On Spectral Efficiency of Using Relay with

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Cognitive Radio and Networks Symposium

On Spectral Efficiency of Using Relay with Opportunistic Channel Assignment Chuyi Qian, Yi Ma and Rahim Tafazolli CCSR, T he University of Surrey, Guildford, UK, GU2 7XH Email:{c.qian.y.ma.r.tafazolli}@surrey.ac.uk

Abstract-Relay with opportunistic channel assignment (OCA) is

an intermediate

wireless node,

which forwards

messages

through temporarily unused licensed channels. The spectral effi ciency of OCA relay largely depends on the channel usage. This paper shows that, with a practical model of channel usage, the OCA relay outperforms the relay with fixed channel assignment by up to 0.8 bits/slHz/user. This interesting result is observed through our extensive investigation of the demodulation-and forward relay adopting various resource allocation algorithms, which include the round-robin, joint channel and power alloca tion, best-user selection, and combinations of them. Moreover, the communication delay of all the considered OCA relaying schemes is evaluated through Monte Carlo simulations.

I.

I NT RODUCTION

In the relay-assisted cellular networks, the orthogonal relay forwards received signals through the channels, which are orthogonal to those allocated to the sources. Conventionally, the relays are allocated with dedicated resources (time slots, frequencies, or spreading codes), which if underused result in loss of the spectral efficiency. Alternatively, if the relays are allowed to opportunistically reuse the channels allocated to the sources, less or even no dedicated resources are needed for the relaying uses. This is the concept called relaying with opportunistic channel assignment (OCA). Unlike the concept of cognitive radio and cognitive relay [1]-[3], the OCA relay is not a secondary node but instead one of key players in the primary system. As an advantage, it has perfect knowledge of the channel usage without need of spec trum sensing. In an optimistic case when the channel usage is less than 50%, the OCA relay reuses the unused channels, and consequently improves the spectral efficiency. However in the worst case when the channel usage is 100%, the OCA relay has no resource to help the direct communications. In such situation, the system sutlers performance loss in terms of both the diversity gain and coverage. In practice, the channel usage is a random parameter obeying a certain probability distribution. Then, it would be interesting to know whether or not the OCA relay improves the spectral efficiency. If yes, how much spectral efficiency gain is obtained? This work is motivated by the above questions. To the best of our knowledge, there is very few work so far directly related to the OCA relay. On the other hand, those contributions on opportunistic channel allocation and resource scheduling are useful tools for our investigation. The early work in [4] has investigated the time slot allocation in multi-user, single-relay and single-channel scenario. The

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maximum stable throughput of the proposed protocol has been derived and analysed from an information theoretic view. In [5], an opportunistic scheduling and frequency reuse algorithm is proposed for a relay-based cellular downlink model. It has been shown that a interference-limited spectral efficiency gain can be achieved by a time slotted frequency reuse protocol. A cooperation-based spectrum leasing model for cognitive radio has been proposed in [6], where the primary user shares a fraction of its channel resource with the secondary user in exchange for its assist to the transmission of primary traffic. The performance improvement of both the primary and the secondary systems can be observed. In [7] and [8], it has been proved that power allocation and subchannel assignment are separable to achieve optimal spectral efficiency without the direct source-destination link, for a single-relay orthogonal frequency-division multiplexing (OFDM) system. Main contribution of this paper is our extensive investigation on the spectral efficiency of the OCA relaying network with various resource scheduling schemes to be adopted. The re laying protocol is demodulation-and-forward (DF). The first resource scheduling scheme is the round robin, where the relay helps the source's transmission one after one; the second one is joint channel and power allocation, where the relay allocates the available channels to as many sources as possible; the third one is best-user selection, where the relay always picks the source with the best source-relay link to help. In addition, a combination of the above scheduling schemes with a power allocation algorithm are also included in the investi gation for a fair comparison. All the scheduling schemes are aimed to maximize the spectral efficiency, satisfying different constraints. A practical channel usage model is adopted in the investigation. It is observed that the OCA relaying network efficiently reuse the underused channel resource and improve the spectral efficiency. Our simulation results demonstrate significant performance gain up to 0.8 bits/s/Hz/user of the proposed schemes over conventional fixed relaying schemes. Also, the maximum communication delay of the considered OCA relaying network is evaluated. A trade-otl between the spectral efficiency gain and the maximum communication delay can be observed from the simulation results. II.

