# Resource Allocation in a Cognitive Radio System with

Authors: Tao Qin; Cyril Leung; Chunyan Miao; Zhiqi Shen
Journal: Journal of Electrical and Computer Engineering
 (2010)

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## Abstract

Cognitive radio (CR) is a promising concept for improving the utilization of scarce radio spectrum resources. Orthogonal frequency division multiplexing (OFDM) is regarded as a technology which is well matched for CR
systems. It is shown that channel estimation errors can result in a severe performance degradation
in a multiuser OFDM CR system. A simple back-off scheme is proposed, and simulation results are provided which show that the proposed scheme is very effective in mitigating the negative impact of channel estimation errors.


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## Body

## 1. Introduction

It is believed that the cognitive radio (CR) concept can be used to greatly improve spectral utilization by allowing secondary (unlicensed) users (SUs) to use frequency bands not currently being used by the primary (licensed) users (PUs) in a certain location [1, 2]. Orthogonal frequency division multiplexing (OFDM) is regarded as a good modulation scheme for CR systems due to its flexibility in allocating resources among SUs [3]. In CR systems, it is important to manage mutual interference problems effectively since primary and secondary users will often simultaneously use adjacent bands.The problem of power, bit, and subchannel loading for multiuser OFDM CR systems has been studied in [4], in which it is assumed that perfect channel state information is available. In practice, this assumption is often unrealistic, and it is therefore important to study the performance degradation due to imperfect channel state estimation. In [5], the effect of partial channel information in a non-CR multiuser MIMO-OFDM system is discussed. However, the effect of mutual interference which would arise between primary and secondary users in a CR system is not addressed.A reduced complexity (RC) resource allocation (RA) scheme is proposed for a multiuser OFDM CR system in [4], and it is shown that the scheme provides good performance when perfect channel estimates are available. In this paper, the performance degradation due to imperfect channel state estimation for the RC RA scheme is shown to be quite severe. A simple back-off scheme is proposed and found to be very effective in reducing this degradation.


## 2. System Model

The system model used in this paper is the same as in [4] and is summarized here for the convenience of the reader. We consider the problem of allocating resources on the downlink of an OFDM CR system in which a CR base station (CRBS) serves one primary and M secondary users. The PU band is Wp Hz wide. On each side of the PU band, there are K/2 OFDM subchannels, each of width Ws Hz. As the CRBS can transmit simultaneously to the PU and SUs, the PU signal can cause interference to the SUs and vice versa.The baseband power spectral density (PSD) of thekth subchannel SU signal is modeled as [6]
(1)Φk(f)=PkTs(sinπfTsπfTs)2,
where Pk is the transmit power of the kth subchannel signal and Ts is the symbol duration. The interference power introduced by this signal into the PU band is
(2)Ik(dk,Pk)=PkIFk,
where
(3)IFk=∫dk-Wp/2dk+Wp/2|gk|2Ts(sinπfTsπfTs)2df
is the interference factor for the kth subchannel. In (2) and (3), gk is the channel gain from the CRBS to the PU for the kth subchannel, and dk is the spectral distance between the kth subchannel and the center frequency of the PU band.The interference power introduced by the PU signal into thekth subchannel band at SU m is(4)Smk(dk)=∫dk-Ws/2dk+Ws/2|hmk|2ΦPU(f)df,
where hmk is the subchannel k gain from the CRBS to SU m, and ΦPU(f) is the PSD of the signal destined for the PU.It is assumed that each subchannel can be used for transmission to at most one SU at any given time. LetPmk denote the transmit power allocated to subchannel k of SU m. From [7], the maximum number of bits in a symbol transmitted on this subchannel is set to(5)bmk=⌊log2(1+|hmk|2PmkΓ(N0Ws+Smk))⌋,
where ⌊·⌋ denotes the floor function, N0 is the one-sided noise PSD, and Smk is given by (4). For convenience, the parameter Γ is set to unity in the remainder of this paper.Letamk∈{0,1} be a subchannel allocation indicator, that is, amk=1 if and only if subchannel k is allocated to SU m. Our objective is to maximize the total bit rate for all SUs subject to total transmit power, fairness, and PU interference constraints. Specifically, the optimization problem is expressed as follows:
(6)maxWs∑m=1M‍∑k=1K‍amkbmk
subject to
(7)amk∈{0,1},∀m,k(8)∑m=1Mamk≤1,∀k,(9)Pmk≥0,∀m,k,(10)∑m=1M‍∑k=1K‍amkPmk≤Ptotal,(11)∑m=1M∑k=1K‍amkPmkIFk≤Ith,
where Ptotal is the total SU power budget, and Ith is the PU's maximum tolerable interference power. Inequality (8) follows from the assumption that a subchannel can be allocated to at most one SU. Inequalities (10) and (11) correspond to the power and interference constraints, respectively. The nominal bit rate weight (NBRW) for SU m is denoted by λm so that λm/∑i=1Mλi is the fraction of the total number of SU bits loaded that is to be fairly allocated to SU m. It is also convenient to denote the total number of bits per symbol period allocated to SU m by Bm≜∑k=1Kbmk and define the total bit rate, Rm, of SU m as Rm≜WsBm. The total bit rate for all SUs is Rs≜∑m=1MRm.Channel state estimation errors are modeled as follows: leth denote the actual (complex) gain of a channel. This channel could correspond to the kth OFDM subchannel from the CRBS to SU m or to the PU. For simplicity, all channels are assumed to be independently Rayleigh faded, that is, their complex gains are drawn from circularly symmetric, complex Gaussian distributions. The estimated (complex) channel gain is given by
(12)ĥ=h+e,
where e is the channel estimation error. For the simulation results presented below, e is assumed to be the outcome of an independent, circularly symmetric, complex Gaussian random variable.The impact of channel estimation errors on the total SU bit rate,Rs, can be described as follows. The maximum bit rate, Rmk≜Wsbmk, that can be achieved for SU m on subchannel k depends on the channel gain, hmk, the transmit power, Pmk, and the total interference-plus-noise power, as shown in (5). However, the CRBS knows only ĥmk and not hmk. It thus calculates an estimated maximum transmit bit rate, R̂mk. If R̂mk<Rmk, then the opportunity for a higher transmit bit rate is lost. On the other hand, if R̂mk>Rmk, then R̂mk exceeds the channel capacity and the actual achieved transmit bit rate is zero. Therefore, the channel estimation errors, if not carefully taken into account in the design of the RA scheme, can result in a severe throughput degradation.


