Power Allocation for Adaptive OFDM Index Modulation in Cooperative Networks
PPower Allocation for Adaptive OFDM IndexModulation in Cooperative Networks
Shuping Dang, Gaojie Chen and Justin P. Coon
Department of Engineering ScienceUniversity of OxfordParks Road, Oxford, OX1 3PJ, UKEmail: { shuping.dang, gaojie.chen, justin.coon } @eng.ox.ac.uk Abstract —In this paper, we propose a power allocation strat-egy for the adaptive orthogonal frequency-division multiplexing(OFDM) index modulation (IM) in cooperative networks. Theallocation strategy is based on the Karush-Kuhn-Tucker (KKT)conditions, and aims at maximizing the average network capacityaccording to the instantaneous channel state information (CSI).As the transmit power at source and relay is constrainedseparately, we can thus formulate an optimization problemby allocating power to active subcarriers. Compared to theconventional uniform power allocation strategy, the proposeddynamic strategy can lead to a higher average network capacity,especially in the low signal-to-noise ratio (SNR) region. Theanalysis is also verified by numerical results produced by MonteCarlo simulations. By applying the proposed power allocationstrategy, the efficiency of adaptive OFDM IM can be enhancedin practice, which paves the way for its implementation in thefuture, especially for cell-edge communications.
Keywords — Index modulation, OFDM, power allocation, capac-ity optimization, cooperative networks.
I. I
NTRODUCTION
Stemming from parallel combinatorial signaling, spatialmodulation (SM) and orthogonal frequency-division multiplex-ing (OFDM) index modulation (IM) have been regarded astwo of the most promising modulation techniques for nextgeneration networks [1]–[5]. SM is designed for multiple-input-multiple-output (MIMO) systems and exploits the spatialdimension, while OFDM IM is mainly applied to multicarriersystems by conveying information via the frequency dimen-sion. The investigations into SM are relatively full-fledgedand a complete framework regarding performance analysis,resource allocation and practical implementation has beenconstructed [2]. Compared to SM, OFDM IM is relatively newand many aspects require attention. The concept of OFDMIM is first proposed in [6], and then systematically improvedand generalized in [7] and [8], respectively. Subsequently, thetransmission rate of OFDM IM is analyzed in [9] and theextension of OFDM IM to cooperative networks is presentedin [10], in which the outage performance, network capacityand error performance of OFDM IM are analyzed in detail.However, in most existing works, the transmit power issimply allocated to each subcarrier in a uniform manner, andthe analysis of the power allocation problem is still lacking.As shown in conventional OFDM systems and SM systems,an optimized power allocation strategy would significantlyenhance the system performance in terms of throughput and
Fig. 1: System block diagram of adaptive OFDM IM, reproducedfrom [10] with permission. reliability [11]–[13]. In [14] and [15], power allocation prob-lems are analyzed and solved for OFDM systems with DFrelays based on the Karush-Kuhn-Tucker (KKT) conditionsand KKT multipliers. A similar approach is also proved tobe effective for OFDM-based cognitive radio systems andmultiuser scenarios [16], [17]. Following the analysis givenin [10], we thereby adopt a similar KKT conditions-basedapproach and carry out the analysis regarding power allocationfor adaptive OFDM IM in cooperative networks in this paper.Finally, we formulate the optimization problem and propose adynamic power allocation strategy aiming at maximizing theaverage network capacity. Numerical results verify that withthe proposed power allocation strategy, the average networkcapacity can be improved compared to that with uniform powerallocation strategy, especially in the low signal-to-noise ratio(SNR) region. This makes the proposed strategy particularlyuseful for cell-edge communications.The rest of the paper is organized as follows. Section IIpresents the system model. We then formulate the optimizationproblem and analyze the power allocation strategy in SectionIII. Subsequently, numerical results are shown and discussedin Section IV. Finally, the paper is concluded in Section V.II. S
YSTEM M ODEL
A. System framework
