Goodput-maximizing Resource Allocation in
Cognitive Radio BIC-OFDM systems with DF Relay
Selection
Jeroen Van Hecke
1, Paolo Del Fiorentino
2, Riccardo Andreotti
2, Vincenzo Lottici
2,
Filippo Giannetti
2, Luc Vandendorpe
3, and Marc Moeneclaey
1Abstract—We propose a novel resource allocation (RA) strategy for a cognitive radio packet-oriented bit-interleaved coded orthog-onal frequency division multiplexing (BIC-OFDM) system with decode-and-forward (DF) relays. The aim of the RA is maximizing the goodput (GP) of the source-relay-destination link, which is the number of information bits correctly received at the destination node per unit of time. Therefore, we derive an accurate analytic approximation for this figure of merit, which allows us to find the optimum constellation size, code rate and energy allocation per subcarrier. Further, this expression also serves as a novel relay selection criterion. Finally, we validate the proposed RA method, and compare its performance to capacity-maximizing algorithms through numerical simulations.
Keywords—Cognitive radio, Cooperative network, OFDM, Decode-and-forward, Goodput.
I. INTRODUCTION
Wireless communication systems have shown a significant development in the last two decades, which still continues unabated. This evolution tries to solve the limitations of the current wireless networks, in order to support the increasing amount of traffic. Hence, the future wireless communication networks have to provide services with higher data rates, a wider area coverage, a higher quality of service and more efficient use of transmission resources. Cognitive radio (CR) [1], [2] has been proposed in order to increase spectral efficiency. This technology is employed by unlicensed or secondary users (SUs) that adapt their parameters to transmit over sections of spectrum owned by licensed or primary users (PUs), without harming the quality of service of the latter. In addition, the combination of multicarrier orthogonal frequency division multiplexing (OFDM) transmissions, efficient channel coding techniques such as bit interleaved coded modulation (BICM) [3] and resource allocation (RA) mechanisms [4] can lead to satisfactory performances even when operating in a harsh fading environment. RA consists of the adaptation of transmission parameters, such as energy per subcarrier, constellation size and code rate, to the actual state of the
1
Department of Telecommunications and Information Processing (TELIN), Ghent University, 9000 Ghent, Belgium.
2
Department of Information Engineering, University of Pisa, I-56122 Pisa, Italy.
3
Institute of Information and Communication Technologies, Electronics and Applied Mathematics (ICTEAM), Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium.
channel. In order to make this possible the transmitter must have knowledge of the current channel state information (CSI). The CSI available at the transmitter is often imperfect, due to for example the presence of noise, and outdated, because of the time-varying channel. The problem of RA in presence of imperfect CSI is addressed in many works as in [5], where the fundamental limit imposed on the information rate of an OFDM system is analyzed. The work [6] focuses on adaptive modulation in OFDM systems quantifying the system limits in terms of bit error rate (BER) with both perfect and imperfect CSI and points out how the performance can be improved considering the use of multiple channel estimates. [7] proposes an adaptive modulation and coding (AMC) scheme for a BIC-OFDM system that is robust against outdated CSI.
In this paper, we evaluate a RA technique that selects the optimal constellation size, code rate and transmission energy, for a packet-oriented CR BIC-OFDM systems with imperfect CSI. We extend the cognitive scenario as in [8], to a decode-and-forward (DF) relaying scheme [9]. The majority of the literature develops RA strategies that use capacity or mutual information as their respective performance metric (see [10] and references cited therein); in addition [11] and [12] present a RA technique for BIC-OFDM and MIMO-BICM systems, respectively. Instead in our work, we use a different metric called goodput (GP) [13], which is the number of correctly received information bits per unit of time. The GP metric is more adequate to quantify the actual performance of packet-oriented multicarrier systems and it depends on the allocated energy per subcarrier, modulation and coding schemes. We approximate the GP by using an effective SNR mapping (ESM), which describes the error performance of the system by means of a single scalar value [13].
