Improving the Cognitive Access Efficiency by Non-Uniform Bandwidth Allocation

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Improving the Cognitive Access Efficiency by

Non-Uniform Bandwidth Allocation

Song Huang, Anthony Ephremides and Di Yuan

Linköping University Post Print

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Song Huang, Anthony Ephremides and Di Yuan, Improving the Cognitive Access Efficiency

by Non-Uniform Bandwidth Allocation, 2015, IEEE Transactions on Wireless

Communications, (14), 11, 6435-6447.

http://dx.doi.org/10.1109/TWC.2015.2453420

Postprint available at: Linköping University Electronic Press

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SUBMITTED TO IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 1

Improving the Cognitive Access Efﬁciency by

Non-uniform Bandwidth Allocation

Song Huang, Member, IEEE, Anthony Ephremides, Life Fellow, IEEE, and Di Yuan, Senior Member, IEEE

Abstract—In cognitive communication, dynamic sensing and

opportunistic access enable secondary users to recognize and utilize the white spaces of the licensed bandwidth. Most present efforts focus on designing smarter channel sensing and access algorithms for secondary users, with the aim of optimizing the overall throughput and bandwidth utilization efficiency, under the condition of not interfering with primary users’ communication. However, as the transmissions of the primary users are inherently random and unpredictable, sensing and sharing spectrum with the primary users inevitably make the cognitive process of the secondary users complex and ineffective. In this paper, a non-uniform bandwidth allocation scheme is proposed that regularizes the primary users’ bandwidth occupancy pattern. The regularization is not designed to reshape the primary users’s traffic, but to improve the sensing efficiency and throughput of the secondary users by optimizing the spectrum allocation. After the description of the new allocation scheme, we demonstrate its performance by theoretic analysis. Then we verify the validity of the non-uniform scheme with numerical simulations under non-fading and fading situations respectively. Through comparisons with the conventional uniform bandwidth allocation scheme, the non-uniform one shows higher sensing efficiency and better spectrum utilization due to lower sensing cost and reduced bandwidth loss.

Index Terms—Cognitive communication, non-uniform

band-width allocation, sensing efﬁciency.

I. INTRODUCTION

C

OGNITIVE radio techniques [1] [2] provide the

capa-bility to share the spectrum in an opportunistic manner. Dynamic spectrum access techniques [3] enable the secondary users (SUs) to determine which portions of the spectrum are available and detect the presence of primary users (PUs). In addition, SUs can select an available channel and access this channel with other SUs, and vacate the channel when a PU is detected [4]. As PUs can claim their frequency bands anytime, in order to prevent interference to and from PUs, the SUs should be able to identify the presence of PUs as quickly as possible and vacate the band immediately. To that end, each SU has to be sufﬁciently intelligent during the spectrum sharing process. Most existing techniques in the literature concentrate on improving the smartness and ﬂexibility of the

S. Huang is with the School of Computer Science and Engineering, South China University of Technology (SCUT), GZ, China 510641 (e-mail: crshuang@scut.edu.cn).

A. Ephremides is with the Department of Electrical and Computer Engi-neering, University of Maryland, College Park, MD, 20742, USA (e-mail: etony@umd.edu).

D. Yuan is with the Department of Science and Technology, Link¨oping University, Sweden and ISR, University of Maryland, College Park, MD, 20742, USA (e-mail: diyuan@umd.edu).

SU sensing algorithms and accessing polices. Due to the inherent randomness of PU trafﬁc, such algorithms are usually complex and not easy to implement. However, as the source of the complexity is the randomness of PU’s access, if the PU’s resource occupancy pattern becomes more regular and predictable, it may be helpful to simplify the design and to improve the access efﬁciency for the SUs.

Multi-channel transmission is effective to improve efﬁciency and reliability of network communication. Both OFDM [5]– [7] and MIMO [8]–[10] techniques are broadly adopted in the next generation mobile telecommunication infrastructures. In cognitive communication networks, multi-channel techniques are also employed to enhance the service quality under oppor-tunistic spectrum access [11]. However, conventional multi-channel schemes are usually based on uniform bandwidth allocation. Such a design may not be effective in cognitive communication.

In this paper, we propose a non-uniform bandwidth parti-tion and allocaparti-tion scheme for PUs, together with a tailored channel sensing and access policy for the SUs. The pro-posal combines cognitive communication with multi-channel transmission so as to regularize the PU resource occupancy pattern and, in turn, to improve the SU sensing efﬁciency and throughput. The conventional uniform spectrum allocation scheme splits the spectrum equally and yields equally sized blocks (channels or sub-channels) as the resource unit. Thus the term ‘uniform’ applies to the size of blocks. In our non-uniform resource allocation scheme, the overall spectrum is partitioned unevenly, giving a set of unequal-sized blocks.

The rest of the paper is organized as follows. In Section II, related work is discussed. In Section III, we describe our system model. The non-uniform scheme for bandwidth division and channel access is presented in Section IV. The performance of the new scheme are analyzed and compared with those of conventional schemes in Section V. In Sec-tion VI, numerical simulaSec-tions are performed to verify the effectiveness of our scheme. In Section VII, the non-uniform scheme is extended to fading situations, together with numeri-cal evaluations. In Section VIII we summarize our conclusion.

II. RELATEDWORK

For cognitive communication, to enable SUs to access a licensed bandwidth without interfering with the PUs, existing solutions can be generally divided in three categories [12]: the spectrum underlay [13]–[15], the spectrum overlay and the spectrum interweave. The interference temperature model [16]–[18] is a typical spectrum underlay solution, which was

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introduced originally in [19]. This model manages interference at the receiver through the interference temperature limit, which is represented by the amount of new interference that the receiver could tolerate. The difﬁculty of this model lies in how to effectively measure the interference temperature [3].

Another approach for spectrum sharing is spectrum

inter-weave, which is also referred to as opportunistic spectrum

access [12]. Unlike spectrum underlay, SUs will only access the licensed spectrum while the PUs are not transmitting, so there is no interference temperature limit imposed on SUs. Instead, SUs need to sense the licensed frequency band and detect the spectrum white space. To obtain a better sensing efﬁciency, a rational method is to discretize the spectrum allocation and usage, and then to separate the usage of PU trafﬁc and SU access in frequency, with the aim for reducing the interactive interference among them. To that end, OFDM [20]–[23] is a feasible solution.

An OFDM-based cognitive radio network is proposed in [24], which considers various deployment scenarios over the heterogeneous network environment and develops cross-layer operations for the dynamic spectrum access. One of the main requirements of spectrum sharing is the detection of the PU traffic in a very short period of time. OFDM serves well this purpose. In addition, OFDM can convert a frequency-selective fading channel into a set of parallel frequency-flat subchannels, thereby simplifying channel equalization and symbol decoding. However, in a broadband system, adopting an OFDM-based scheme usually leads to dozens or hundreds of subcarriers. Hence, a spectrum allocation and access ac-tion would involve many sensing and negotiaac-tion operaac-tions, which make the spectrum management and access procedure inefficient.