Following the system model constructed in [10], we con-sider a two-hop OFDM IM system with N T subcarriers, inwhich one source, one relay and one destination exist. Thetransmit power at source and relay is constrained separately bythe same bound P t . This system operates in a slow frequency-selective fading environment and the fading on each subcarriercan be regarded as independent and identically distributed a r X i v : . [ c s . I T ] A ug i.i.d.). Then, N S ( ≤ N S < N T ) subcarriers are selected bya certain criterion (details given in Section II-C) to construct a mapping scheme for OFDM IM . After that, a bit stream witha variable-length B ( k ) = B S + N A ( k ) B M can be modulatedby both the subcarrier activation pattern and the conventional M -ary amplitude and phase modulation (APM) scheme (e.g. M -PSK and M -QAM), where k ∈ { , , , . . . , N S } denotingthe index of the subcarrier activation pattern and N A ( k ) is thenumber of active subcarriers for the k th pattern; B S = N S is the length of the bit stream which will be modulated bythe subcarrier activation pattern in an on-off keying (OOK)manner, and on each active subcarrier, a symbol generated bya B M -bit stream is transmitted. This is termed adaptive OFDMIM and the system block diagram is illustrated in Fig. 1.However, one might note that, as the subcarriers are activatedin an OOK manner, there is a possibility that all subcarriersare inactive when an all-zero B S -bit stream is transmitted(we denote this case as k = 1 ). This is termed zero-activesubcarrier dilemma , and a complementary subcarrier fromthose N T − N S unselected subcarriers will be activated toundertake the transmission of at least one APM symbol .Meanwhile, we assume there is no direct transmission linkbetween source and destination due to deep fading and thesignal propagation must go through relay. Also, a half-duplexdecode-and-forward (DF) forwarding protocol is adopted at therelay, and two orthogonal temporal phases are required for onecomplete transmission from source to relay, and from relay todestination. B. Channel model
It is assumed that the channels in the first and second hopsare slow frequency-selective Rayleigh faded with exponentiallydistributed channel gains. Here, the slow property indicatesthat quasi-static block fading channels are considered and thechannel gains are random but would remain unchanged for asufficiently large period of time [18], so that the overheads fortransmitting the selected mapping scheme and information ofpower allocation via feedforward links to relay and destinationfor decoding purposes are negligible [19]. Denoting the set ofall subcarriers as N = { , , . . . , N T } , ∀ n ∈ N , the proba-bility density function (PDF) and the cumulative distributionfunction (CDF) of the channel gain | h i ( n ) | are f i ( s ) = exp ( − s/µ i ) /µ i ⇔ F i ( s ) = 1 − exp ( − s/µ i ) (1)where µ i denotes the average channel gain of the i th hop. C. Mapping scheme selections
In OFDM IM systems, a general N T × transmit OFDMblock in frequency domain can be written as x = [ x (1) , x (2) , . . . , x ( N T )] T ∈ C N T × , (2)where ( · ) T denotes the matrix transpose operation and C isthe field of complex numbers.After selecting an arbitrary c th mapping scheme, c ∈ C ,where C is the set of all possible mapping schemes, and Note that, by such a selection process, the constructed mapping scheme isNOT the same as the inherent activation pattern used in OFDM IM systems. More details of this dilemma can be found at [10]. obtaining a subset N S ( c ) ⊂ N for OFDM IM, the reducedOFDM block determined by the B ( k ) -bit stream is given by x ( k ) = [ x ( m , , x ( m , , . . . , x ( m N S , N S )] T ∈ C N S × , (3)where x ( m n , n ) = (cid:26) χ m n , n ∈ N A ( k )0 , otherwise (4)corresponds to the data symbol transmitted on the n th sub-carrier, and N A ( k ) ⊆ N S ( c ) is the subset of N A ( k ) activesubcarriers for the k th subcarrier activation pattern; χ m n is the M -ary APM symbol and we can normalize it by χ m n χ ∗ m n = 1 .Therefore, for k (cid:54) = 1 (i.e. there is at least one activesubcarrier), we can obtain the received SNR in the i th hop forthe n th subcarrier when the k th subcarrier activation patternis utilized by γ i ( k, n ) = (cid:40) P t,i ( k,n ) N | h i ( c, n ) | , ∀ n ∈ N A ( k )0 , ∀ n ∈ N S ( c ) \ N A ( k ) (5)where P t,i ( k, n ) is the allocated transmit power to the n thsubcarrier in the i th hop and N is the additive white Gaussiannoise (AWGN) power; | h i ( c, n ) | is the channel gain regardingthe n th subcarrier after performing mapping scheme selection.On the other hand, when k = 1 , we can have γ i (1 , ˜ n i ) = P t N | h i (˜ n i ) | and γ i (1 , n ) = 0 , ∀ n ∈ N S ( c ) , (6)where ˜ n i denotes the index of the complementary subcarrierselected for the i th hop.