Several novel results are presented. First, we define a GP metric for the dual-hop transmission, which is able to evaluate the total GP performance between the source and the destination node. Second, a novel relay selection criterion based on the GP metric is introduced. Third, our link perfor-mance prediction (LPP) combines the ESM method [13] with outdatedand imperfect CSI at the transmitter [14], in order to obtain the predicted GP (PGP). This PGP function represents the objective function of our RA problem. This extends the work in [15] to a dual-hop scenario. Finally, for validation purposes we compare our technique with a RA technique that uses the capacity as an objective function.
net-work and the BIC-OFDM system, along with the channel model and the interference constraints of the SU network. In section III we formulate and solve the RA problem together with the relay selection. The performance of these algorithms is compared to the capacity-maximizing RA algorithm in section IV. We also investigate the performance as a function of the imperfection of the CSI. The most important conclusions are presented in section V.
Notations. Expectation operator is E[·], matrices (vectors) are in upper (lower) case bold, [·]T is the transpose operator,
x ∼ CN (0, Σ) is a circular symmetric zero-mean Gaussian complex random variable (RV) with covariance matrix Σ and the matrix I denotes the identity matrix. The Kronecker product is denoted⊗.
II. SYSTEMMODEL
A. Cooperative Cognitive Radio Network
We consider a cooperative network in a CR scenario. The SU network consists of a SU transmitter (ST), a SU receiver (SR) and M DF relay nodes (RNs); the ST operates in the same bandwidth as NPU PUs according to the underlay paradigm
[2]. We assume that there is no direct link between the ST and the SR, which means that the transmission of a data message always occurs in two time slots. In the first time slot, the ST sends the data message to the RNs. In the second time slot, only the selected RN will decode and forward the received information to the SR. During this process, the ST and the RN must keep the interference to the PUs below a given interference threshold.
B. BIC-OFDM system
The data message is transmitted from the ST to the RN, and from the RN to the SR by means of a packed-oriented BIC-OFDM communication system consisting of N subcar-riers within a bandwidth B [13]. A transmission packet is divided into Np bits of payload and NCRC bits for the cyclic
redundancy check (CRC) section, and has a total length of Nu = Np+ NCRC bits. This packet is encoded by a
convo-lutional encoder with rate r ∈ Dr. In the following step, the
coded sequence of Nu/r bits are randomly interleaved. The
resulting bit sequence is then Gray-mapped into Ns symbols
of a unitary-energy QAM constellation. These symbols are transmitted through a frame ofNOFDM = ⌈Ns/N ⌉ consecutive
OFDM symbols over a frequency-selective fading channel, which is assumed to be stationary for the whole packet transmission duration. The duration of a OFDM symbol is equal to Ts. The received sample of the OFDM symbol on
subcarriern ∈ N , {1, . . . , N} is
zn,pEnHnxn+ wn, (1)
where En is the transmit energy on the nth subcarrier, Hn
is the channel coefficient, xn is the constellation symbol
transmitted on subcarriern corresponding to mn∈ Dmcoded
bits and E[|xn|2] = 1, and wn ∈ CN 0, σ2w is the ambient
noise. Further we assume that the total transmit energy is limited
1 N
XN
n=1En≤ S, (2)
where S is the average allocated energy per subcarrier. The received signal-to-noise ratio (SNR) is defined as
γn,
En|Hn|2
σ2 w
. (3)
Let us define Γ , [γ1, . . . , γn] for further use. Finally, the
receiver first performs soft metric evaluation on the received symbols, then de-interleaves and decodes the packet. We assume that for both the link between the ST and the selected RN, and the link between the selected RN and the SR we can choose a different transmission mode (TM) φ , {m, r} ∈ DN
m× Dr, with m , [m1, . . . , mN]T and energy allocation
E, [E1, . . . , EN]T.