To improve the spectrum access efﬁciency, subcarrier group-ing was adopted, which bundles the subcarriers into groups and manage the groups instead of the individual ones. Sub-carrier grouping was originally proposed in [25] for multiuser interference elimination and later in [26] for peak-to-average power ratio reduction. It was also suggested in [27] to reduce the design and decoding complexity while preserving both the diversity and coding advantages. In [28], subcarrier grouping was used to reduce the overhead associated with link adap-tation, where all the subcarriers are divided uniformly into several groups. The subcarriers within a group are treated as a single entity. Only the subcarrier located in the center of each group is monitored and tracked with the aim to infer the channel state information of all subcarriers in the same group. In this way, the management efﬁciency is improved.

However, a drawback of the uniform subcarrier grouping scheme is that bandwidth waste may occur during the grouping operation. For example, as stated in [28], the last group need not utilize its subcarriers fully. Besides that, as the volume of the PU traffic is not necessarily an integer multiple of the capacity of a subcarrier group, there may be bandwidth loss incurred by the PU traffic allocation, that may lower the overall spectrum utilization. The tradeoff is that a larger group size can improve the spectrum access efficiency, but at the same time it may also result in a larger bandwidth loss.

To resolve this conﬂict, we propose a non-uniform

allo-cation scheme in this paper. Our purpose is to improve the spectrum access efficiency and reduce the bandwidth loss in spectrum use simultaneously. As our scheme mainly con-centrates on regulating the PU’s resource occupation pattern, and improving the sensing efficiency of the SU, it creates neither restrictions nor any influence on the PU’s traffic profile, such as power of transmission, preambles, midambles and pilot patterns. Therefore, almost all existing spectrum sensing algorithms [29]–[33] can be adopted in our scheme without altering their implementation or their properties.

The major contributions of this paper are as follows. (1) We investigate the necessity and feasibility of improving the spectrum efficiency from the aspect of PU traffic allocation; (2) a non-uniform scheme of spectrum management and traffic allocation for cognitive communication is introduced; (3) the benefits of the new scheme on improving the sensing efficiency and reducing the spectrum waste are analyzed and compared with those of conventional uniform allocation schemes. Its effectiveness is also verified by numerical simulations under non-fading and fading situations respectively. The basic con-cept of the non-uniform allocation scheme was presented in a preliminary work [34], which only gave a brief introduction of our idea. In this paper, we further provide detailed descrip-tions of the allocation algorithms, more thorough theoretical discussions on the performance benefits and analysis of the simulations.

III. SYSTEMMODEL

A cognitive communication system is shown below to illustrate the spectrum sharing scenario, which is composed of a PU transmitter and a SU transmitter. We assume that both the PU and the SU can utilize the entire licensed bandwidth. The PU’s bandwidth demands are within the limits of the licensed bandwidth, but its transmissions are stochastic. The SU continuously performs dynamic sensing and accesses the spectrum opportunistically on the condition of not interfering with PU’s communication.

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Fig. 1: A cognitive communication scenario.

The sensing and transmission operations are separated. The SU could not reuse the spectrum during the sensed OFDM symbol. The transmissions of both the PU and the SU are slot-based. At the beginning of each timeslot, the SU can sense the status of a subcarrier to determine the status of the corresponding channel. If there is no PU transmission, the SU can utilize the remaining symbols of the same timeslot for its transmission. Each sensing operation by the SU has its cost.

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When the SU is sensing a channel, its data transmission has to be temporarily suspended. The more frequently the sensing operation is performed, the higher the loss in bandwidth utilization.

There are basically two sensing and transmission policies for an SU: (1) transmitting after sensing (TAS), where the SU begins its transmission when all sensing operations for the current timeslot are completed, or all channels have been sensed, and (2) transmitting while sensing (TWS), where the SU transmits data immediately after ﬁnding an idle channel.

In our case, the only assumption at the physical layer is the use of subcarrier-based allocation. The assumption of subcarrier-based physical layer of primary and secondary systems has been considered in similar studies [21], [35]. Apart from this, the system model does not assume any further common physical layer implementation (e.g., modulation and coding schemes, error control mechanism, etc.) These can be different for PU and SU.

Our assumptions and notation about the cognitive system are summarized as follows. The licensed bandwidth is denoted by W (bps). It can consist either of contiguous or of non-contiguous components. The entire licensed bandwidth is divided into subcarriers. The subcarriers are grouped into channels, either uniformly or non-uniformly. Data transmis-sions of the PU and the SU are both slot-based. All timeslots have duration of T (seconds). At the beginning of a timeslot, the SU performs channel sensing. Based on the sensing results and corresponding statistics of the PU trafﬁc, the SU decides whether to transmit its data or not.

The PU trafﬁc at the moment nT (n ∈ Z) is denoted by

R(n) (bits per timeslot) and is assumed to be memoryless,

i.e., independent in time, and following a truncated Poisson distribution on [0, W ] with parameter λ. The bandwidth

de-mand of the SU at moment nT is denoted by D(n) (bits

per timeslot). We assume that D(n) is independent of R(n). There is no upper limit to the volume ofD(n). However, when

D(n) exceeds the remaining bandwidth, it will be truncated.

We also assume that the SU demand is stochastic, and there is no assumption about its probability distribution. Since the timeslot durationT is constant, without loss of generality, in the rest of this paper we assume thatT = 1 (second). We note that such an assumption does not change the conclusions of our analysis.

We employ the truncated Poisson distribution with the aim to ease the comparison with the conventional uniform allocation scheme. This does not mean that the scheme is restricted to specific probability distributions. The non-uniform spectrum allocation scheme can be applied to any type of PU traffic, as long as the PU transmission is timeslot based and PU traffic volume does not exceed the overall bandwidth.

In [36] a Hidden Markov Models (HMM) based algorithm was used to predict the spectrum occupancy of licensed radio bands. In [37] a neural network model multi-layer perception (MLP) was employed to predict the channel usage pattern. Compared to these studies, our scheme is based on the assump-tion that the PU trafﬁc in each timeslot is memoryless, and our discussion concentrates on reducing the amount of sensing operations through the non-uniform spectrum allocation.

IV. NON-UNIFORMSPECTRUMALLOCATION

The non-uniform spectrum allocation involves three aspects as follows.