1) Decentralized mapping scheme selection:
Now, we canspecify the method of mapping scheme selection. Two map-ping scheme selection methods are introduced in this paper,which are applied to different types of networks dependingon the processing capability of the relay node. If both sourceand relay can get access to CSI and perform mapping schemeselections independently, we can adopt the decentralized map-ping scheme selection method in each hop by the criterion: ˆ c i = arg max c ∈C (cid:88) n ∈N S ( c ) γ i (2 N S , n ) . (7)Also, the complementary subcarrier in each hop can be se-lected by ˜ n i = arg max n ∈N \N S (ˆ c i ) | h i ( n ) | . (8)
2) Centralized mapping scheme selection:
On the otherhand, for a simple relay which is unable to perform map-ping scheme selection due to limited system complexity andprocessing capability, we can utilize the centralized mappingscheme selection method, by which the mapping schemeselection is only performed at the source and utilized by therelay. The selection criterion can be written as ˆ c = ˆ c = ˆ c = arg max c ∈C (cid:88) n ∈N S ( c ) min (cid:8) γ (2 N S , n ) , γ (2 N S , n ) (cid:9) , (9) ig. 2: An example of (a): a two-hop system with the decentralizedmapping scheme selection; (b): a two-hop system with the centralizedmapping scheme selection, when N T = 4 , N S = 3 and N A ( k ) = 2 . and the complementary subcarrier can be similarly selected by ˜ n = ˜ n = ˜ n = arg max n ∈N\N S (ˆ c ) min (cid:8) | h ( n ) | , | h ( n ) | (cid:9) . (10) The two-hop systems with decentralized and centralizedmapping scheme selections are illustrated in Fig. 2 for clarity.
D. Network capacity
By the max-flow min-cut theorem [20], the average net-work capacity in two-hop networks can be expressed by ¯ C = E { C ( k ) } [bit / s / Hz] , (11)where E {·} represents the expectation over all channels andsubcarrier activation patterns; C ( k ) is the network capacitywhen the k th subcarrier activation pattern is utilized and canbe written as C ( k ) = min { log (1 + γ (1 , ˜ n )) , log (1 + γ (1 , ˜ n )) } , if k = 1 (cid:80) n ∈N A ( k ) 12 min { log (1 + γ ( k, n )) , log (1 + γ ( k, n )) } , if k > (12) The average network capacity will be adopted in the followinganalysis to evaluate the system throughput, and the maximiza-tion of the average network capacity is the objective of theformulated optimization problem in the next section .III. P ROBLEM F ORMULATION AND A NALYSIS
A. Dynamic power allocation strategy
For the adaptive OFDM IM systems in two-hop networksintroduced in the previous section, we can formulate the For a typical OFDM system, there are two kinds of optimization problems:1) maximizing the network capacity under a limited total transmit power; 2)minimizing the total transmit power beyond a threshold network capacity [21].Because the user experience is regarded as one of the most important metricsin next generation networks [22], we take the former optimization scenario inthis paper. optimization problem infra: max P t, ( k ) P t, ( k ) (cid:8) ¯ C (cid:9) s . t . (cid:88) n ∈N A ( k ) P t, ( k, n ) ≤ P t , (cid:88) n ∈N A ( k ) P t, ( k, n ) ≤ P t P t, ( k, n ) ≥ , P t, ( k, n ) ≥ , ∀ k ∈ K , n ∈ N A ( k ) . (13)where P t,i ( k ) = (cid:2) P t,i ( k, n ) , . . . , P t,i ( k, n N A ( k ) ) (cid:3) T , ∀ k ∈ K .By (11), we can reduce the expression of ¯ C to ¯ C = E k ∈K (cid:26) E h ( n ) ,h ( n ) { C ( k ) } (cid:27) [bit / s / Hz] , (14)From (14), we observe that as long as the network capacity ofeach instant can be optimized, the average network capacitywill be optimized. As a result, we can equivalently transfer theoptimization problem formulated in (13) to max P t, ( k ) P t, ( k ) { C ( k ) } s . t . (cid:88) n ∈N A ( k ) P t, ( k, n ) ≤ P t , (cid:88) n ∈N A ( k ) P t, ( k, n ) ≤ P t P t, ( k, n ) ≥ , P t, ( k, n ) ≥ , ∀ k ∈ K , n ∈ N A ( k ) . (15)
1) Decentralized mapping scheme selection:
When k = 1 ,the complementary subcarrier ˜ n i is the only one active sub-carrier in the i th hop and thus all transmit power P t will beallocated to it. For such a special case, there is only a uniquesolution to (15), and the power allocation is easy to deal with.On the other hand, when k (cid:54) = 1 , because the power allocationsin two hops are independent when the decentralized mappingscheme selection method is employed, we can further split thereduced optimization problem formulated in (15) into max P t,i ( k ) { C i ( k ) } s . t . (cid:88) n ∈N A ( k ) P t,i ( k, n ) ≤ P t , P t,i ( k, n ) ≥ , ∀ k ∈ K , n ∈ N A ( k ) . (16)for each hop, where C i ( k ) = (cid:80) n ∈N A ( k ) 12 log (1 + γ i ( k, n )) .Besides, by (5), it is obvious that C i ( k ) is continuous anddifferentiable with respect to P t,i ( k, n ) , ∀ n ∈ N A ( k ) .We can find the optimization problem formulated in (16)to be a standard nonlinear programming problem [23]. Now,by employing the KKT conditions-based approach, we canconstruct the KKT function for the i th hop as follows L i ( P t,i ( k, n ) , P t,i ( k, n ) , . . . , P t,i ( k, n N A ( k ) ) ,(cid:15) i , ε i ( n ) , ε i ( n ) , . . . , ε i ( n N A ( k ) ))= C i ( k ) + (cid:15) i P t − (cid:88) n ∈N A ( k ) P t,i ( k, n ) + (cid:88) n ∈N A ( k ) ε i ( n ) P t,i ( k, n ) , (17) where (cid:15) i and ε i ( n ) are the KKT multipliers for the i th hop, ∀ n ∈ N A ( k ) . For simplicity, we will use L i as a shorthand in the following analysis. ubsequently, we can derive the KKT conditions to be ∂ L i ∂P t,i ( k,n ) = | h i (ˆ c i ,n ) | (2 ln 2) ( N + | h i (ˆ c i ,n ) | P t,i ( k,n ) ) − (cid:15) i + ε i ( n ) = 0 ∂ L i ∂P t,i ( k,n ) = | h i (ˆ c i ,n ) | (2 ln 2) ( N + | h i (ˆ c i ,n ) | P t,i ( k,n ) ) − (cid:15) i + ε i ( n ) = 0 ... ∂ L i ∂(cid:15) i = P t − (cid:80) n ∈N A ( k ) P t,i ( k, n ) = 0 ε i ( n ) P t,i ( k, n ) = 0 ε i ( n ) P t,i ( k, n ) = 0 ... ε i ( n N A ( k ) ) P t,i ( k, n N A ( k ) ) = 0 (18) Solving the equation set given in (18) yields the optimal P ∗ t,i ( k ) . In order to perform numerical evaluation later, we cangenerally express the standard waterfilling