C. Channel Model
The channel between any two nodes during the transmission of the ith OFDM symbol is modeled as a time-varying multipath channel with impulse response h(m, i). Without any loss of generality, we can assume that h(m, i) = 0 for m < 0 and for m > ν. The samples h(m, i) (0 ≤ m ≤ ν) are assumed to be independent circular symmetric zero-mean Gaussian complex RVs. According to Jakes’ model [16], we take E[h(m, i + j)h∗(m, i)] = J
0(2πfdjTs)σ2m, where
J0(x) represents the zeroth-order Bessel function of the first
kind, and fd denotes the Doppler spread. For later use,
we define1 R
h , diag(σ20, . . . , σ2ν) and the vector h(i) ,
[h(0, i), . . . , h(ν, i)]T.
Defining the Fourier matrix F∈ CN ×(ν+1) as
Fk,l, e−j2π(k−1)(l−1)/N, k = 1, . . . , N ; l = 1, . . . , ν + 1, (4) the frequency response of the channel can be written as H(i) = Fh(i). The kth component of H(i) denotes the channel gain seen by the kth subcarrier in the ith OFDM symbol.
The transmitting nodes require some form of CSI in order to perform the RA algorithm. We assume that the transmitter only has the followingP delayed and noisy estimates available [17]
˜
H(i − pD) = H(i − pD) + ˜e(i − pD), p = 1, . . . P, (5) where˜e(i) ∼ CN (0, σe2IN). We have defined σe2,σ2w
Ep, where
Ep denotes the energy per pilot symbol. As shown in (5), the
transmitter receives an estimate everyD OFDM symbols. The transmitter will then use the previous P channel estimates to make a linear minimum-mean-square-error (MMSE) prediction
ˆ
h of the channel. This predicted channel ˆh is linked to the actual channel h(i) as follows [14]:
h(i) = ˆh(i) + e(i), (6)
1Note that if we have a number of paths L < ν + 1, only L diagonal
whereˆh(i) ∼ CN (0, Rh−Re) and e(i) ∼ CN (0, Re), where Re= Rh− Rhz PR −1 zPzPR H hzP. (7)
Introducing the matrix J ∈ CP ×P with entries J k,l ,
J0(2πfdDTs(k − l)), k = 1, . . . , P ; l = 1, . . . , P , the
cor-relation matrices can be written as follows Rhz
P = [J0(2πfdDTs), . . . , J0(2πfdP DTs)] ⊗ Rh, (8)
RzPzP = J ⊗ Rh+ IP ⊗ (FHF)−1σ2
e. (9)
The predicted channel gains for the subcarriers are the compo-nents of the vector ˆH(i) = Fˆh(i). The index i will be omitted in the sequel for simplicity.
D. Interference Constraint
The ST and the selected RN transmit in the same bandwidth as NPU PUs. Therefore, the ST and the RN must keep the
interference to the PU receivers below a given interference threshold Iq,q ∈ Q , [1, . . . , NPU]T, this value depends on
the amount of interference each PU is able to accept. We define the average interference from ST and the RN to the qth PU receiver as the following conditional expectation
Il,q, E " N X n=1 El,n|Hl,q,n|2 n ˆHl,q,m, m = 1, ..., N o # , = N X n=1 El,nE h |Hl,q,n|2 n ˆHl,q,m, m = 1, ..., N oi , = N X n=1 El,n ˆ Hl,q,n 2 + (FReFH)n,n , (10)
where, for the last step, we have used the Fourier transform of (6). Further, Hl,q,n and ˆHl,q,n represent the actual channel
coefficient and the predicted channel coefficient, respectively from ST to theqth PU receiver when the index l = 1, or from the RN to theqth PU receiver when l = 2.