A. Bandwidth Partition

We denote the number of channels byM. Then we partition the bandwidth W uniformly into 2M subcarriers, denoted by

α0, α1, · · · , α2M₋₁. We let

A =α0, α1, · · · , α2M₋₁ (4.1)

denote the set of subcarriers. Each of them has the bandwidth of σ = W/2M bps, and σ is the basic unit of resource allocation for the PU trafﬁc.

Except one subcarrier used for the control messages delivery of the PU, which is denoted byβc, all the remaining (2M−1)

subcarriers are grouped intoM channels, which compose the setB: B =β0, β1, · · · , βM−1, (4.2) where βk = α(0)k , α(1)k , ...α(Lk k−1) , Lk= 2k. (4.3)

Here α(i)_k (0 ≤ i ≤ Lk− 1) is the (i + 1)th subcarrier of the

channelβk, and the bandwidth ofβkequals 2kσ bps. The

min-imal channel bandwidth isσ, and the maximum one is 2M−1σ. We name β0 andβM−1 the Least Signiﬁcant Channel (LSC)

and the Most Signiﬁcant Channel (MSC) respectively.

α α α αα α α α α α α α α α α β β β β 6XEFDUULHUV 7LPH &KDQQHOV 'XUDWLRQRIDWLPHVORW

Fig. 2: Grouping subcarriers into channels.

When we compose a channel from subcarriers, there is no restriction on the contiguousness of spectrum occupancy. Subcarriers in one channel may be adjacent in the spectrum or not. This provides ﬂexibility in composing the channels.

A schematic plot of bandwidth partition and subcarrier grouping is shown in Fig. 2, where subcarriers (α0 ∼ α14) are grouped into channels (β0 ∼ β3). Although in Fig. 2 the subcarriers are shown in a contiguous manner, their practical locations can be scattered across the entire spectrum.

Note that our bandwidth allocation scheme is not restricted to a system model using a control channel βc. In a more

general setting, the PU communication may opt for any means for the receiver to receive data. For example, the PU receiver can basically scan the subcarriers and identify the intended message (e.g., using preamble). Even if there is

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(a) PU trafﬁc samples.

β β β β 7LPH β β β β β &KDQQHOV ,GOH 8VHG %DQGZLGWK .ESV 7 'XUDWLRQRIDWLPHVORW

(b) Resource occupancy after the PU trafﬁc allocation.

Fig. 3: Example of the non-uniform allocation.

control signaling, the PU may choose other means than a separate and dedicated channel. In case there is a dedicated subcarrier for the PU for the purpose of signaling, one cannot assume that the SU may access it. This is because PU and SU are not peers but, in general, totally separate and different users, bound by different rules and protocols; that is, the SU is passive and can only access the available resources when they are not used.

B. PU Trafﬁc Allocation

For each sample of the PU trafﬁc, we round its magnitude up based on the channel’s minimal capacity. As the bit rate that each subcarrier can accommodate is σ bps, and the timeslot durationT is assumed to be equal to 1 second, the number of subcarriers required is

KR(n) = R(n)/σ. (4.4)

Then we represent KR(n) by its binary form:

Kb R(n) = b(n)M−1, b(n)M−2, ...b(n)1 , b(n)0 , (4.5)

whereb(n)_k (0 ≤ k < M) is the (k+1)th digit of K_Rb(n). Digits

b(n)_M−1andb(n)₀ correspond to the MSC and LSC respectively. Finally, we allocate R(n) to the channel set B based on the values ofb(n)_k (0 ≤ k < M) by the steps shown in Algorithm 1. Such allocation steps are executed every timeslot.

Algorithm 1 Resource allocation for PU trafﬁc.

1: ComputeK_Rb(n) by Eq. (4.4, 4.5)

2: fork = M − 1 to 1 step -1

3: ifb(n)_k = 0

4: allocate 2kσ trafﬁc to channel βk

5: R(n) := R(n) − 2kσ

6: end if

7: end for

8: allocateR(n) to channel β0

An example of the PU traffic allocation is illustrated in Fig. 3. The traffic shown in Fig. 3 (a) is composed of eight samples. The non-uniform resource occupancy pattern after the PU traffic allocation is shown in Fig. 3 (b). It is evident that every timeslot-channel block is either fully occupied by the PU or completely idle, except forβ0for which there could be some amount of bandwidth loss. The bandwidth loss is due to the fact that the bandwidth demanded by a traffic sample may not be exactly an integer multiples ofσ. The bandwidth loss may vary from slot to slot. But it only appears onβ0, and is bound by [KR(n)σ − R(n)] (bps) which is less than σ.

C. Spectrum Sensing

It is evident that all subcarriers within a channel are of the same status which is either busy or idle. When sensing the licensed spectrum for white spaces, the SU does not need to check all subcarries one by one. Instead, sensing any single subcarrier in each channel enables the SU to infer the entire channel’s occupancy status. Hence the number of sensing operations is reduced fromO(2M) to O(M), which decreases the SU’s sensing overhead significantly. In addition to the non-uniform partition, the sensing order of MSC first (MSCF) can be adopted by the SU to further improve its sensing efficiency, i.e. the SU always sense the widest channel first.

As stated earlier, the PU trafﬁc follows a truncated Poisson distribution on [0, W ]. The occupancy frequency of every channel is not necessarily uniform. Therefore, starting the sensing process from the channels that are less likely to be occupied can further reduce the number of sensing operations, particularly when the SU’s demand for bandwidth is relatively small. To this end, before sensing begins, we sort all channels in ascending order of their usage frequencies by the PU. More speciﬁcally, we count the occupancy frequency of every channel by the PU and denote it byf(βk)(k ∈ [0, M)). Then

we sort all channels to ensure that:

fβk1 k1 ≤ fβk2 k2 , ∀(0 ≤ k1_{< k2}_{< M),} _(4.6)

wherek1 andk2 are the new sequence numbers ofβk1 and

βk2after sorting. We call this the Least Frequently used

Chan-nel First (LFCF) sequence. Here the sensing order denoted by

LFCF refers to the secondary system. If two channels have equal usage frequency, the one with larger bandwidth should be sensed ﬁrstly.

Suppose the SU demand for bandwidth at timeslot n is

D(n). The main steps of SU’s sensing and access operations

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Algorithm 2 SU’s sensing and access steps.

1: Loop fromk= 0 to M − 1 step 1

2: check the state ofβ_kk

3: ifβk_k is idle

4: allocate SU’s trafﬁc of 2kσ to β_kk

5: D(n) := D(n) − 2kσ 6: end if 7: ifD(n) ≤ 0 8: terminate 9: end if 10: end loop

channels are checked. If D(n) ≤ W − R(n), the loop

terminates when D(n) ≤ 0.