solution given by P ∗ t,i ( k, ˙ n ) = (cid:20) (cid:15) i − ε i ( ˙ n )) − N | h i (ˆ c i , ˙ n ) | (cid:21) + , (19)where [ x ] + = max { , x } ; (cid:15) i and ε i ( ˙ n ) satisfy P t − (cid:88) n ∈N A ( k ) (cid:18) (cid:15) i − ε i ( n )) − N | h i (ˆ c i , n ) | (cid:19) = 0 (20) and ε i ( n ) (cid:20) (cid:15) i − ε i ( ˙ n )) − N | h i (ˆ c i , ˙ n ) | (cid:21) + = 0 . (21)A general and closed-form expression of (19) independentfrom (cid:15) i and ε i ( ˙ n ) does not exist, since the solution is asso-ciated with the quantitative relation among all channel gains.However, for a given network realization, the solution can beanalytically determined by an iterative algorithm (see Theorem1 in [24]), and the algorithm is implemented by the MATLABfunction fmincon .
2) Centralized mapping scheme selection:
However, whenthe centralized mapping scheme selection is performed, thepower allocations in the first and second hop are not in-dependent anymore and should be considered jointly. As aconsequence, we cannot split (15) into (16) for two hopsindependently. In this case, we have to integrate the channelsin two hops into a link and define the link gain as | l (ˆ c, n ) | = min (cid:8) | h (ˆ c, n ) | , | h (ˆ c, n ) | (cid:9) . (22)For k = 1 , again, there is only one possibility of powerallocation and we can simply allocate all transmit power to thecomplementary subcarrier ˜ n . On the other hand, when k (cid:54) =1 , we can employ the KKT conditions-based approach andconstruct the KKT function for a whole end-to-end link asfollows: L ( P t ( k, n ) , P t ( k, n ) , . . . , P t ( k, n N A ( k ) ) ,(cid:15), ε ( n ) , ε ( n ) , . . . , ε ( n N A ( k ) ))= C ( k ) + (cid:15) P t − (cid:88) n ∈N A ( k ) P t ( k, n ) + (cid:88) n ∈N A ( k ) ε ( n ) P t ( k, n ) , (23) where (cid:15) and ε ( n ) are the KKT multipliers, ∀ n ∈ N A ( k ) . Similar to the decentralized case, we have the KKT con-ditions as follows: ∂ L ∂P t ( k,n ) = | l (ˆ c,n ) | (2 ln 2) ( N + | l (ˆ c,n ) | P t ( k,n ) ) − (cid:15) + ε ( n ) = 0 ∂ L ∂P t ( k,n ) = | l (ˆ c,n ) | (2 ln 2) ( N + | l (ˆ c,n ) | P t ( k,n ) ) − (cid:15) + ε ( n ) = 0 ... ∂ L ∂(cid:15) = P t − (cid:80) n ∈N A ( k ) P t ( k, n ) = 0 ε ( n ) P t ( k, n ) = 0 ε ( n ) P t ( k, n ) = 0 ... ε ( n N A ( k ) ) P t ( k, n N A ( k ) ) = 0 (24) Solving the equation set given in (24)yields the optimal P ∗ t, ( k ) = P ∗ t, ( k ) = (cid:2) P ∗ t ( k, n ) , P ∗ t ( k, n ) , . . . , P ∗ t ( k, n N A ( k ) ) (cid:3) T . Again, wecan only generally express the solution of optimal powerallocated to each active subcarrier by P ∗ t, ( k, ˙ n ) = P ∗ t, ( k, ˙ n ) = (cid:20) (cid:15) − ε ( ˙ n )) − N | l (ˆ c, ˙ n ) | (cid:21) + , (25)where (cid:15) and ε ( ˙ n ) satisfy P t − (cid:88) n ∈N A ( k ) (cid:18) (cid:15) − ε ( n )) − N | l (ˆ c, n ) | (cid:19) = 0 (26) and ε ( n ) (cid:20) (cid:15) − ε ( n )) − N | l (ˆ c, n ) | (cid:21) + = 0 . (27)There does not exist a general and closed-form expression of(25) either, and for a given network realization, the solutioncan be determined by the iterative algorithm presented in [24],which is implemented by the MATLAB function fmincon . B. Uniform power allocation strategy
