = ν P0 (1−Pf )+P1 Pm −Imax (32) 0 Imax < Pm .

Fig. 11. Achievable throughput Rmax versus PUs’ traffic rates.

Letting Pf = Pm = 1 − Pd and considering of Pm = 1 − Pd , (32) is directly turned into (8). A PPENDIX B P ROOF OF T HEOREM 1

F Fig. 12. Throughput gap ΔR/Rmax versus PUs’ traffic rates.

OSA system performance, which will benefit OSA protocol optimization. A PPENDIX A C ALCULATION OF THE I NTERFERENCE FACTOR TO P RIMARY U SERS W ITH THE D URATION -VARIABLE F RAME According to the system model, the transmission time within each DV frame duration is a fixed value Td . Thus, the average interference to PUs due to SUs’ transmissions under the hypothesis H1 and that under the hypothesis H0 can be, respectively, deduced according to [7] as

I1 = P1 (1 − Pd ) e−μp,1 Td Td + (1 − e−μp,1 Td )P1 Td = P1 Pm Td P0 e−μp,1 Td + P1 (28)

−λ T −λp,1 Td p,1 d I0 = P0 (1 − Pf ) e · 0 + (1 − e )P1 Td = P0 P1 Td (1 − Pf )(1 − e−λp,1 Td ).

(29)

The average interference factor, defined as the expected fraction of the transmission time of PUs disturbed by the transmission

According to (3) and (4), the sensing time of SUs and the decision threshold of the spectrum detector to make Pf (ε, τ ) = Pm (ε, τ ) can be derived as 2 2 erfc−1 (2 − 2Pd ) − α (33) τ= 2 γ W √ γ + 1 + 2γ + 1 √ = 2κτ W (34) ε = 2τ W 1 + 2γ + 1 √ √ where√ α = erfc−1 (2Pd ) 2γ + 1, κ = (γ + 1 + 2γ + 1)/ (1 + 2γ + 1). By substituting (34) into (3) and noting that m = τ W , the false alarm probability is rewritten as τW 1 . (35) Pf (ε, τ ) = erfc (κ − 1) 2 2 By replacing Pf in (10) with (35) and taking the first derivative of RV (τ ) with τ , we have Pn Tˆd RV (τ ) (1 − δ)(τ + Tˆd )b − r˜ = C 0 P0 (τ + Tˆd )2 Ph Tˆd + (36) 2 (1 − δ)(τ + Th + Tˆd )b − r˜ τ + Th + Tˆd where r˜ =(1−Pf)+δPf , b = (κ−1)/(2∗ τ) (τ W/2π) exp(−((κ− 1)2 τW/2)), and δ = (C1 P1)/(C0 P0). From Pd (ε, τ ) ≥ P¯d and Pf = Pm , we can deduce that τ√≥ τˆ = 2/(γ 2∗ W )(erfc−1 (2 − 2P¯d ) − α0 )2 , α0 = erfc−1 (2P¯d ) 2γ + 1. Together with m = τ W 1, which implies b → 0, and κ > 1, we can have RV (τ ) < 0. The throughput RV (τ ) is therefore a decreasing function of τ when τ ∈ [ˆ τ , +∞). As a result, the optimal sensing time to maximize the throughput of SUs is derived as 2 2 erfc−1 (2 − 2P¯d ) − α0 (37) τ ∗ = τˆ = 2 γ W


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which, together with the optimal transmission time Td∗ = Tˆd , constitutes the optimal DV MAC frame structure. A PPENDIX C C ALCULATION OF THE I NTERFERENCE FACTOR TO P RIMARY U SERS W ITH THE D URATION -F IXED F RAME According to the system model, the transmission time within a DF frame duration is Tt when no handoff occurs and Tt = Tt − Th when a handoff is successfully performed. Thus, the interference factor to PUs due to SUs’ transmissions when no handoff occurs and that after a successful channel handoff can be deduced, respectively, as I¯n = Pm (P0 e−μp,1 Tt + P1 ) + P0 (1 − Pf ) 1 − e−λp,1 Tt . = P0 (1 − Pf ) + P1 Pm − P0 (1 − Pf −Pm ) e−νTt (38) I¯h = Pm P0 e−μp,1 Tt +P1 +P0 (1−Pf ) 1−e−λp,1 Tt . (39) = P0 (1 − Pf ) + P1 Pm − P0 (1 − Pf − Pm ) e−νTt where ν = max{λp,1 , μp,1 }. The average interference factor during an effective transmission frame is therefore deduced as Pn I¯n + Ph I¯h I¯F = = P0 (1 − Pf ) + P1 Pm Pn + Ph 1 − Pf − Pm − P0 Pn e−νTt + Ph e−ν(Tt −Th ) . Pn + Ph

