2.3.1 Resource Allocation in SC-FDMA Systems
The key feature of the multi-channel and multi-user wireless systems is their inherit frequency, time, and multi-user diversities. Resource allocation techniques can be used to take advantage of these diversities of the system in order to op- timize the use of the available resources. These techniques exploit the available channel state information (CSI) at the transmitter side for accomplishing adaptive modulation, and sharing the resources (powers, sub-channels, slots, etc.) among
the users.
Most of the previous work on resource allocation in multi-channel and multi- user systems has focused on power and sub-channels allocation in downlink OFDMA systems (e.g., [36, 46–49, 55, 56]). One of the well known approaches for solving the OFDMA resource allocation problem is exploiting its time-sharing property [57]. Based on this property, it is shown in [49], and [57] that for practical number of sub-channels, the resource allocation problem in OFDMA systems can be solved by Lagrange multipliers method with zero duality gap. However, none of above is directly applicable to uplink SC-FDMA. This is due to the fact that in localized SC-FDMA in addition to the restriction of allocating a sub-channel to one user at most, the multiple sub-channels allocated to a user should be adja- cent to each other as well. Furthermore, a frequency domain equalizer is used in SC-FDMA over all the sub-channels allocated to the user which makes the signal to noise ratio (SNR) expression much more complicated than in OFDMA where the SNR on each sub-channel is independent from the other sub-channels. This further adds to the difficulty of the resource allocation problem.
In most of the previous work on SC-FDMA, the implementation problems in the physical layer are studied (e.g., [58–62]). In [58], a comparative analysis of the PAPR characteristics of OFDMA, I-FDMA, and L-FDMA is peformed. In [59], the authors have proposed maximum likelihood detection for I-FDMA system and have investigated that in comparison with multi-carrier code-division multiple- access it has better performance with some additional advantages. In [60], SC- FDMA is considered as the multiple access scheme for the uplink of broadband wireless systems that allows users to transmit simultaneously with different data rates. In [61], the capacity behavior of single carrier modulation with frequency domain equalization is studied. The effective signal to interference and noise ratio (SINR) for SC-FDMA with frequency domain equalizers is derived in [62].
The resource allocation problem in uplink SC-FDMA has also been addressed in a number of publications. In [63], a heuristic opportunistic scheduler for allo- cating frequency bands to the users in the uplink of 3G LTE systems is proposed.
In [64], the authors have proposed a greedy sub-optimal schedular for uplink SC-FDMA systems that is based on marginal capacity maximization. In [65], the authors revise the same framework used in [64] for developing a proportional fair scheduling scheme. However, in addition to being sub-optimal, the proposed schedulers in both [64] and [65] do not consider the sub-channels adjacency con- straint which is an important physical layer requirement for localized SC-FDMA. In [66], a set of greedy sub-optimal proportional fair algorithms for localized SC- FDMA systems is proposed in the frequency-domain setting. This work respects the sub-channels adjacency constraint but does not consider any constraint on the power. The authors, in [67] use the so-called Hungarian algorithm to pro- pose dynamic sub-carrier allocation algorithm for SC-FDMA but it has very high computational complexity and does not consider power allocation. In [68], radio resource management for QoS provisioning in LTE with emphasis on admission control and handover is studied. Similarly, a case study of LTE for scheduling and link adaptation for uplink SC-FDMA Systems is performed in [69]. The works in both [68] and [69] are simulation based works that do not provide any analytical model for resource management. In [3], a weighted-sum rate maximization in localized SC-FDMA systems is considered where the problem is formulated as a pure binary-integer program. Though the proposed binary-integer program- ming framework captures all the basic constraints of the localized SC-FDMA and allows to perform resource allocation without resorting to exhaustive search, it is still not the best solution as the 0-1 requirement turns the problem into combi- natorial with exponential complexity. Thus, keeping in view the computational complexity of the binary-integer programming, the authors have also proposed a greedy sub-optimal algorithm that is similar in spirit to the approach in [64] with an additional constraint on the adjacency of the allocated sub-channels. In [70], some greedy sub-optimal resource allocation algorithms are proposed that are inspired from that work carried out in [3]. A chunk based greedy sub-optimal resource allocation framework is proposed in [71] where the sub-channels are divided into chunks with equal number of sub-channels and the total number
of chunks equal to the number of users. Each user is then assigned with a sin- gle chunk such that the sum-rate is maximized. In [72], a Hungarian method based distributed SC-FDMA resource allocation for multi-cell network is pro- posed. However, this work could not prove the convergence of the proposed algorithm, and its proximity to the global optimal solution; and these issues are left for future work.
All the cited work is limited to simplifying this exponentially complex prob- lem by taking some assumptions, and proposing some greedy sub-optimal solu- tions. None of the above works has solved this problem optimally or provided analytical investigation for the proximity of the proposed solution to the optimal solution. The only work where the problem is attacked from optimal solution perspective is formulating the problem as a binary-integer program [3]. How- ever, due to the exponential complex solution of the binary-integer program, the authors of [3] are also reverted to proposing a greedy sub-optimal iterative algo- rithm.