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Non-Orthogonal Multiple Access (NOMA) for Downlink Multiuser MIMO Systems: User Clustering, Beamforming, and Power Allocation

Md Shipon Ali, Ekram Hossain, Dong In Kim

arXiv:1611.07425v1cs.ITcs.NI

TL;DR

The paper tackles high interference in downlink MIMO-NOMA when UE receive antennas outnumber BS transmit antennas. It combines dynamic clustering, equivalent-channel multi-cluster ZF beamforming, SIC-based NOMA, and two-stage power allocation; simulations report spectral-efficiency gains over MIMO-OMA and existing MIMO-NOMA solutions.

  • Problem

    MIMO-NOMA with more receive than transmit antennas produces high interference, motivating a robust downlink design that minimizes net interference and maximizes capacity.

  • Method

    The paper dynamically clusters UE receive antennas, uses equivalent-channel multi-cluster ZF-BF with decoding scaling, and allocates power dynamically across and within clusters.

  • Results

    The simulations demonstrate spectral-efficiency enhancement of the proposed MIMO-NOMA model over MIMO-OMA and other existing MIMO-NOMA solutions.

  • Takeaways & Limitations

    The proposed clustering, beamforming, and power-allocation combination supports higher spectral efficiency in the studied downlink MIMO-NOMA setting.

Abstract

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We investigate the application of non-orthogonal multiple access (NOMA) with successive interference cancellation (SIC) in downlink multiuser multiple-input multiple-output (MIMO) cellular systems, where the total number of receive antennas at user equipment (UE) ends in a cell is more than the number of transmit antennas at the base station (BS). We first dynamically group the UE receive antennas into a number of clusters equal to or more than the number of BS transmit antennas. A single beamforming vector is then shared by all the receive antennas in a cluster. We propose a linear beamforming technique in which all the receive antennas can significantly cancel the inter-cluster interference. On the other hand, the receive antennas in each cluster are scheduled on power domain NOMA basis with SIC at the receiver ends. For inter-cluster and intra-cluster power allocation, we provide dynamic power allocation solutions with an objective to maximizing the overall cell capacity. An extensive performance evaluation is carried out for the proposed MIMO-NOMA system and the results are compared with those for conventional orthogonal multiple access (OMA)-based MIMO systems and other existing MIMO-NOMA solutions. The numerical results quantify the capacity gain of the proposed MIMO-NOMA model over MIMO-OMA and other existing MIMO-NOMA solutions.

I. INTRODUCTION

The paper addresses interference and clustering challenges in downlink multiuser MIMO-NOMA when receive antennas outnumber BS transmit antennas. It proposes new beamforming, clustering, and dynamic power-allocation methods, supported by broad simulations.

  • MIMO-NOMA superposes users on shared spectrum, while multiuser MIMO uses beamforming to improve system throughput.
  • More receive antennas than BS transmit antennas create strong inter-cluster interference, making multi-cluster beamforming essential.
  • The proposed model introduces a multi-cluster ZF-BF technique based on each cluster’s equivalent channel gain rather than one particular user’s channel.
  • A low-complexity clustering scheme targets maximum cell sum-spectral efficiency by exploiting both NOMA and MIMO principles.
  • Dynamic power allocation separately handles inter-cluster and intra-cluster power, while simulations cover varied antenna counts, cluster sizes, and Rayleigh channels.

C. Paper Organization

The system model considers a single-cell BS with more total UE receive antennas than transmit antennas, grouping receive antennas into MIMO-NOMA clusters. Signals combine beamformed cluster streams, intra-beam interference, inter-beam interference, and noise.

  • A. System Model: The BS has Nt transmit antennas, L total UE receive antennas with L > Nt, and N clusters satisfying N ≥ Nt.
  • A. System Model: When N = Nt, every cluster uses the full bandwidth with its own beam; when N > Nt, clusters may share beams using orthogonal spectrum resources.
  • B. Signal Model: Each cluster’s data stream superposes user messages weighted by their transmit powers before beamforming through matrix M.
  • B. Signal Model: At each receiver, a decoding scaling weight factor multiplies the received signal before decoding, with the channel vector and Gaussian noise defining reception.
  • B. Signal Model: Dynamic intra-cluster allocation lets higher-channel-gain users decode and suppress lower-channel-gain users’ intra-cluster interference before SINR and throughput evaluation.
  • B. Signal Model: Overall cell throughput depends on beamforming, user clustering, and inter-cluster and intra-cluster power allocation.