Our analysis has been developed for the steady state of the system. However, there may be an initialization phase before the SU has sufﬁcient amount of samples for observing how frequent each channel is occupied. In order to avoid any potential instability in the training process, we propose to use the MSCF sensing order in the initialization of the non-uniform scheme, which will switch to the LFCF sensing order after this initialization phase. In Section VI, we will present simulation results of using MSCF. It turns out that MSCF requires more sensing for low SU demand, but performs very closely to LFCF when the demand becomes higher.

V. PERFORMANCEANALYSIS

To demonstrate the advantage of the non-uniform allocation scheme, we evaluate its performance from several points of view and compare them with those of the uniform allocation scheme, which is a conventional practice in cognitive commu-nication. We consider several performance objectives, namely the sensing efﬁciency, the SU throughput, and the bandwidth

loss of the PU trafﬁc allocation. A. Sensing Efﬁciency

We use the number of sensing operations to indicate the sensing efficiency. The less the number of sensing operations that the SU has to carry out before each data transmission, the higher the sensing efficiency. Since every sensing attempt carries a cost, a higher sensing efficiency can lower the total bandwidth waste and in turn improve the SU’s throughput as well as reduce energy consumption.

1) Uniform Scheme: In the uniform scheme, all channels

have the same bandwidth of θ = W/M bps. To achieve the

best sensing efﬁciency, without loss of generality, we suppose that the channel allocation forR(n) follows a sequential order fromβ0toβM−1, and the sensing operations of the SU follow

the reverse order, originating fromβM−1. Then the number of

sensing operations is given by

Nu= ⎧ ⎨ ⎩ D(n)/θ, D(n) + R(n) < W, M − R(n)/θ, D(n) + R(n) ≥ W. (5.1)

We denote the average ofNubyNu. Then the average number

of sensing operations over the probability distribution ofR(n) is: Nu= E(Nu) = 1 Fλ(W ) D(n) θ W −D(n) k=0 _e_−λ_λ_k k! + W k=W −D(n)+1 _e_−λ_λ_k k! M −k_θ , (5.2)

where E(·) represents the expectation function, and

Fλ(W ) = e−λ W k=0

λk

k!. (5.3)

2) Non-uniform Scheme: We denote the number of sensing

operations by Nnu. In following, we discuss Nnu and its

expectation in cases ofD(n)+R(n) < W and D(n)+R(n) ≥

W respectively.

Achieving the minimal number of sensing operations is equivalent to allocating the minimal number of idle channels to D(n) from the set B. In the non-uniform scheme, since every channel has different capacity, following a proper access sequence is critical for reducing the number of channels sensed. To this end, we introduce the following proposition. Proposition 1. Suppose B is composed of all idle channels of the set B after the PU trafﬁc allocation, and WB is the

total bandwidth ofB. IfD(n) < WB, to accommodateD(n)

with the minimal number of channels ofB, the optimal access sequence is MSC ﬁrst (MSCF).

We omit the proof of Proposition 1, as it is easy to get the result by following a greedy strategy. Here the sensing order denoted by MSCF refers to the secondary system. We note thatB of Proposition 1 is composed of all the idle channels ofB. Hence the effect of the MSCF on B is not necessarily equivalent to the one onB. We denote the number of sensing operations of the SU with the optimal sensing sequence by

N∗

nu. Since the optimal sequence of the sensing operation is

unknown, a closed-form expression of N_nu∗ is not available. Therefore we analyze the upper bound ofN_nu∗ instead. To this end, we introduce another proposition as follows.

Proposition 2. Consider the channel set B =

{β0, β1, · · · , βM−1} = {σ, 2σ, · · · , 2M−1σ} based on

the non-uniform bandwidth partition. To accommodate bandwidth demand 0 < D(n) ≤ (2M − 1)σ under the prerequisite that the non-zero bandwidth loss only appears on at most one channel, the allocated channel set that is composed of contiguous channels starting from β0 has the

largest cardinality.

The above conclusion is intuitive and the proof is omitted. Proposition 2 actually provides an upper bound forN_nu∗ . We denote such an upper bound by N_nu (N_nu ≥ N_nu∗ ). The following proposition gives a closed-form expression ofN_nu .

Proposition 3. Consider a channel set B =

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bandwidth of WB. Suppose the bandwidth demand is

x (0 ≤ x ≤ WB). If we denote the minimal number of

channels that accommodatex by nnu(x), we have

nnu(x) = − log2(1 − x/WB). (5.4)

Proof. When x = 0, since there is no channel occupied, it is

clear that Nnu(0) = 0. Considering that − log2(1 − 0) = 0, we have

nnu(x)_x=0= − log2(1 − x/WB)_x=0= 0. (5.5)

When 0< x ≤ WB, the range ofx/WBcan be represented

by a group of M contiguous intervals as follows:

B WB = βM−1 WB , βM−2 WB , · · · , β0 WB = 0,1₂ , ₁ 2 , 1 2+ 1 4 , · · · , _M−1 i=0 1 2 i − 1, M i=0 1 2 i − 1 = _k i=0 1 2 i − 1, k+1 i=0 1 2 i − 1 , (5.6)

whereM −1 ≥ k ≥ 0. For MSCF and any bandwidth demand

x that satisﬁes k i=0 1 2 i − 1 < _Wx B ≤ k+1 i=0 1 2 i − 1, (5.7)

and since the channels from βM−1 to βM−k−1 are all

occu-pied, we have

nnu(x) = k + 1. (5.8)

At the same time, by applying the geometric series formula to Eq. (5.7), we have 1 −1₂k< _Wx B ≤ 1 − 1 2 k+1 , (5.9) Then k < − log2(1 − x/WB) ≤ k + 1, (5.10) and − log2(1 − x/WB) = k + 1. (5.11)

From Eq. (5.8) and Eq. (5.11), we have

nnu(x)_0<x≤W_B= − log2(1 − x/WB)_0<x≤W_B. (5.12)

By combining the conclusions of Eq. (5.5) and Eq. (5.12), the proposition is proved.

In Proposition 3, we actually assume that all the free band-width is composed of consecutive channels starting from β0. Such an assumption, according to Proposition 2, leads to a set with the largest number of channels. Therefore it provides an upper bound for N_nu∗ , because usually the free bandwidth is composed of a group of non-consecutive channels.