(40)

It can be inferred that Pm ≤ I¯F ≤ P0 (1 − Pf ) + P1 Pm due to Pf ≤ Pd and Tt ≥ 0. Let I¯F ≤ Imax ; we can obtain (41) when Imax < P0 (1−Pf )+ P1 Pm and Tt ≤ T˜t = +∞ when Imax ≥ P0 (1−Pf )+P1 Pm 1 Pn + Ph eνTh ˜ Tt ≤ Tt = ln ν Pn + Ph P0 (Pd − Pf ) + ln (41) P0 (1 − Pf ) + P1 Pm − Imax It is clear that the secondary item of T˜t is negative when Imax < Pm , which may result in Tt < 0, contrary to Tt ≥ 0. Using T˜t = 0 for Imax < Pm , Tt can be thus expressed as ⎧ Pn +Ph eνTh 1 ⎪ ⎪ ⎨ν ln Pn +Ph P0 (Pd −Pf ) Tt ≤ T˜t = , Imax ≥ Pm (42) + ln ⎪ P (1−P )+P P −I 0 1 m max f ⎪ ⎩ 0, Imax < Pm . By letting Pf = Pm and considering Pm = 1 − Pd , (42) is directly turned into (17). A PPENDIX D P ROOF OF T HEOREM 2 Replacing Pf in (19) with (35) and taking the first derivative of RF (τ ) with τ , we have RF (τ ) Pn Tˆt +Ph (Tˆt −Th ) (1−δ)(τ + Tˆt )b− r˜ = (43) C 0 P0 (τ + Tˆt )2 where r˜ =(1−Pf )+δPf , b = (κ−1)/(2∗ τ) τ W/2π exp(−((κ− 1)2 τ W/2)), δ = (C1 P1 )/(C0 P0 ), κ is given in (34). From Pd (ε, τ ≥ τˆ = 2/(γ 2∗ W ) τ ) ≥ P¯d and Pf = Pm , we can deduce that √ −1 −1 2 (erfc (2−2P¯d )− α0 ) , α0 = erfc (2P¯d ) 2γ +1. Together

with m = τ W 1, which results in b → 0 and κ > 1, we can have RF (τ ) < 0. The throughput RF (τ ) is therefore a decreasing function of τ when τ ∈ [ˆ τ , +∞). As a result, the optimal sensing time to maximize the throughput is derived as τ ∗ = τˆ =

2 2 erfc−1 (2 − 2P¯d ) − α0 γ2W

(44)

which, together with the optimal transmission time Tt∗ = Tˆt , constitutes the optimal DF MAC frame structure. A PPENDIX E P ROOF OF THE L EMMA Since T¯h = Ph Th /(Pn + Ph ), the transmission time gap between the DV frame and the DF frame is deduced as ΔTd =

Pn +Ph eνTh 1 1 −κνTh ln ln χe +κeχνTh (45) ¯h = ν T ν (Pn +Ph )e ν

where κ = Ph /(Pn + Ph ), χ = Pn /(Pn + Ph ), and κ + χ = 1. Obviously, there is ΔTd = 0 when Th = 0. In addition, if the number of channels is N = 0, the DV frame and the DF frame become the same; now, there is also ΔTd = 0. Let f (a) = χa−κ + κaχ , a = eνTh > 1. Taking the first derivative of f (a) with a, we have f (a) = κχa−κ (1 − a−1 ) > 0

(46)

which indicates that f (a) is an increasing function of a. Given Th > 0, we have f (a) > f (1) = 1; thus, there is ΔTd =

1 1 ln(χa−κ + κaχ ) = ln f (a) > 0. ν ν

(47)

Due to 0 < κχ ≤ 1/4, 0 < a−κ < 1, and 0 < 1 − a−1 1, we can infer that 0 < f (a) 1, i.e., f (a) → 0, which results in f (a) → 1; accordingly, ΔTd → 0. As a result, we can conclude that the transmission time gap tends to zero. A PPENDIX F P ROOF OF T HEOREM 3 According to (24) and (25) and considering T¯d = Td∗ + . ΔTd = Td∗ , we can have Ph Td∗ (Pn +Ph )Td∗ . Pn T ∗ − ∗ ηv −ηf = ∗ d ∗ + ∗ ∗ τ +Td τ +Th +Td τ +κTh +Td∗

(48)

where κ = Ph /(Pn +Ph ). It is clear that ηv = ηf when Th = 0. Define the function g(u) = Pn Td∗ /(τ ∗ +Td∗ )+Ph Td∗ /(τ ∗ +Td∗ + u) − (Pn + Ph ) Td∗ /(τ ∗ + Td∗ + κu), u > 0; thus, we have . ηv − ηf = g(Th ), Th > 0. Taking the first derivative of g(u) with u and considering 0 < κ < 1, we can obtain g (u) =

Ph Td∗ Ph Td∗ − >0 (τ ∗ + Td∗ + ku)2 (τ ∗ + Td∗ + u)2

(49)

which means that g(u) is an increasing function of u. Thus, we can conclude that g(Th ) > g(0) = 0, i.e., ηv > ηf . In addition, due to the fact Th Td , we can further infer according to (48) that ηv − ηf → 0.