E. PGP function and LPP approach
A practical performance metric is the GP, which is the number of correctly received information bits per unit of time [18]. Ideally, the transmitter should be able to optimize the GP by a proper selection of the transmission parameters. However, because the transmitter only has outdated and imperfect CSI available, the PGP will be optimized instead. The PGP is defined as the GP which would be achieved when the actual channel H equals the predicted channel ˆH. The PGP function depends on the packet error rate PERBIC-OFDM(φ, Γ), which
is difficult to evaluate analytically in a coded OFDM system. Therefore we will base our LPP method on the κESM ap-proximation proposed in [13]. By using this approach, we are able to compress the vector of the SNRs Γ into a scalar value called effective SNR γeff, such that the following relationship
holds (within a small approximation error)
PERAWGN(r, γeff) ∼= PERBIC-OFDM(φ, Γ), (11)
where PERAWGN(r, γeff) is the packet error rate (PER) for an
equivalent coded BPSK system with code rater operating over an additive white Gaussian noise (AWGN) channel with SNR equal to γeff. The κESM expression is calculated as follows
[13] γeff, − log " 1 PN j=1mj · N X n=1 αn· e−ˆγnβn # , (12) whereαnandβnare constant values depending onmn, which
is the number of coded bits per constellation symbol on the nth subcarrier, and ˆγn is the predicted SNR that is defined as
ˆ γn, En ˆ Hn 2 σ2 w . (13)
Because the actual SNRs are not known to the transmitter, we have used the predicted SNR for each subcarrier in the formula ofγeff(12). This method is different from the original
formulation of theκESM where Γ is assumed to be perfectly known by the transmitter.
Now, the PGP function can be derived as the ratio of the number of correctly received information bits and the actual transmission time. If we normalize the PGP function by dividing by the actual bandwidthN/Tswe get
ζ(φ, E) = Ts N
Np· (1 − PERAWGN(r, γeff)) NuTs rPnmn , = Np N Nu rX n
mn· (1 − PERAWGN(r, γeff)). (14)
This is the result for a single hop, we now consider the for-mula for our DF network. If we first introduce the probability of a packet error from the ST to the SR
PERs,r,dAWGN(r1, r2, γ1,eff, γ2,eff) = PERAWGN(r1, γ1,eff)
+ (1 − PERAWGN(r1, γ1,eff)) · PERAWGN(r2, γ2,eff), (15)
we can write the normalized PGP (in bits/s/Hz) of the DF network as follows
ζ(φ1, φ2, E1, E2) =
Ts
N
Np(1 − PERs,r,dAWGN(r1, r2, γ1,eff, γ2,eff)) NuTs r1Pnm1,n + NuTs r2Pnm2,n , = Np N Nu
(1 − PERs,r,dAWGN(r1, r2, γ1,eff, γ2,eff)) 1 r1Pnm1,n + 1 r2Pnm2,n , (16) whereφ1= {m1, r1}, φ2= {m2, r2}, E1and E2respectively
denote the TM for the ST-RN and RN-SR link and the transmit energy per symbol for the ST-RN and RN-SR link. Note that we have implicitly assumed that the duration of the first time slot can be different from the second time slot. The PGP function (16) is the objective function of the RA problem presented in the next section.
For the simulation results we are interested in the average performance of the described algorithms, which is described by the following average PGP (APGP) metric
where the average is taken over the distribution of the predicted channel.
III. RATECHNIQUE IN THECRDUAL-HOP SCENARIO
In this section the RA algorithm is derived for the system model illustrated in Sect. II. In the first part, we introduce the considered RA problem with the corresponding solution, while in the second part we introduce the criterion of the relay selection.
A. RA problem formulation and solution
In this section, a RA optimization problem (OP) is for-mulated that tries to find the TM and the energy allocation per subcarrier for both the ST and the selected RN that maximizes the total PGP (16), so that a robust and spectrally-efficient transmission over frequency selective channels can be obtained. Let us define the optimal TM and energy allocation vector that are the transmission parameters for the generic link l ∈ {1, 2} as
φ∗l , {m∗l, r∗l}, (18)
E∗
l , [El,1∗ , . . . , El,N∗ ]T, (19)
where m∗l = [m∗l,1, · · · , m∗l,N]T is the vector of the optimal
number of bits per subcarrier andr∗
l is the optimal code rate.