III. BEAMFORMING IN DOWNLINK MIMO-NOMA

The beamforming design adapts zero-forcing to MIMO-NOMA’s excess receive antennas by constructing an equivalent channel matrix and adding receiver-side scaling.

  • Conventional ZF-BF completely removes inter-cluster interference only when total receive antennas do not exceed total transmit antennas.
  • The proposed precoding manipulates cluster channel matrices into an equivalent channel matrix with dimensions compatible with ZF-BF.
  • A decoding scaling weight factor is introduced to reduce inter-cluster interference and increase desired signal strength.

A. Precoding Matrix

The proposed precoding constructs an equivalent channel for each MIMO-NOMA cluster and obtains the beamforming matrix from the equivalent channel of all clusters.

  • A. Precoding Matrix: Each cluster’s K×N channel matrix is represented using its users’ radio channel vectors and singular value decomposition.The n-th cluster channel matrix H_n contains the channel vector h_n,k for each user.
  • A. Precoding Matrix: A single beamforming vector is assigned to each MIMO-NOMA cluster, producing an equivalent 1×N channel matrix for that cluster.The equivalent channel is formed after applying the cluster-specific transformation derived from the SVD.
  • A. Precoding Matrix: The equivalent channel matrix H̄ ∈ C^N×N is formed by combining the equivalent channel matrices of all MIMO-NOMA clusters.
  • A. Precoding Matrix: The BS precoding matrix M ∈ C^N×N is obtained from the right pseudo-inverse of the combined equivalent channel matrix.The columns of the pseudo-inverse are denoted by m̄_n, and the Frobenius norm is used in the precoding expression.

B. Decoding Scaling Weight Factor

The decoding scaling factor uses the cluster-head channel estimate to improve decoding for other users in a MIMO-NOMA cluster, with the factor communicated before transmission.

  • B. Decoding Scaling Weight Factor: Users are clustered to maximize distinctive channel gains, then ordered so the strongest user is the cluster-head and the weakest is the K-th user.The cluster-head is the first user under the paper’s ascending-order convention for channel gains.
  • B. Decoding Scaling Weight Factor: When the cluster-head has sufficiently higher gain, the cluster’s equivalent channel gain is nearly similar to the cluster-head’s gain, enabling near-complete inter-cluster interference cancellation.
  • B. Decoding Scaling Weight Factor: Each k-th user’s channel is scaled by a decoding weight before decoding to obtain the best estimate of the n-th cluster-head’s channel.The BS sends this scaling factor before data transmission, alongside the power information needed for SIC.

IV. DYNAMIC USER CLUSTERING IN DOWNLINK MIMO-NOMA

The paper develops low-complexity, channel-aware clustering for downlink MIMO-NOMA, using channel gains, correlations, UE separation, and MIMO-specific precoding and decoding considerations.

  • IV. Dynamic User Clustering in Downlink MIMO-NOMA: MIMO-NOMA clustering groups receive antennas from different UEs into clusters sharing a beam, while users within each cluster use NOMA.
  • IV. Dynamic User Clustering in Downlink MIMO-NOMA: The proposed sub-optimal clustering scheme exploits channel-gain differences and correlations to enhance cell sum-spectral efficiency.Unlike conventional NOMA clustering, MIMO-NOMA clustering also depends on MIMO precoding and decoding.
  • IV. Dynamic User Clustering in Downlink MIMO-NOMA: The low-complexity algorithm sets N = N_t when N_t < L ≤ 2N_t and N = ⌈L/2⌉ when L > 2N_t.
  • IV. Dynamic User Clustering in Downlink MIMO-NOMA: Lower-gain users can suffer strong intra-cluster and inter-cluster interference, especially when their gains approach the cluster-head’s gain.
  • IV. Dynamic User Clustering in Downlink MIMO-NOMA: Higher-order clusters may require excessive power for their weakest users under per-antenna power limits, motivating a sophisticated 2-user clustering algorithm.The paper states that 3-user and higher-order clustering follows a similar process.
  • IV. Dynamic User Clustering in Downlink MIMO-NOMA: Users are sorted by channel gain, with the higher-gain users selected as cluster-heads and additional users assigned using correlation and distinct-UE conditions.The algorithm separately handles correlated and uncorrelated channel gains while updating the candidate user sets.

5. Final MIMO-NOMA clusters: while k ≥1

The final clustering procedure accounts for channel-gain correlation and otherwise seeks maximum gain differences between cluster-heads and their paired users.