For the case ofD(n) + R(n) < W , we denote the average

N

nu byNnu(a). According to Proposition 3, we have

N(a) nu = − log2 1 −_{W − R(n)}D(n) . (5.13)

For the case ofD(n) + R(n) ≥ W , the bandwidth demand of D(n) will be truncated and all idle channels will be

occupied by the bandwidth demandD(n). The SU may have

to sense all M channels. Therefore we have

N(b)

nu = M. (5.14)

Based on above discussions, we have

N nu= ⎧ ⎪ ⎨ ⎪ ⎩ − log2 1 −_{W − R(n)}D(n) , D(n) + R(n) < W, M, D(n) + R(n) ≥ W. (5.15) Since R(n) is assumed to follow a truncated Poisson dis-tribution, by making the average ofN_nu over the probability distribution ofR(n), we have Nnu= E(N nu) = 1 Fλ(W ) _{W −D(n)} k=0 e−λ_λk k! − log2 1 −_{W − k}D(n) + M W k=W −D(n)+1 e−λ_λk k! , (5.16)

where Fλ(W ) is deﬁned by Eq.(5.3).

Nnu provides an upper bounded for N∗nu. Since it is difﬁcult to compare Nu and Nnu analytically, we compare

them later by simulations in Section VI.

Our discussion of the amount of sensing in the non-uniform scheme is based on the following assumption. WhenD(n) <

W −R(n), achieving the minimal sensing amount is equivalent

to allocating, among all free ones that comprise W − R(n), the least number of channels to the SU. Since the channels occupied by the PU trafﬁc are located randomly across the

spectrum, the free channels comprising W − R(n) may be

scattered randomly as well. According to Proposition 1, among all channels forW −R(n), we should allocate the widest ones forD(n) ﬁrst (i.e., the greedy strategy). Proposition 2 states

that when W − R(n) is composed of contiguous channels

originating fromβ0, the total number of free channels reaches its maximum, and so does the number of channels allocated for

D(n). Such a situation actually provides an upper bound for

the number of channels allocated forD(n), and Proposition 3 aims to provide a closed-form expression for this bound.

B. SU Throughput

In the case of D(n) + R(n) < W , the bandwidth is

sufﬁcient. For both the uniform and the non-uniform schemes, the SU throughput is the same and equals D(n). Hence, we only discuss the case ofD(n) + R(n) ≥ W , where due to the total bandwidth limit, the demandD(n) is truncated, and the

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7UDQVPLVVLRQSHULRG 6HQVLQJSHULRG 6HQVLQJVWHSVLQGLFDWLRQ D7$6IRUXQLIRUPVFKHPH E7:6IRUXQLIRUPVFKHPH F7$6IRUQRQXQLIRUP VFKHPH G7:6IRUQRQXQLIRUP_VFKHPH Fig. 4: Sensing costs in a timeslot.

actual SU throughput is less then D(n). In this case, the SU throughput represents the amount of resource that is effectively utilized by the SU, i.e., the resource left after allocating PUs trafﬁc, minus that used for SU in its sensing operation.

Basically, there are two factors that may inﬂuence the SU throughput, namely the sensing cost and the bandwidth loss. The bandwidth loss will be discussed later. Here we focus on the impact of the sensing cost. According to our assumption about the system model, each sensing operation by the SU has its cost. When the SU is sensing a channel, its data transmission has to be temporarily suspended. As shown in Fig. 4, the more frequently the sensing operation is performed, the higher the loss in bandwidth utilization. There are basically two sensing and transmission policies, namely TAS (Fig. 4 (a), (c)) and TWS (Fig. 4 (b), (d)). In these ﬁgures,

δ represents the average sensing time duration.

1) Uniform Scheme: As shown in Fig. 4 (a) (b), all channels

have the same bandwidth. Suppose M is large and λ is

relatively small. An estimation about the average sensing cost under the TAS policy is:

cu= EδNu(M − R(n)/θ)θ

= δ · EM − R(n)/θM − R(n)/θθ. (5.17) The average sensing cost under the TWS policy is:

cu≈ 0.5cu. (5.18)

2) Non-uniform Scheme: As shown in Fig. (4-c, 4-d), the

channels have non-uniform bandwidths. Since the accurate value of Nnu is not available, we use the maximumM for

evaluation. The average sensing cost under the TAS policy is:

cnu≤ δM[W − E(R(n))]. (5.19)

Under the TWS policy, the average sensing cost is bounded as follows. cnu≤ M k=1 2M−kσδk T = δW M k=1 k 2k . (5.20) Since lim M→∞ M k=1 k 2k = 2, (5.21)

asM keeps increasing, the upper bound of cnuwill approach 2δW .

C. Bandwidth Loss

As the trafﬁc volume of PU is stochastic, its value may not be exactly an integer multiple of the minimal channel capacity. Thus there is a bandwidth loss due to the gap between

the bandwidth required by R(n) and the actual bandwidth

allocated to it.

1) Uniform Scheme: Considering the conventional uniform

allocation scheme withM channels, we denote the bandwidth loss by εu(n). The ratio of the bandwidth loss to the entire

licensed bandwidth is:

ru(n) = εu/W = R(n)/θ/M − R(n)/W. (5.22)

Its average value is:

ru= εu/W = ER(n)/θ/M − E[R(n)]/W. (5.23)

Since

E[R(n)]/θ ≤ ER(n)/θ< E[R(n)]/θ + 1, (5.24) it clearly follows that:

0 ≤ ru< 1/M. (5.25)

WhenM keeps increasing, the value of ruoscillates between

0 and 1/M and approaches zero.

2) Non-uniform Scheme: According to Eq. (4.4), the

band-width loss at momentn can be represented by:

εnu(n) = KR(n)σ − R(n). (5.26)

Becauseεnu(n) appears only on channel β0, a nonzeroεnu(n)

indicates that there is currentlyεnu(n) bps of bandwidth not

used. Since 0 ≤ εnu(n) < σ, the smaller the value of σ,

the less the error εnu(n). We assume that εnu(n) follows

a uniform distribution on the interval [0, σ), the average bandwidth loss will be

εnu= σ/2 = 2−(M+1)W. (5.27)

The ratio of the average bandwidth loss to the entire licensed bandwidth is:

rnu= εnu/W = 2−(M+1). (5.28)

When M ≥ 1, we have 2−(M+1) < 1/M. When M increases, the decrease ofrnu follows a negative exponential

function, which decays far more rapidly than that ofru. This

demonstrates the superiority of the non-uniform scheme over the uniform one with respect to the bandwidth loss.

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VI. VERIFICATION BYSIMULATION

We use Monte-Carlo simulations to verify our analysis. The licensed bandwidth is set to 7.5Mbps. A random series number is generated following the truncated Poisson distribution on [0, W ] with parameter λ, which is used to emulate the PU trafﬁc. Changingλ alters the average PU trafﬁc volume. The ratio of the average sensing time duration to the timeslot length is δ/T = 0.01. Without loss of generality, we use

λ = 0.35W and λ = 0.75W emulating the light and heavy

PU traffics respectively. When studying the influence of SU demand to the sensing efficiency, we let M = 9. To emulate

the low SU demand D(n), we use another random series

number following Poission distribution with the parameter

λD = 0.35W . We execute the algorithms introduced in

Section IV, then collect the results and make statistics of the performance parameters.