S Y STEM MODEL AND P ROBLEM FORMULATION

Fig. 1 is the system model, where a finite number of N sources S communicate over N dedicated orthogonal channels to the destination D with one DF relay R in the middle. The

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� Channel occupied by source _ Channel Occl1pied by relay

�_�

Channell Ch"nnel2

_�� . . .

ChannelN

(3)

' -time .

��.

Fig. l. The system model of the OCA relaying network with multiple sources and channel utilization model for spectrum sharing between the sources and the OCA relay.

sources occupy their own channels while activated and the re lay opportunistically accesses the idle channels to help with the transmission of the activated sources. Let S £ { S1, '" denote the set of all N sources. This model can be practically used to describe the uplink of a cellular network. First, we describe the channel accessing model for the relay ing network. All the channels are orthogonal and slotted, a slot . equaI to a f'rame duratlOn. . Let I [1't1, 1't2 " '" 't t 1 denote IS the channel availability indicator vector, where i � 0, or indicates whether the nth channel is vacant or occupied by the corresponding source at time slot t and n ... , N. Also the expectation of i � over time slot t, E(i �) can represent the probability Pn that the nth source is active and the nth channel is occupied. The activity of each source is indepen dent and identically distributed (i.i.d.), so we can have that Pn=1, P, which is estimated empirically by observing status of the channel at the same time instant, averaged over several days [9]. In this work, we use Bernoulli process to describe the channel availability that allows us to consider a fixed duration time slot with a binary on/off decision on the source activity. The probability of channel availability can then be expressed as:

,SN}

=

·

·

·

N

=

=

. .N

1,2,

1

=

ifi � ifi �

= =

1.

0,

(1)

Pr(Nidle

=

k)

=

where Xn denotes the transmitted symbols from the nth source and Vnd is the AWGN with zero mean and variance No. Meanwhile, the signal received at the relay can be expressed as: (4) where Vnr is the AWGN for the nth S-R link. We assume that the relay has an infinite length buffer that can restore the received signal from the sources. If there is one or more idle channels, Nidle ::.:: the relay decodes Ynr and re-encodes it as Xr, then transmits Xr to the destination. Thus, the received signals from the relay at the destination through the lth R-D link for the nth source are given by:

1,

(5) where gnl is the channel gain of the R-D link when the nth source is assigned the lth relaying channel, and Vnl is the AWGN part for the corresponding R-D link. At the destination, a posteriori probability of the received signal is calculated and maximum a posteriori probability (MAP) algorithm is implemented to combine the two signals for detection and decoding. The system switches between direct transmission and DF relaying mode depending on the channel availability for the OCA relay. A fundamental performance measurement of the communication network is spectral efficiency. Throughout the paper, the spectral efficiency is defined as the average data rate per Hertz per user. It is considered that sources employ a modulation set with the size of !vIs bits and the relay with !vIr bits. We assume that the symbol duration is fixed to T for all the transmissions and the corresponding Nyquist bandwidth W �. According to the definition, the overall spectral efficiency of the single-user DF relaying network can be expressed as: =

It is assumed that the status of channel usage varies slowly and all the transmission can be finished before the channel usage status changes. It is also assumed that the channel usage is modelled as i.i.d .. To characterize the channel availability, we now define a discrete random variable Nidle representing the total number of idle channels in S. Obviously, Nidle £ N L:=1i�. Then the probability mass function for Nidle is given by:

(�)p(N-k)(1 - p)k

communication channels between any two nodes in the net work (i.e., Sn-D, Sn-R, R-D channels) are assumed to be independent block Rayleigh fading with the notation of hnd, hnr, gnl, respectively, and v is the additive white Gaussian noise (AWGN) part. When the sources transmit a packet at time slot t, the received signal at the destination from the source can be expressed as:

(2)

Next, we describe the transmission between the nodes over time slot t. The modulated symbols, based on the channel information feedback at source, are transmitted through the channel using energy Es for each symbol. The wireless

7)DF

=

B bits/s/Hz W(BT/ks + BT/kr)

(6)

where B is the number of bits in one frame, ks log 2 ( .!VIs) and kr log 2 (Mr) are the number of bits per symbol (BPS) for the source and relay node respectively. Since the relay can transmit instantaneously with the source using the idle channels, the time consumed by the relay transmission can be neglected. For the above OCA relaying system, we employ the same adaptive modulation scheme as in [10] to further improve the spectral efficiency subject to a given BER and individual trans mit power constraint at the relay (PR), the source transmits

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with fixed power (Ps). In this paper the optimization goal is to maximize the overall spectral efficiency by allocating the available channels and power at the relay node. Let T)n represent the spectral efficiency when the nth source is activated, the objective function can be written as: N

max

2..: T)n

n=l

s.t. BERn � BERtarget, N

2..: i;

=

n=l

Nid1e

B. Joint Channel and Power Allocation

(7)

Nidk

2..: PI

�

1=1

PR

where BERn is the overall bit error rate of the nth source transmission. BERtarget is a predetermined BER threshold for the adaptive modulation, Pz is the power allocated to the lth idle channel at the relay. III.