## 3. A Scheme for Mitigating  Throughput Degradation

In order to reduce the overall throughput degradation caused by the use of inaccurate channel gain values, we introduce a back-off factor,BG,0≤BG≤1, such that the RA algorithm uses BG×|ĥmk|2 instead of |ĥmk|2 as the channel power gain in calculating the estimated maximum transmit bit rate, R̂mk. Therefore, (4) and (5) are modified accordingly as
(13)Ŝmk(dk)=BG∫dk-Ws/2dk+Ws/2|ĥmk|2ΦPU(f)df,(14)b̂mk=⌊log2(1+BG|ĥmk|2PmkΓ(N0Ws+Ŝmk))⌋.LetIPU≜∑k=1KPkIFk be the total interference power introduced into the PU band by SU signals. To control the probability, Po, that IPU exceeds Ith, the proposed scheme uses a second back-off factor, BI, such that the RA algorithm uses BI×Ith instead of Ith as the target PU interference power threshold value. A lower value of Po generally requires a lower BI value.From (14), the incremental power required for transmitting one bit to SU m on subchannel k is given by
(15)ΔPmk=N0Ws+ŜmkBG|ĥmk|22b̂mk.
From (2) and (15), the incremental interference power generated by such a transmission to the primary user is
(16)ΔImk=ΔPmkIFk.The MP, MI, and RC RA algorithms were proposed in [4] to improve the throughput in a multiuser OFDM-based CR system. In this paper, modified versions, referred to as m-MP, m-MI, and m-RC, are proposed to mitigate the negative impact of channel estimation errors. Pseudocode listings of these three algorithms are provided below. In the algorithms, B̂m is the estimated total number of bits allocated to SU m and PSU is the total transmit power of SUs.The m-MP algorithm is used to determine the interference power,IMP, introduced into the PU band if, at each bit loading, we choose the subchannel which minimizes the incremental power needed for the selected SU.Algorithm m-MP
(1) Step 1—Initialization  (a)
SetPSU=0,IMP=0.(b)
SetB̂m=0 for m∈{1,2,…,M}.(c)
Setb̂mk=0, and calculate ΔPmk as in (15), for m∈{1,2,…,M} and k∈{1,2,…,K}.
(2) Step 2(a)
Determinem*=argminmB̂m/λm; ties are first broken in decreasing order of λ then randomly.(b)
DeterminekP=argminkΔPm*k.(c)
IfPSU+ΔPm*kP≤Ptotal, perform the following updates: B̂m*=B̂m*+1,PSU=PSU+ΔPm*kP,  b̂m*kP=b̂m*kP+1, calculate ΔPm*kP as in (15), ΔPmkP=∞,∀m≠m*, and go to step 2(a).(d)
IfPSU+ΔPm*kP>Ptotal, then set m* to be the user with the next higher value of B̂m/λm and go to step 2(b). Stop if all users have been considered.Similarly, the m-MI algorithm is used to determine the total power,PMI, required for transmitting to the SUs if, at each bit loading, we choose the subchannel which minimizes the incremental interference power introduced into the PU band.Algorithm m-MI
(1) Step 1—Initialization  (a)
SetPMI=0,IPU=0.(b)
SetB̂m=0 for m∈{1,2,…,M}.(c)
Setb̂mk=0 and calculate ΔImk as in (16), for m∈{1,2,…,M} and k∈{1,2,…,K}.
(2) Step 2(a)
Determinem*=argminmB̂m/λm; ties are first broken in decreasing order of λ then randomly.(b)
DeterminekI=argminkΔIm*k.(c)
IfIPU+ΔIm*kI≤BIIth, perform the following updates: B̂m*=B̂m*+1, IPU=IPU+ΔIm*kI,PMI=PMI+ΔIm*kI/IFkI, b̂m*kI=b̂m*kI+1, calculate ΔIm*kI as in (16), set ΔImkI=∞,∀m≠m*, and go to step 2(a).(d)
IfIPU+ΔIm*kI>BIIth, then setm* to be the user with the next higher value ofB̂m/λm and go to step 2(b). Stop if all users have been considered.The relative importance of the SU power and PU interference is measured using(17)VP=PMI-PtotalPtotal,VI=IMP-BIIthBIIth,
respectively. Note that VP is negative when Ptotal>PMI, and VI is negative when BIIth>IMP.The m-RC algorithm usesVI and VP as follows.Algorithm m-RC
(1) Step 1—Initialization(a)
SetPSU=0,IPU=0.(b)
SetB̂m=0 for m∈{1,2,…,M}.(c)
Setb̂mk=0, and calculate ΔPmk as in (15) and ΔImk as in (16), for m∈{1,2,…,M} and k∈{1,2,…,K}.
(2) Step 2(a)
Determinem*=argminmB̂m/λm; ties are first broken in decreasing order of λ then randomly.(b)
DeterminekP=argminkΔPm*k.(c)
DeterminekI=argminkΔIm*k.(d)
ComputeX=VI(ΔPm*kPIFkP-ΔIm*kI)/ΔIm*kI and Y=VP(ΔIm*kI/IFkI-ΔPm*kP)/ΔPm*kP(e)
IfX≥Y, set k*=kI; otherwise set k*=kP.(f)
IfPSU+ΔPm*k*≤Ptotal and IPU+ΔIm*k*≤BIIth, perform the following updates: B̂m*=B̂m*+1,b̂m*k*=b̂m*k*+1,IPU=IPU+ΔIm*k*,PSU=PSU+ΔPm*k*, calculate ΔPm*k* as in (15) and ΔIm*k* as in (16), set ΔPmk*=∞,ΔImk*=∞,and∀m≠m*, and go to step 2(a).(g)
IfPSU+ΔPm*k*>Ptotal or IPU+ΔIm*k*>BIIth, then set m* to be the user with the next higher value of B̂m/λm, and go to step 2(b). Stop if all users have been considered.(h)
Calculatebmk as in (5),Ifb̂mk>bmk, then set bmk=0. Otherwise, set bmk=b̂mk. Update Bm.Good values for the back-off factors,BG and BI, are chosen as follows  (1)
For given values ofPtotal and Ith, both Po and the throughput, Rs, increase with BI, whereas BG has little effect on Po. We therefore choose to use the largest value of BI which can satisfy the Po requirement.(2)
Once the value ofBI is chosen, we determine the throughput for different values of BG and select the BG value which yields the highest throughput.