The PGP defined in (16) represents the objective function of the RA problem over which the transmission parameters are optimized. The RA problem will be divided into two consecutive steps:
• given a generic TM φl(l = 1, 2), find the optimal energy
allocation vector E∗l (l = 1, 2), • the best TM φ∗
l (l = 1, 2) is selected in order to
maximize the total PGP metric.
Optimal energy allocation. It follows from (16) that the total PGP depends on the energy allocation vector El (l = 1, 2)
only through the effective SNR γl,eff(φl, El) (l = 1, 2).
Because the PERs,r,dAWGN will only decrease as a function of γl,eff(φl, El) (l = 1, 2), the optimal energy allocation vector
E∗
l (l = 1, 2) can be found for a fixed value of φl (l = 1, 2),
by maximizingγl,eff(φl, El).
So we can introduce for each link the following independent OP E∗l = arg max El {γl,eff(φl, El)}, (20) = arg min El {Fl(ml, El)}, (21) s.t. 1 N XN n=1El,n≤ S, El,n≥ 0, ∀n ∈ N , Il,q≤ Iq, ∀q ∈ Q,
where the new objective function is Fl(ml, El) =
N
X
n=1
αl,n· e−ˆγl,nβl,n. (22)
It is easy to see that the OP remains unchanged when re-placing the objective function (20) by (21). The considered OP (21) is a convex optimization problem [19], which means that the optimal solution can be found by the method of Lagrange multipliers. However, the convergence of such algorithms is often slow. Therefore we will use the successive set reduction (SSR) approach introduced in [8]. In [8], the SSR algorithm is shown to achieve almost the same performance as the method of Lagrange multipliers but with a much faster convergence. We also note that the optimal value of E∗ only depends on the modulation vector m and ˆHn (n ∈ N ).
Optimal TM. The optimal TMφ∗ is obtained by exhaustively
solving the following problem (φ∗1, φ∗2) = arg max
φ1,φ2
{ζ(φ1, φ2, E∗1, E∗2)}, (23)
s.t.φl∈ DmN × Dr, ∀l ∈ {1, 2},
ml,n= ml, ∀n ∈ N , ∀l ∈ {1, 2},
where a uniform bit allocation (UBA), mn = m, ∀n ∈ N ,
has been adopted for simplicity. We note that this exhaustive search is made possible due to the low complexity of the SSR algorithm.
B. Relay Selection
From a set ofM active RNs, a single relay will be selected which provides the “best” GP between the ST and SR. In the first step we maximize the PGP ζk(φ1, φ2, E1, E2) with
γk,l,eff(φl, El) (l = 1, 2) for each possible relay selection k ∈
[1, . . . , M ]. Note that the subscript k is shown here explicitly to indicate that the kth RN has been selected. The optimal solution is found according to the RA described in III-A, and is denoted by φ∗1(k), φ∗2(k), E∗1(k) and E∗2(k). In the next
step, we select the RN which has the highest total PGP: ˜
k, arg max
k∈[1,...,M](ζk(φ ∗
1(k), φ∗2(k), E∗1(k), E∗2(k))), (24)
After the optimal RN has been selected, the RN starts to process the received packet from the ST. Clearly, the relay selection procedure does not have to be carried out for each transmitted packet, but is reactivated only after a time interval of the same order of magnitude as the channel coherence time.
In Tab. I the pseudo-code of the RA problem is shown. IV. SIMULATIONRESULTS
In this section, the effectiveness of the proposed RA method is demonstrated, by comparing its performance to the perfor-mance of a RA method which uses the classic capacity metric for the relay selection and the energy allocation. The latter reference system differs from the proposed RA method in the following way
• The optimal value of E∗
l is found by maximizing the
sum capacity Cl = PNn=1log(1 + γl,n) instead of the
effective SNRγl,eff (l = 1, 2) in the OP (20).
