# Joint Resource Allocation for Multiuser Opportunistic Beamforming Systems with OFDM-NOMA
###### Abstract  
Opportunistic beamforming (OBF) is an effective technique to improve the spectrum efficiencies (SEs) of multiple-input-multiple-output (MIMO) systems, which can obtain multiuser diversity gains with both low computation complexity and feedback information. To serve multiple users simultaneously, many multiple-access schemes have been researched in OBF. However, for most of the multiple-access schemes, the SEs are not satisfactory. To further improve the SE, this paper proposes a downlink multiuser OBF system, where both orthogonal frequency division multiplexing (OFDM) and non-orthogonal multiple-access (NOMA) methods are applied. The closed-form expressions of the equivalent channels and SE are derived in frequency selective fading channels. Then, an optimization problem is formulated to maximize the SE, although the optimization problem is non-convex and hard to solve. To obtain the solution, we divide the optimization problem into two suboptimal issues, and then a joint iterative algorithm is applied. In the proposed optimization scheme, the subcarrier mapping \(\theta\), user pairing \(k_{u_{t}}\) and allocated power \(P_{k_{u_{t}}}\) are determined to maximize spectrum efficiency (SE) and reduce bit error ratio (BER). According to numerical results, the proposed method achieves approximately 5 dB gain on both SE and BER, compared to the existing beamforming methods with low feedback information. Moreover, the SE of the proposed method is approximately 2 (bps/Hz) higher than sparse code multiple-access (SCMA), when the number of waiting users and the ratio of transmit power to noise variance are respectively 10 and 20 dB. It is indicated that the proposed scheme can achieve high and low BER with the limited feedback and computation complexity, regardless of the transmit power and the number of waiting users. opportunistic beamforming; multiuser; OFDM; NOMA; spectrum efficiency +
Footnote †: journal: Applied Soft Matter and Quantum Information  
Due to the low complexity and high SE, many works have been done on OBF. In ref. [15], two transmission mechanisms are proposed for OBF systems, i.e., maximum-capacity-based and fairness-based mechanisms. The closed-form expressions of ergodic capacities and the theoretical bounds of BERs are derived. Ref. [16] analyzes the performances in Rician fading channels and presents the maximum likelihood estimation method of OBF systems. The authors of [17] propose a SNR pre-estimation scheme matching beamforming process, which improves ergodic capacities of OBF systems. In ref. [18], an OBF system based on multiple variable weights is proposed, and the optimal number of OBF weights is derived in a fast-changing independent Rayleigh fading channel. Ref. [19] extends OBF systems from independent fading channels to correlated fading channels, and proposed a low-latency transmission scheme, where the mapping between antenna gain and SNR is pre-loaded at BS for user selection. The conventional OBF systems only provide single user transmission, then many works began to research the multiple-access schemes of OBF. In [20], multibeam OBF scheme is proposed, and the closed-form expression of ergodic capacity is derived, according to the asymptotic theory of limit distribution of statistics. Then, the authors present the trade-off between multiuser diversity and multiplexing gains. Ref. [21] considers the impact of user location distribution on outage capacity of a multibeam OBF system, and derives the outage capacity, when the locations of users obey Poisson point distributions. Time division multiple-access-based (TDMA-) and space division multiple-access-based (SDMA-) OBF systems are studied in [22], and an algorithm for handoff between TDMA and SDMA schemes is proposed according to the distribution, number and SNRs of users. The above multibeam OBF systems use orthogonal resources to achieve multiuser multiplexing. To further improve the SE, non-orthogonal patterns are applied. Ref.