For the purpose of comparison, the uniform allocation scheme is also performed. The simulations and comparisons are made from three main aspects: the sensing efﬁciency, the SU throughput and the bandwidth loss, corresponding to the analysis in Section V. In the uniform scheme, the channel allocation for R(n) follows a sequential order from β0 to

βM−1. Such an allocation sequence of the PU data is known

to the SU. Therefore, the sensing operations of the SU follow the reverse order starting from βM−1. This represents the

most favorable design for the uniform scheme with minimum possible SU sensing.

A. Sensing Efﬁciency

In Fig. 5-(a), there are four curves showing the average number of sensing operations versus SU demand. The abbre-viations in the legend are as follows: (1) uniform, the number of sensing operations of the SU of the uniform allocation scheme. (2) non-uniform with LFCF, the number of sensing operations of the SU of the non-uniform allocation scheme using the LFCF sequence. (3) non-uniform with MSCF, the number of sensing operations of the SU of the non-uniform allocation scheme using the MSCF sensing sequence. (4)

uniform upper bound, a theoretical upper bound of the

non-uniform allocation scheme using the LFCF sequence, namely Eq. (5.16). Fig. 5-(a) shows that the curves of both the uniform and the non-uniform schemes agree well with our analysis in Section V. Both of them follow staircase functions. The former one is a staircase function with a uniform tread depth. The latter one’s tread depths form a geometric series.

For the case ofD(n)+R(n) < W , the evident difference of the curves proves the better performance of the non-uniform scheme over the uniform scheme in the aspect of sensing efﬁciency. The curve of MSCF resembles that of the non-uniform scheme with LFCF very closely, due to the fact that its sensing efﬁciency is close to that of LFCF. The curve of non-uniform upper bound is above that of the non-uniform scheme, which matches well with our previous analysis.

For the case ofD(n) + R(n) ≥ W , since the non-uniform

scheme senses all M channels, the maximum number of its

sensing operations is equal to M and is always larger than that of the uniform one.

0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Ratio of SU demand to the whole bandwidth

Ratio of the average number of sensing operations

to the number of channels

uniform

non−uniform with LFCF non−uniform with MSCF non−uniform upper bound

(a)λ = 0.35W ; M = 9. 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

uniform

non−uniform with LFCF non−uniform with MSCF non−uniform upper bound

(b)λ = 0.75W ; M = 9.

Fig. 5: Average sensing efﬁciency versus the SU demand.

0 5 10 15 20 0 1 2 3 4 5 6 7 8 Number of channels

Number of sensing operations

uniform

non−uniform with LFCF non−uniform with MSCF

Fig. 6: Average number of sensing operations versus the number of channels under light PU trafﬁc and low SU demand.

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The situation in Fig. 5-(b) is similar, except thatλ is larger than that of Fig. 5-(a). In the case of D(n) + R(n) < W , the performance gap between the uniform scheme and the non-uniform one is not evident. This is because a smaller WB

makes the function deﬁned in Eq. (5.4) rise faster. Besides that, the poor performance of the MSCF curve shows that it is not optimal under heavy PU trafﬁc, because the channels with relatively large bandwidth have already been used by the PU.

In Fig. 6, the three curves plot the average number of sensing operations versus the number of channels. The simulation is performed under light PU traffic and low SU demand. With the increase of the channel number, the number of sensing operations of the uniform scheme grows steadily, while the curve of the non-uniform scheme remains flat at a very low level. The results are well in line with our analysis in Section V. The curve of MSCF is completely overlapping with that of LFCF. This confirms that the MSCF access sequence is almost identical to the LFCF sequence under light PU traffic and low SU demand.

ForM = 2, a sudden rise in the curve of LFCF is observed.

The reason is as follows. When M = 2, the number of

subcarriers is 2M = 4, with channel bandwidths given by

{β0, β1} = {0.25W, 0.5W }.

Since the average PU trafﬁc is λ = 0.35W > 0.25W ,

following the algorithm of the non-uniform scheme, PU’s trafﬁc is allocated to β1. When the SU starts its sensing operation fromβ1, it fails at the ﬁrst time and succeeds at the second time. Thus the sensing operation is performed twice. When M = 3, the number of subcarriers is 2M = 8, with channel bandwidths given by

{β0, β1, β2} = {0.125W, 0.25W, 0.5W }.

Since the average PU trafﬁc is λ = 0.35W < 0.125W +

0.25W = 0.375W , following the algorithm of the non-uniform scheme, PU’s traffic is allocated to β0andβ1. When the SU starts its sensing operation fromβ2, it succeeds at the first time. Thus only one sensing operation is sufficient. When

M > 3, the situation is similar to that of M = 3. B. SU Throughput

In Fig. 7-(a), the policy of TWS is adopted. The average PU trafﬁc occupies a bandwidth of 0.35W , and the average SU demand is greater than (W −λ). Fig. 7-(a) shows that with the non-uniform allocation scheme, the SU throughput increases rapidly with the growing number of channels. Eventually the average SU throughput stays steadily at a level near (W − λ). This trend is consistent with the bandwidth loss analysis in Section V and the non-uniform curve of bandwidth loss of Fig. 8.

For the uniform allocation scheme, the SU throughput behaves in an oscillating manner. This is mainly due to the oscillating property of its bandwidth loss (Fig. 8). The gap between the curves of uniform and non-uniform exhibits the superiority of the latter. It also demonstrates the signiﬁcant inﬂuence of the bandwidth loss to the SU throughput.

0 5 10 15 20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Number of channels

Ratio of the average throughput of SU

to the whole bandwidth

uniform

(a) Average SU throughput under the TWS policy.

0 5 10 15 20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Number of channels

uniform

(b) Average SU throughput under the TAS policy.

Fig. 7: Average SU throughput

0 5 10 15 20 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Number of channels

Ratio of average bandwidth loss

uniform non−uniform uniform upper bound non−uniform upper bound

Fig. 8: Channel bandwidth and average bandwidth loss.

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uniform scheme is twice as large as that of the non-uniform

scheme. The reason is as follows. For the uniform

alloca-tion scheme, when M = 2, there are two channels with

bandwidths {0.5W, 0.5W }. Since the average PU trafﬁc is 0.35W , the PU occupies one channel and the SU occupies the other. Therefore the average SU throughput is 0.5W . For

the non-uniform scheme, when M = 2, the channel set is

{β0, β1} = {0.25W, 0.5W }. The average PU trafﬁc is 0.35W and it is allocated toβ1. Therefore the SU demand is allocated to β0 to the limit of 0.25W . When M ≥ 3, the proportion of βc in the entire bandwidth is increasingly smaller, and

the non-uniform scheme begins to show its superiority in SU throughput over the uniform scheme.