• The relay selection selects the relay for which the following end-to-end capacity is maximal
Ctot= 1 1 C1 + 1 C2 , (25)
PGP Maximization based RA Strategy Fork = 1 : M; Initialize:m1= 0, m2= 0, ζ(k) = 0; Form1= 2 : 2 : m1,max; Form2= 2 : 2 : m2,max; ∀l ∈ {1, 2}, Evaluate Elaccording to (21); ∀l ∈ {1, 2}, Compute γk,l,eff(φl, El) in (12);
Select(r1, r2) = arg maxr1,r2∈Drζk(φ1, φ2, E1, E2);
Ifζk(φ1, φ2, E1, E2) ≥ ζ(k) Then ∀l ∈ {1, 2} Setφ∗ l(k) = {ml, rl}, E∗l(k) = El, ζ(k) = ζk(φ1, φ2, E1, E2); End If End For End For End For
Return∀l ∈ {1, 2}, ˜k = arg maxk{ζ(k)} and φ∗l(˜k) and E ∗ l(˜k)
TABLE I.
which is the capacity of the dual-hop network if we consider the possibility of unequal time slots [20]. • The optimal TM φl(l = 1, 2) is still found by
maximiz-ing the PGP (16), but the values of E∗l are now found
by maximizing the sum capacity.
In Tab. II we summarized the simulation parameters for the packet-oriented CR BIC-OFDM transmission system. The con-sidered channel model is the ITU vehicular A, and the wireless channel between the nodes is normalized: Pν
t=0σ2t = 1. In
each simulation the number of PUs is NPU = 1. For each
S/N0ratio (with S given in (2)), the corresponding numerical
result is obtained by averaging over 1000 independent packets which experience independent channel realizations. The aver-age GP (AGP) is calculated as the averaver-age of the normalized GP of each packet (bits/s/Hz):
AGP= 1 1000 Ts N 1000 X i=1 B(i) Tp(i) , (26)
whereB(i) is equal to Npif the packet was correctly received,
or0 when delivery fails, TP(i) is equal to the transmission time
of the packet.
Figure 1 shows the AGP resulting from both the RA algorithms optimizing the PGP and the capacity, respectively. The memory of the predictor is P = 4 and the interference threshold is I1/σ2w = 50 dB. We have shown the results
for a total number of RNs M = 1, 2, 3. The solid lines and the dashed lines represent the AGP that result from the maximization of the PGP and the capacity, respectively. As we can see from the figure, the solid lines are always above the dashed lines for the same value of M . Hence, the first important result is that the PGP metric always guarantees better performance in terms of AGP compared to the use of capacity. In this scenario, the AGP is improved by more than 10 percent by using the PGP metric instead of the capacity
Parameter Value Information bits (Np) 1024 CRC (NCRC) 32 Subcarriers (N ) 1320 FFT size 2048 Bandwidth (B) 20 MHz Cyclic prefix (ν) 160 4-, 16-, 64-QAM modulation (mn∀n ∈ N ) 2, 4, 6
Convolutional code with rate (r) 1/2, 2/3, 3/4, 5/6
Doppler frequency (fd) 144 Hz
CSI update interval (D) 7
Estimation error (σ2
e) N0/S
TABLE II. SYSTEM PARAMETERS
metric. Therefore, the PGP is a better metric for estimating the performance of a real packet-oriented transmission system and it is also more suitable to select the transmission parameters. Moreover, the performance improves when the number of available RNs increases. However we notice that the additional gain when going fromM = 2 to 3 is rather limited.
Figure 2 shows the AGP as a function of the interference constraintI1using the PGP and the capacity as objective
func-tion, with a fixed SNR = 25 dB. The figure confirms that the AGP is always better when the RA maximizes the PGP instead of the capacity, and that the system performance improves when M grows. We can also clearly see that when I1 ≥ 55
dB, the AGP tends towards a limiting value that is independent of I1. This is the region where the maximal transmit energy
per symbol, rather than the interference constraints, becomes the limiting factor.