In contrast to our proposed dynamic power allocationstrategy depending on CSI, the conventional uniform powerallocation strategy is simple and does not rely on CSI, butwill lead to a suboptimal average capacity. We also brieflyintroduce the uniform power allocation strategy here, as itis a commonly used strategy and will be adopted as thecomparison benchmark in next section. When adopting theuniform power allocation strategy, the transmit power allocatedto each subcarrier is the same and can be written as P t, ( k, ˙ n ) = P t, ( k, ˙ n ) = P t N A ( k ) . (28)IV. N UMERICAL R ESULTS
We normalize µ = 1 , µ = 1 and N = 1 andcarried out the numerical simulations regarding the relationbetween P t /N and the average network capacity for systemsadopting different mapping scheme selection methods andpower allocation strategies. In this paper, we directly employthe MATLAB function fmincon to solve the optimal P ∗ t, ( k ) and P ∗ t, ( k ) . The numerical results are shown in Fig. 3. Fromthis figure, we can observe that the systems with the dynamic −1 P t /N (dB) A v e r age ne t w o r k c apa c i t y ( b i t/ s / H z ) Dynamic N S =32Uniform N S =32Dynamic N S =64Uniform N S =64Dynamic N S =127Uniform N S =127 (a) Decentralized mapping scheme selection: N T = 128 . −1 P t /N (dB) A v e r age ne t w o r k c apa c i t y ( b i t/ s / H z ) Dynamic N S =32Uniform N S =32Dynamic N S =64Uniform N S =64Dynamic N S =127Uniform N S =127 (b) Centralized mapping scheme selection: N T = 128 . −1 P t /N (dB) A v e r age ne t w o r k c apa c i t y ( b i t/ s / H z ) Dynamic N S =64Uniform N S =64Dynamic N S =128Uniform N S =128Dynamic N S =255Uniform N S =255 (c) Decentralized mapping scheme selection: N T = 256 . −1 P t /N (dB) A v e r age ne t w o r k c apa c i t y ( b i t/ s / H z ) Dynamic N S =64Uniform N S =64Dynamic N S =128Uniform N S =128Dynamic N S =255Uniform N S =255 (d) Centralized mapping scheme selection: N T = 256 .Fig. 3: Average network capacity vs. ratio of total transmit power to noise power P t /N . power allocation strategy outperform the systems with theuniform power allocation strategy in terms of average networkcapacity, which verifies the efficiency of our proposed dynamicstrategy for the adaptive OFDM IM in two-hop networks.Besides, it is well known that the advantage brought bythe dynamic allocation strategy will diminish when P t /N increases. This is because when a sufficiently large totaltransmit power can be provided, the impacts of channel/linkgains on the capacity are relatively trivial, and the powerallocated to each subcarrier will converge to P t /N A ( k ) (i.e.the uniform strategy). Mathematically, by (19) and (25), thisproperty can be derived by lim P t →∞ P ∗ t,i ( k, ˙ n )= lim P t →∞ (cid:32) P t + (cid:80) n ∈N A ( k ) N | h i (ˆ c i ,n ) | N A ( k ) − N | h i (ˆ c i , ˙ n ) | (cid:33) = P t N A ( k ) , (29) and