When M increases, the curves of SU throughput of the

non-uniform schemes eventually stay at a steady level, while

the curve of the uniform scheme shows a declining, but oscillating, trend. The reason lies in the sensing cost. For the

uniform scheme, all channels are of the same bandwidth, so an

increasingM leads to a growing sensing cost. For non-uniform schemes, the sensing sequence is similar to the MSCF, which

always begins from the most signiﬁcant channel. When M

grows, the increase of the sensing cost becomes negligible due to the rapidly shrinking channel bandwidth, which causes the throughput curve to be at a steady level.

In Fig. 7-(b), the policy of TAS is adopted. The situation is similar to that of the Fig. 7-(a), except that both the uniform and the non-uniform curves show a declining trend. This is because the sensing cost is not negligible under TAS policy. Since the non-uniform scheme keeps sensing allM channels, when M keeps increasing, it declines more severely than the uniform one.

C. Bandwidth Loss

In Fig. 8, there is a total of four curves. Two curves are for the bandwidth loss and two for the channel bandwidth granularity. The abbreviations in the legend are as follows: (1)

uniform, the average bandwidth loss of the uniform allocation

scheme; (2) non-uniform, the average bandwidth loss of the non-uniform allocation scheme; (3) uniform upper bound, the ratio of the channel bandwidth in the uniform scheme to W , namely 1/M; (4) non-uniform upper bound, the ratio of the channel bandwidth granularity of the non-uniform scheme to W , namely σ/W . The results clearly demonstrate the superiority of the non-uniform scheme over the uniform one, which is also consistent with the analysis in previous section.

VII. EXTENSION TOCHANNELFADING

In this section, we extend the non-uniform scheme to study whether its advantage is still present under fading situations. As for the case of ﬂat fading, since all the channels are subject to the same percent of capacity loss, the exact geometric structure of the capacity of βi(i ∈ [0, M)) remains,

there-fore the scheme for the PU trafﬁc allocation introduced in Algorithm 1 remains applicable. In the following discussion, we concentrate on the case of frequency selective fading, in which every subcarrier is subject to a random loss of capacity at each timeslot.

A. Problem Description

Under selective fading, the capacity of each channel is subject to random loss at every timeslot. Here we denote the actual capacity of channel βk(k = 1, . . . , M) at the nth

timeslot byqk(n), obtained by summing up the amount of data

supported by the subcarriers in channelβk. Due to the fading

effect, we have qk(n) ≤ 2kσ. For PU trafﬁc allocation, the

task is to select which channels to assign, such that the total capacity of the selected channels is at leastR(n) for timeslot

n.

In this section, we focus on moderate fading situations where the total bandwidth under fading is sufﬁcient to accom-modateR(n), which means R(n) ≤M_k=0qk(n). Under such

an assumption, there is an optimization problem to allocate the channels to PU such that the channels can accommodateR(n), and the waste in bandwidth loss is minimum. We formalize the optimization problem as follows

min _M k=0 b(n)_k qk(n) s.t. M k=0 b(n)k qk(n) − R(n) ≥ 0, (7.1)

where b(n)_k is the coefﬁcient of qk(n), with its value being

either 0 or 1. It is used to represent if the channel is allocated to PU or not.b(n)_M−1andb(n)₀ correspond to the MSC and LSC respectively.

B. A Heuristic Solution

Algorithm 3 PU trafﬁc allocation for fading channels.

1: Initializebk_k(n)(0 ≤ k < M) to be 1 2: fork= M − 1 to 0 step -1 3: w =_bj(n) j =0q j j(n) − qk k (n) 4: ifw < R(n) 5: continue 6: else 7: bk _(n) k = 0 8: ifw = 0 9: terminate 10: end if 11: end if 12: end for

To ﬁnd the optimal value ofb(n)_k (0 ≤ k < M), a heuristic algorithm is introduced as follows. First, we sort all channels in the ascending order ofqk(n) to ensure that

qk1

k1(n) ≤ qk2

k2 (n), ∀(0 ≤ k1< k2< M), (7.2)

wherek1, k2 are the new sequence numbers ofβk1andβk2

after sorting, andqk_k(n) is the actual capacity of channel β_kk at thenth timeslot. Then we optimize the channel coefﬁcient

bk_k(n)(0 ≤ k < M) using Algorithm 3. After the PU trafﬁc allocation, the SU performs spectrum sensing and data transmission following an algorithm similar to Algorithm 2, except that the amount of SU trafﬁc allocation to channelβk

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0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

uniform non−uniform uniform with fading non−uniform with fading

(a)λ = 0.35W ; M = 9. 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(b)λ = 0.75W ; M = 9.

Fig. 9: Comparison of average sensing efﬁciencies versus the SU demand.

C. Comparison by Simulation

We demonstrate the effectiveness of the non-uniform scheme with a set of numerical simulations. Most simulation related parameters are the same to that of Section VI. To emu-late the frequency selective fading effect, we treat the capacity of each subcarrier as a random number. We further assume the subcarrier capacity loss follows an uniform distribution on [0, μσ], where μ ∈ [0, 1] is a ratio of capacity loss determined by the fading severity. Changing the value of μ can alter the impact of selective fading on both the uniform and the non-uniform schemes. The smaller the μ, the less severity of the channel fading. In our simulations, we setμ = 0.20 to emulate the channel fading and the capacity loss at a moderate level.

Similar to Section VI, the simulations for fading are focus-ing on three aspects, namely the sensfocus-ing efﬁciency, the SU throughput and the bandwidth loss. The sensing operations of the uniform scheme also follow the reverse order of the PU trafﬁc allocation to minimize the SU sensing amount. For the

0 2 4 6 8 10 12 14 16 18 0 1 2 3 4 5 6 7 8 9 Number of channels

Number of sensing operations

Fig. 10: Comparison of average number of sensing operations versus the number of channels under light PU trafﬁc and low SU demand.

sake of comparison, the results of fading-ignorant performance are also presented in ﬁgures.

1) Sensing Efﬁciency: In Fig. 9-(a), it is evident that

chan-nel fading decrease the sensing efficiency of the non-uniform scheme to some extend, because the loss of channels’ capacity leads to more amount of sensing. However, the non-uniform scheme still has better sensing efficiency than the uniform one when the SU demand D(n) is relative low. In Fig. 9-(b), the PU traffic load is heavier than that of Fig. 9-(a). For low SU demands, the performance gap between the uniform scheme and the non-uniform one is not evident. In Fig. 10, the PU traffic is light and the SU demand is low. The performance degradation of the non-uniform is not so significant.