Finally, figure 3 compares the performance of the κESM technique when the CSI at the transmitter is perfect, with the performance when the memoryP of the predictor is equal to 1 and 4. The number of RNs M is equal to 2. We have shown both the AGP and the APGP. The latter is calculated as in (17), involving the κESM approximation. As we can see, the AGP and APGP are very close in the case of perfect CSI and with imperfect CSI if P = 4. So in these cases the APGP is a reliable estimate of the AGP. When the memory P of the channel predictor is equal to 1, we notice that we get a large gap between the APGP and the AGP. In this case theκESM is unable to make a correct prediction of a suitable transmission mode, because of the large uncertainty on the current CSI. When P ≥ 4 however, the channel predictor provides the ST with very reliable CSI and the proposed algorithm is able to reach nearly the same performance as with the perfect CSI scenario.
V. CONCLUSION
This paper provides a novel RA strategy for CR BIC-OFDM systems with DF relays. The simulation results have shown that the PGP acts as a more reliable objective function than the capacity metric in a practical packet-oriented system. Further, the PGP makes it possible to jointly optimize the modulation/code rate pair and the transmit energy vector for the ST and the RN. Moreover, numerical results show that the combination of the LPP based on κESM and a channel predictor provides robustness against CSI that is outdated and imperfect. Finally, we have shown that the total PGP is an
0 5 10 15 20 25 0 0.5 1 1.5 2 S/N0(dB) go o d p u t (b it s/s /Hz ) PGP (M = 1) PGP (M = 2) PGP (M = 3) C (M = 1) C (M = 2) C (M = 3)
Fig. 1. AGP as a function ofS/N0(M = 1, 2, 3)
0 10 20 30 40 50 60 70 0 0.5 1 1.5 2 2.5 I1(dB) go o d p u t (b it s/s /Hz ) PGP (M = 1) PGP (M = 2) PGP (M = 3) C (M = 1) C (M = 2) C (M = 3)
Fig. 2. AGP as a function of the interference threshold I1 (M = 1, 2, 3)
0 5 10 15 20 25 0 0.5 1 1.5 2 S/N0(dB) go o d p u t (b it s/s /Hz )
APGP (perfect CSI) AGP (perfect CSI) APGP (P = 4) AGP (P = 4) APGP (P = 1) AGP (P = 1)
Fig. 3. APGP and AGP performance considering perfect and imperfect CSI withM = 2.
accurate estimate of the AGP in a dual-hop transmission and that it can be used as a reliable relay selection criterion. In future work, we will extend this work to RA strategies and path selection problems in multi-hop packed-oriented transmission systems.
APPENDIX
ACKNOWLEDGMENT
J. Van Hecke is supported by a Ph. D. fellowship of the Research Foundation Flanders (FWO).
This work was supported by the European Commission in the framework of the FP7 Network of Excellence in Wireless COMmunications NEWCOM# (Grant agreement no. 318306), and the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office.
REFERENCES
[1] Haykin, Simon, "Cognitive radio: brain-empowered wireless communi-cations," Selected Areas in Communications, IEEE Journal on , vol.23, no.2, pp.201,220, Feb. 2005.
[2] Goldsmith, A; Jafar, S.A; Maric, I; Srinivasa, S., "Breaking Spectrum Gridlock With Cognitive Radios: An Information Theoretic Perspec-tive," Proceedings of the IEEE , vol.97, no.5, pp.894,914, May 2009. [3] Caire, G.; Taricco, Giorgio; Biglieri, Ezio, "Bit-interleaved coded
mod-ulation," Information Theory, IEEE Transactions on , vol.44, no.3, pp.927,946, May 1998.
[4] Goldsmith, AJ.; Soon-Ghee Chua, "Variable-rate variable-power MQAM for fading channels," Communications, IEEE Transactions on , vol.45, no.10, pp.1218,1230, Oct 1997.