lim P t →∞ P ∗ t, ( k, ˙ n ) = lim P t →∞ P ∗ t, ( k, ˙ n )= lim P t →∞ (cid:32) P t + (cid:80) n ∈N A ( k ) N | l (ˆ c,n ) | N A ( k ) − N | l (ˆ c, ˙ n ) | (cid:33) = P t N A ( k ) , (30) for decentralized and centralized cases, respectively. This in-dicates that our proposed dynamic power allocation strategywill play a more important role and result in a significant gainof channel capacity for cell-edge communications.Another phenomenon shown in the numerical results is thatsystems with different number of selected subcarriers N S havea similar average network capacity in the low SNR region,when the dynamic power allocation strategy is utilized. Thiscan be explained by the fact that all transmit power will beallocated to the strongest channel/link at low SNR, regardless N S . In this scenario, the OFDM IM system will degrade to aconventional OFDM system unable to convey information byhe subcarrier activation pattern. As a consequence, the gainof average network capacity brought by the dynamic powerallocation strategy can also be viewed as yielded by a modeselection mechanism switching between the OFDM IM modeand the conventional OFDM mode.V. C ONCLUSION
We proposed a power allocation strategy for the adaptiveOFDM IM in cooperative networks. Under a constrainedtotal transmit power, the power allocation strategy utilizesthe instantaneous CSI to allocate the total transmit power toeach active subcarrier based on the KKT conditions, aimingat maximizing the average channel capacity. We analyze theformulated optimization problem and equivalently transfer itto another optimization problem for each instant. We alsogive two examples of adaptive OFDM IM systems withdecentralized and centralized mapping scheme selections toillustrate the efficiency of the proposed power allocation strat-egy. Meanwhile, the general forms of the final solutions to theformulated optimization problems have also been given andtheir values can be provided by an iterative algorithm for agiven network realization. By numerical results provided byMonte Carlo simulations, our proposed dynamic strategy canlead to a higher average network capacity than uniform powerallocation strategy. By applying the proposed power allocationstrategy, the efficiency of adaptive OFDM IM can be enhancedin practice, which paves the way for its implementation in thefuture, especially for cell-edge communications.A
CKNOWLEDGMENT
This work was supported by the SEN grant (EPSRC grantnumber EP/N002350/1) and the grant from China ScholarshipCouncil (No. 201508060323).R
EFERENCES[1] P. K. Frenger and N. A. B. Svensson, “Parallel combinatory OFDMsignaling,”
IEEE Transactions on Communications , vol. 47, no. 4, pp.558–567, Apr. 1999.[2] M. D. Renzo, H. Haas, A. Ghrayeb, S. Sugiura, and L. Hanzo,“Spatial modulation for generalized MIMO: challenges, opportunities,and implementation,”
Proceedings of the IEEE , vol. 102, no. 1, pp.56–103, Jan. 2014.[3] N. Ishikawa, S. Sugiura, and L. Hanzo, “Subcarrier-index modulationaided OFDM - will it work?”