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Jing Zhang (M’13) received the B.E. degree in telecommunication engineering and the Ph.D. degree in electrical engineering from Nanjing University of Posts and Telecommunications (NUPT), Nanjing, China, in 2003 and 2011, respectively. From 2003 to 2006, she was an Assistant with Huaiyin Institute of Technology, Huaiyin, China. In July 2011, she joined the Key Laboratory of Wireless Communications of Jiangsu Province, NUPT, as a Lecturer. She is currently doing postdoctoral research with the National Mobile Communications Research Laboratory, Southeast University, Nanjing. Her research interests include wireless communications and networks, optimization in wireless systems, cognitive radios, and adaptive resource allocation.

Fu-Chun Zheng (SM’95) received the B.Eng. and M.Eng. degrees in radio engineering from Harbin Institute of Technology, Harbin, China, in 1985 and 1988, respectively, and the Ph.D. degree in electrical engineering from the University of Edinburgh, Edinburgh, U.K., in 1992. From 1992 to 1995, he was a Postdoctoral Research Associate with the University of Bradford, Bradford, U.K. Between May 1995 and August 2007, he was with Victoria University, Melbourne, Australia, first as a Lecturer and then as an Associate Professor of mobile communications. In September 2007, he joined the University of Reading, Reading, U.K., as a Professor (Chair) of signal processing. He is currently with the State Key Laboratory of Mobile Communications, Southeast University, Nanjing, China. Over the past 15 years, he has also carried out and managed many industry-sponsored projects. He has been both a short-term Visiting Fellow and a long-term Visiting Research Fellow with British Telecom, U.K. His current research interests include signal processing for communications, multiple antenna systems, and green communications. Dr. Zheng served as the General Chair of the 2006 Spring IEEE Vehicular Technology Conference (IEEE VTC), Melbourne, Australia (http://ieeevtc.org/ vtc2006spring/), which is the first ever VTC held in the southern hemisphere. He will be the Technical Program Committee Chair for 2016 Spring VTC in Nanjing, China (the first VTC in mainland China). He served as an Editor for IEEE T RANSACTIONS ON W IRELESS C OMMUNICATIONS from 2001 to 2004. He has received two U.K. Engineering and Physical Sciences Research Council Visiting Fellowships, both hosted by the University of York, York, U.K., first from August 2002 to July 2003 and then from August 2006 to July 2007.

Xi-Qi Gao (SM’07) received the Ph.D. degree in electrical engineering from Southeast University, Nanjing, China, in 1997. In April 1992, he joined the Department of Radio Engineering, Southeast University, where he has been a Professor of information systems and communications since May 2001. From September 1999 to August 2000, he was a Visiting Scholar with the Massachusetts Institute of Technology, Cambridge, MA, USA, and Boston University, Boston, MA. From August 2007 to July 2008, he visited the Darmstadt University of Technology, Darmstadt, Germany, as a Humboldt scholar. His current research interests include broadband multicarrier communications, multiple-input–multiple-output wireless communications, channel estimation and turbo equalization, and multirate signal processing for wireless communications. Dr. Gao served as an Editor for the IEEE T RANSACTIONS ON W IRELESS C OMMUNICATIONS from 2007 to 2012 and as an Associate Editor for the IEEE T RANSACTIONS ON S IGNAL P ROCESSING from 2009 to 2013. He received the Science and Technology Awards of the State Education Ministry of China in 1998, 2006, and 2009 and the National Technological Invention Award of China and the IEEE Communications Society Stephen O. Rice Prize Paper Award in the field of communications theory in 2011.

Hong-Bo Zhu received the B.E. degree in telecommunication engineering from Nanjing College of Posts and Telecommunications, Nanjing, China, in 1982 and the Ph.D. degree in electrical engineering from the Beijing University of Posts and Telecommunications, Beijing, China, in 1998. He is currently a Professor with Jiangsu Province Key Laboratory of Wireless Communications, Nanjing University of Posts and Telecommunications, Nanjing, China. He is the Vice Chair of SG3 of ITU Radio Communication Bureau (ITU-R). He is the author and coauthor of over 200 technical papers published in various journals and conferences. His research interests include wireless communication theory and radio propagation in wireless communications.