[5] Yingwei Yao; Giannakis, G.B., "Rate-maximizing power allocation in OFDM based on partial channel knowledge," Wireless Communications, IEEE Transactions on, vol.4, no.3, pp.1073,1083, May 2005. [6] Sigen Ye; Blum, R.S.; Cimini, L.J., "Adaptive OFDM Systems With
Imperfect Channel State Information," Wireless Communications, IEEE Transactions on, vol.5, no.11, pp.3255,3265, November 2006. [7] Jin Soo Choi; Chang-Kyung Sung; Sung-Hyun Moon; Inkyu Lee,
"Adaptive Bit-Interleaved Coded OFDM over Time-Varying Channels," Vehicular Technology Conference, 2006. VTC 2006-Spring. IEEE 63rd, vol.3, no., pp.1487,1491, 7-10 May 2006.
[8] Andreotti, R.; Stupia, I; Lottici, V.; Giannetti, F.; Vandendorpe, L., "Goodput-Based Link Resource Adaptation for Reliable Packet Trans-missions in BIC-OFDM Cognitive Radio Networks," Signal Processing, IEEE Transactions on , vol.61, no.9, pp.2267,2281, May1, 2013. [9] Laneman, J.N.; Tse, D.N.C.; Wornell, Gregory W., "Cooperative
diver-sity in wireless networks: Efficient protocols and outage behavior," In-formation Theory, IEEE Transactions on, vol.50, no.12, pp.3062,3080, Dec. 2004.
[10] Lozano, A; Tulino, AM.; Verdu, S., "Optimum power allocation for par-allel Gaussian channels with arbitrary input distributions," Information Theory, IEEE Transactions on, vol.52, no.7, pp.3033,3051, July 2006. [11] Kee-Bong Song; Ekbal, A; Seong Taek Chung; Cioffi, J.M., "Adaptive modulation and coding (AMC) for bit-interleaved coded OFDM (BIC-OFDM)," Wireless Communications, IEEE Transactions on , vol.5, no.7, pp.1685,1694, July 2006
[12] Akay, E.; Sengul, E.; Ayanoglu, E., "Bit Interleaved Coded Multiple Beamforming," Communications, IEEE Transactions on , vol.55, no.9, pp.1802,1811, Sept. 2007.
[13] Stupia, I; Lottici, V.; Giannetti, F.; Vandendorpe, L., "Link Re-source Adaptation for Multiantenna Bit-Interleaved Coded Multicarrier Systems," Signal Processing, IEEE Transactions on , vol.60, no.7, pp.3644,3656, July 2012.
[14] Van Hecke, Jeroen; Del Fiorentino, Paolo; Giannetti, Filippo; Lottici, Vincenzo; Vandendorpe, Luc; Moeneclaey, Marc, "Resource Allocation for Multicarrier Cooperative Cognitive Radio Networks with Imperfect Channel State Information," Personal Indoor and Mobile Radio Com-munications (PIMRC), 2013 IEEE 24th International Symposium on, Sept. 2014.
[15] Del Fiorentino, Paolo; Andreotti, Riccardo; Lottici, Vincenzo; Gian-netti, Filippo; Van Hecke, Jeroen; Moeneclaey, Marc, "Link Resource Adaptation for BIC-OFDM Systems with Outdated Channel State Infor-mation," European Wireless 2014; 20th European Wireless Conference; Proceedings of, vol., no., pp.1,6, 14-16 May 2014.
[16] Jakes, W. C., "Microwave Mobile Communications", New York: Wiley (1974).
[17] Wong, IC.; Evans, B.L., "Optimal resource allocation in the OFDMA downlink with imperfect channel knowledge," Communications, IEEE Transactions on, vol.57, no.1, pp.232,241, January 2009
[18] D. Qiao, S. Choi and K.G. Shin, "Goodput analysis and link adaptation for IEEE 802.11a wireless LANs," Mobile Computing, IEEE Transac-tions on, vol.1, no.4, pp.278,292, Oct-Dec 2002
[19] S. Boyd and L. Vandenberghe, "Convex optimization," Cambridge Univ. Press, 2004.
[20] Oyman, O.; Sandhu, S., "Non-Ergodic Power-Bandwidth Tradeoff in Linear Multi-hop Networks," Information Theory, 2006 IEEE Interna-tional Symposium on, pp.1514,1518, 9-14 July 2006