IEEE Access , vol. 4, pp. 2580–2593,2016.[4] E. Basar, “Index modulation techniques for 5G wireless networks,”
IEEE Communications Magazine , vol. 54, no. 7, pp. 168–175, Jul. 2016.[5] M. Chafii, J. P. Coon, and D. A. Hedges, “DCT-OFDM with indexmodulation,”
IEEE Communications Letters , 2017.[6] E. Basar, U. Aygolu, E. Panayrc, and H. V. Poor, “Orthogonal frequencydivision multiplexing with index modulation,”
IEEE Transactions onSignal Processing , vol. 61, no. 22, pp. 5536–5549, Nov. 2013.[7] R. Fan, Y. J. Yu, and Y. L. Guan, “Generalization of orthogonalfrequency division multiplexing with index modulation,”
IEEE Trans-actions on Wireless Communications , vol. 14, no. 10, pp. 5350–5359,Oct. 2015.[8] E. Basar, “Multiple-input multiple-output OFDM with index modula-tion,”
IEEE Signal Processing Letters , vol. 22, no. 12, pp. 2259–2263,Dec. 2015.[9] M. Wen, X. Cheng, M. Ma, B. Jiao, and H. V. Poor, “On the achievablerate of OFDM with index modulation,”
IEEE Transactions on SignalProcessing , vol. 64, no. 8, pp. 1919–1932, Apr. 2016. [10] S. Dang, J. P. Coon, and G. Chen, “Adaptive OFDM index mod-ulation for two-hop relay-assisted networks,”
IEEE Transactionson Wireless Communications , Jun. 2017, (under review). Available:https://arxiv.org/abs/1706.06568.[11] A. Pascual-Iserte, A. I. Perez-Neira, and M. A. Lagunas, “On powerallocation strategies for maximum signal to noise and interferenceratio in an OFDM-MIMO system,”
IEEE Transactions on WirelessCommunications , vol. 3, no. 3, pp. 808–820, May 2004.[12] S. Dang, J. P. Coon, and G. Chen, “Resource allocation for full-duplexrelay-assisted device-to-device multicarrier systems,”
IEEE WirelessCommunications Letters , vol. 6, no. 2, pp. 166–169, Apr. 2017.[13] Y. Shi, M. Ma, Y. Yang, and B. Jiao, “Optimal power allocation inspatial modulation systems,”
IEEE Transactions on Wireless Communi-cations , vol. 16, no. 3, pp. 1646–1655, Mar. 2017.[14] T. Wang and L. Vandendorpe, “Sum rate maximized resource allocationin multiple DF relays aided OFDM transmission,”
IEEE Journal onSelected Areas in Communications , vol. 29, no. 8, pp. 1559–1571, Sept.2011.[15] L. Vandendorpe, R. T. Duran, J. Louveaux, and A. Zaidi, “Powerallocation for OFDM transmission with DF relaying,” in
Proc. IEEEICC , Beijing, China, May 2008.[16] P. Wang, M. Zhao, L. Xiao, S. Zhou, and J. Wang, “Power allocationin OFDM-based cognitive radio systems,” in
Proc. IEEE GLOBECOM ,Washington, DC, USA, Nov. 2007.[17] K. Kim, Y. Han, and S.-L. Kim, “Joint subcarrier and power allocationin uplink OFDMA systems,”
IEEE Communications Letters , vol. 9,no. 6, pp. 526–528, Jun. 2005.[18] G. Chen, Y. Gong, P. Xiao, and R. Tafazolli, “Dual antenna selection inself-backhauling multiple small cell networks,”
IEEE CommunicationsLetters , vol. 20, no. 8, pp. 1611–1614, Aug. 2016.[19] P. Yang, Y. Xiao, Y. Yu, and S. Li, “Adaptive spatial modulation forwireless MIMO transmission systems,”
IEEE Communications Letters ,vol. 15, no. 6, pp. 602–604, Jun. 2011.[20] W. Wang and R. Wu, “Capacity maximization for OFDM two-hoprelay system with separate power constraints,”
IEEE Transactions onVehicular Technology , vol. 58, no. 9, pp. 4943–4954, Nov. 2009.[21] H.-L. Liu and Q. Wang, “A resource allocation evolutionary algorithmfor OFDM based on Karush-Kuhn-Tucker conditions,”
MathematicalProblems in Engineering , vol. 2013, 2013.[22] C. X. Wang, F. Haider, X. Gao, X. H. You, Y. Yang, D. Yuan, H. M.Aggoune, H. Haas, S. Fletcher, and E. Hepsaydir, “Cellular architectureand key technologies for 5G wireless communication networks,”
IEEECommunications Magazine , vol. 52, no. 2, pp. 122–130, Feb. 2014.[23] M. Patriksson,
Nonlinear Programming and Variational InequalityProblems: A Unified Approach , ser. Applied Optimization. SpringerUS, 2013.[24] G. Bansal, Z. Hasan, J. Hossain, and V. K. Bhargava, “Subcarrier andpower adaptation for multiuser OFDM-based cognitive radio systems,”in