P ROT OCOLS DESCRIP TION

In this section, several resource allocation schemes are investigated to show the spectral efficiency improvement for the proposed OCA relaying schemes, which include round robin scheduling, joint channel and power allocation, best-user selection. A. Round Robin Relaying

The first protocol investigated is round-robin relaying with OCA (ORR). Round-robin (RR) is an algorithm that allows each user in a network to have a fair share of the network resource. It has been proved that perfect fairness can be achieved by RR algorithm [11]. Within this protocol, in every time slot, only the information from one activated source is forwarded by the relay to enjoy the diversity gain. Other activated sources can only transmit with its own assigned channel without diversity gain. We assume that the utilization of the channels remain the same for one relaying round which means that Nidle is the same for one transmission round for all the sources and changes independently for the next round. In this case, all the activated sources in one transmission round are allocated the same resource from the relay. Then the objective function in (7) can be modified as:

max

T)n . Pr (i; 2" 1) s.t. BERn � BERtarget, N

2..: i;

=

n=l

2..: PI 1=1

�

Nidle

Following are some important remarks on the above proto col. According to the above description, in the scenarios that the number of idle channels is larger than that of the activated sources, a delay is introduced since sources have to wait for their turn due to the limited resources at the relay node. This is because that the relay can only offer the diversity gain to one source at one time slot. Therefore, the delay and the utilization of channels are interacting.

(8)

The second investigated protocol is joint channel and power allocation relaying (JCPR) , where multiple access can be realized by providing each source with a fraction of the number of channels available at the relay. In such a system, each source experiences a different channel gain when a different channel is assigned to it. When source n is assigned channel l at the relay, the channel gain and the total noise power spectral density for the R-D link are denoted as gnl and Vnl, respectively. The channel SNR function for user n and lth available channel can be indicated by:

Ani

Ignl12 Vnl

(9)

With the Shannon capacity formula for the Gaussian channel [13], we know that the spectral efficiency is related to the receive SNR. Let T)n (Ani) denote the overall spectral efficiency for the nth source assigned with lth relaying channel, then the objective function can be modified as follows:

n=l 1=1 s.t. BERn � BERtarget, N

2..: i;l � Nidle

n=l

for

all l,

for

all n,

(l0)

Nidk

2..: Pnl � PR 1=1

where W is an (N - Nidle) X Nid le matrix of which el ements consist of channel allocation index, i;l' P is an (N - Nid le ) X Nid le matrix of allocated power for source n to the lth channel at the relay. The summed spectral efficiency in (l0) is neither convex nor concave with respect to {W, P}. Thus, obtaining a globally optimum solution is rather difficult. The Hungarian method [14] can be used to solve the channel allocation problem meanwhile the power allocation is carried out with waterfilling algorithm [15]. The waterfilling power allocation solution can be expressed as:

PR PI

It has been well recognized that the exact form of BER is very complex and the closed-form expression of the optimal solu tion of (15) is intractable. Alternatively, we use the exhaustive searching algorithm [12] to solve the optimization problem.

=

1

=

[K--] Ani

+

(11)

where K represents the water-level of the lth channel at the relay for the nth source. Then the spectral efficiency of the nth source with waterfilling power allocation can be expressed

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N�idl('

7]n

=

L 7]n (P1Anl)

(12)

1=1

By adaptively assigning vacant channels of various fre quencies, we can take advantage of channel diversity among sources in different locations, which is called multiuser diver sity. Define a (N - Nid1e) X Nid1e assignment matrix A, each component represents whether or not the channel is assigned to a source:

Xnl

=

{ �:

if source n is assigned the channel Z otherwise .

transmitted by the relay to achieve diversity gain. In BSR, the sources are sorted regarding to the spectral efficiency given in (6). After the "best" source is selected, the relay dedicates all the available resources to forward the information from the selected source. The rest of the sources transmit with direct transmission mode without the aid from the relay. Then the objective function in (7) can be modified as:

max 7]n

max(7]1, ... , 7]N)

S.t. BERn