2) SU Throughput: In Fig. 11-(a), the policy of TWS is

adopted. With the increase ofM, the non-uniform scheme still achieves a steady SU throughput even under fading situations, which shows its superiority to the uniform scheme. In Fig. 11-(b), the policy of TAS is adopted, and the situation is similar to that of the Fig. 11-(a), except that both the uniform and the

non-uniform curves show a declining trend.

3) Bandwidth Loss: From Fig. 12 it is shown that, the

fading effect does not inﬂuence too much about the band-width loss of either the uniform scheme or the non-uniform one. The non-uniform scheme still exhibits its superiority by approaching more rapidly to zero whenM increases.

VIII. CONCLUSION

In cognitive communication, as the PU traffic is generally random, the spectrum white spaces are usually spread random-ly as well. Such randomness increases the sensing workload of the SU. In this paper, we have proposed a non-uniform bandwidth allocation scheme for the PU, with the aim to make PU’s resource occupancy pattern more regular and predictable, and in turn to improve the SU’s sensing and access efficiency. Through theoretical analysis and numerical simulations, it is demonstrated that, under the situation of light PU traffic and

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0 2 4 6 8 10 12 14 16 18 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Number of channels

(a) Average SU throughput under the TWS policy.

(b) Average SU throughput under the TAS policy.

Fig. 11: Comparison of average SU throughputs

Ratio of average bandwidth loss

Fig. 12: Comparison of channel bandwidth and average band-width loss.

low SU demand, the non-uniform scheme has higher sensing efﬁciency and lower bandwidth loss than the uniform scheme. Under the situation with high SU demand, the bandwidth becomes scarce. The non-uniform allocation scheme achieves higher SU throughput with the TWS policy by incurring less bandwidth loss and less sensing cost, and demonstrates its superiority over the uniform scheme. We also extend the non-uniform scheme to selective fading situations and illustrate its superiority over the uniform scheme by simulations. It is evi-dent that the basic idea of non-uniform spectrum partitioning remains valid in presence of fading.

However, as to the bandwidth loss optimization problem, only a heuristic solution is proposed and the moderate fading situations are discussed. A more thorough and comprehensive discussion requires further research on the global optimization algorithms with performance guarantee for traffic allocation under fading conditions. Besides that, we also assume the arrival of PU traffic is memoryless and follows a truncated Poisson distribution. In practice, bursty PU traffic may enable the SU to improve its sensing efficiency further. All these problems will be part of our future work.

ACKNOWLEDGMENT

The ﬁrst author has been supported by China Scholar Council ( CSC ) grant No. 201206155005 and Natural Sci-ence Foundation of Guangdong Province ( CHINA ) grant No. S2011010004773. The work of A. Ephremides has been supported by NSF grant No. CCF1420651 and ONR grant No. N000141410107. The work of D. Yuan has been carried out within European FP7 Marie Curie IOF project 329313.

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2010, pages 1–5.

Song Huang Song Huang received his PhD degree in Communications and Information Systems from South China University of Technology (SCUT) in 2007. He is a lecturer with the School of Computer Science and Engineering, SCUT. From Nov. 2013 to Dec. 2014, he was a visiting researcher at University of Maryland, College Park, MD, USA. His research interests include cognitive communication networks and network information theory.

Anthony Ephremides Anthony Ephremides holds the Cynthia Kim Professorship of Information Tech-nology at the Electrical and Computer Engineering Department of the University of Maryland in Col-lege Park where he is a Distinguished University Professor and has a joint appointment at the Institute for Systems Research, of which he was among the founding members in 1986. He obtained his PhD in Electrical Engineering from Princeton Universi-ty in 1971 and has been with the UniversiUniversi-ty of Maryland ever since. He has been recently named Distinguished University Professor.

He has held various visiting positions at other Institutions (including MIT, UC Berkeley, ETH Zurich, INRIA, etc) and co-founded and co-directed a NASA-funded Center on Satellite and Hybrid Communication Networks in 1991. He has been the President of Pontos, Inc, since 1980 and has served as President of the IEEE Information Theory Society in 1987 and as a member of the IEEE Board of Directors in 1989 and 1990. He has been the General Chair and/or the Technical Program Chair of several technical conferences (including the IEEE Information Theory Symposium in1991, 2000, and 2011,the IEEE Conference on Decision and Control in 1986, the ACM Mobihoc in 2003, and the IEEE Infocom in 1999). He has served on the Editorial Board of numerous journals and was the Founding Director of the Fairchild Scholars and Doctoral Fellows Program, a University-Industry Partnership from 1981 to 1985.

He has received the IEEE Donald E. Fink Prize Paper Award in 1991 and the ﬁrst ACM Achievement Award for Contributions to Wireless Networking in 1996, as well as the 2000 Fred W. Ellersick MILCOM Best Paper Award, the IEEE Third Millennium Medal, the 2000 Outstanding Systems Engineering Faculty Award from the Institute for Systems Research, and the Kirwan Faculty Research and Scholarship Prize from the University of Maryland in 2001, and a few other ofﬁcial recognitions of his work. He also received the 2006 Aaron Wyner Award for Exceptional Service and Leadership to the IEEE Information Theory Society.

He is the author of several hundred papers, conference presentations, and patents, and his research interests lie in the areas of Communication Systems and Networks and all related disciplines, such as Information Theory, Control and Optimization, Satellite Systems, Queueing Models, Signal Processing, etc. He is especially interested in Wireless Networks and Energy Efﬁcient Systems.

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Di Yuan Di Yuan received his MSc degree in Computer Science and Engineering, and PhD degree in Optimization at Linköping Institute of Technology in 1996 and 2001, respectively. He is full professor in telecommunications at the Department of Science and Technology, Linköping University, and head of a research group in mobile telecommunications. At present he is Visiting Professor at University of Maryland, College Park, MD, USA. His current research mainly addresses network optimization of 4G and 5G systems, and capacity optimization of wireless networks. Dr Yuan has been guest professor at the Technical University of Milan (Politecnico di Milano), Italy, in 2008, and senior visiting scientist at Ranplan Wireless Network Design Ltd, United Kingdom, in 2009 and 2012. In 2011 and 2013 he has been part time with Ericsson Research, Sweden. He is an area editor of the Computer Networks journal. He has been in the management committee of four European Cooperation in field of Scientific and Technical Research (COST) actions, invited lecturer of European Network of Excellence EuroNF, and Principal Investigator of several European FP7 and Horizon 2020 projects. He is a co-recipient of IEEE ICC 12 Best Paper Award, and supervisor of the Best Student Journal Paper Award by the IEEE Sweden Joint VT-COM-IT Chapter in 2014. Dr. Yuan is a Senior Member of IEEE.