## 4. Results

Computer simulations were run with the proposed m-RC RA algorithm assuming that the PU signal is an elliptically filtered white noise process and using the same parameter values as in [4]. In addition, let Ve denote the variance of the real (or imaginary) part of the channel estimation error in (12).Figure1 shows the total SU bit rate, Rs, as a function of Ptotal with Ith=6×10-6 W for two different values of Ve and three cases: (1) perfect channel estimation, (2) channel estimation errors with the RC RA algorithm in [4], and (3) channel estimation errors with the proposed m-RC RA algorithm. It can be seen that in the presence of channel estimation errors, the RC RA algorithm in [4] shows a big drop in Rs compared to the perfect channel estimation case. Furthermore, Po for the RC RA algorithm in [4] can be as high as 6%. Using the m-RC RA algorithm with BG=0.84 and BI=0.815, the loss relative to the perfect channel estimation case is small, and Po is negligibly small. The results show that the proposed m-RC RA is quite robust against channel estimation errors.Figure 1
Total bit rate,Rs, as a function of Ptotal with Ith=6×10-6W.Figure2 shows Rs for the m-RC RA algorithm as a function of Ptotal for different values of Ith. It was found from the simulation results that a BG value of 0.84 is near-optimal for maximizing Rs. In this figure, BI was set to 0.905 to achieve a Po of 10-3. As expected, Rs increases with Ith. For comparison, the perfect channel estimation curves are also included in Figure 2. It can be observed that the Rs value for m-RC RA is less than 5%  lower.Figure 2
Total bit rate,Rs, as a function of Ptotal for the m-RC RA algorithm with Po=10-3.


## 5. Conclusion

A simple back-off scheme was proposed to counter the deleterious effect of channel estimation errors in a multiuser OFDM CR system. Simulation results show that the proposed scheme can greatly reduce the loss in the total bit rate to SUs.



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*Source: 419430-2010-05-23.xml*