  • 5. Final MIMO-NOMA clusters: while k ≥1: Correlated users can satisfy a more relaxed maximum gain-difference requirement during clustering.
  • 5. Final MIMO-NOMA clusters: while k ≥1: For uncorrelated gains, the procedure ensures maximum channel-gain differences between each cluster-head and the other user.

V. DYNAMIC POWER ALLOCATION IN DOWNLINK MIMO-NOMA

The proposed system uses two-step dynamic power allocation: first across beams, then among users within each MIMO-NOMA cluster, while accounting for throughput and SIC requirements.

  • Inter-cluster power allocation: Beam transmit power is divided in proportion to the number of users served by each beam.Equal-sized clusters receive equal beam transmit powers.
  • Intra-cluster power allocation: Intra-cluster allocation uses normalized channel gains, guaranteed throughput requirements, and minimum received-power differences needed for SIC.Users in each cluster are ordered by descending normalized channel gain.
  • Intra-cluster power allocation: The intra-cluster optimization follows the dynamic power-allocation formulation developed for downlink single-antenna NOMA.The paper uses the closed-form solution from prior work to obtain the proposed system’s allocation.
  • Intra-cluster power allocation: The optimal power allocation for users other than the first user is expressed using complementary sets of rate requirements and SIC constraints.The terms B′ and C′ represent these complementary sets for the nth cluster.

A. Simulation Assumptions

The evaluation models a single-cell MIMO-NOMA system under LTE-based simulation assumptions, with Rayleigh fading, path loss, clustered users, and extensive channel averaging.

  • Simulation setup: The simulations compare proposed MIMO-NOMA throughput and spectral efficiency with conventional MIMO-OMA and conventional MIMO-NOMA.The simulation parameters follow 3GPP-LTE assumptions.
  • Channel and cell model: The radio channel combines free-space path loss with zero-mean, unit-variance Rayleigh fading in a single-sector hexagonal cell.The BS is located at a corner of the cell area.
  • Simulation setup: Channel gains are averaged over twenty thousands of channel realizations, with the number of clusters set equal to the number of BS transmit antennas.This lets all clusters use full spectrum resources through the MIMO principle.
  • MIMO-OMA baseline: For MIMO-OMA, users receive orthogonal spectrum resources, and each user’s transmit power is proportional to its allocated spectrum resource.The BS also provides decoding scaling weights and transmit-power information before transmission.
  • Illustrative configuration: The illustrated 3-user MIMO-NOMA setup contains 3 transmit antennas, 9 receive antennas, and 9 UEs.These dimensions are denoted Nt = 3, L = 9, and X = 9.

B. Simulation Results

The simulations show that proposed MIMO-NOMA generally exceeds MIMO-OMA and conventional MIMO-NOMA in spectral efficiency, while gains depend on clustering, channel correlation, transmit-antenna count, and user coverage. Higher-order clusters and MIMO can increase gains, but inter-cluster interference, power limits, and coverage constraints restrict feasible deployments.

  • 2-user clusters: The proposed MIMO-NOMA achieves higher spectral efficiency than MIMO-OMA, with larger comparative gains when lower-channel-gain users have higher guaranteed throughput requirements.The comparison uses 50% and 25% of cluster bandwidth for the lower-channel-gain users’ OMA throughput requirements.
  • 2-user clusters: Moving cluster-heads within 50m of the BS produces larger spectral-efficiency gains than distributing them within 150m.The enhancement is attributed to improved cluster-head channel gains and reduced inter-cluster interference from the proposed precoding and decoding mechanisms.
  • Higher-order clusters: Higher-order user clusters yield larger gains over MIMO-OMA, but require more cell-edge users and are confined to smaller coverage areas.For the assumed parameters, proposed clusters with more than four users are infeasible because of strong inter-cluster interference and transmit-power limitations.
  • Transmit-antenna scaling: With 5 transmit antennas, both MIMO-NOMA and MIMO-OMA have higher spectral efficiency than with 3 transmit antennas, while MIMO-NOMA coverage for lower-channel-gain users decreases.The reduction follows increased inter-cluster interference in higher-order MIMO scenarios.
  • Correlated channel gains: The proposed MIMO-NOMA provides much higher spectral efficiency than conventional MIMO-NOMA under correlated channel gains with ρ = 0.5.In Fig. 11, cluster-heads are within 150m of the BS while other users are distributed near cell-edge areas.
  • Correlated channel gains: Highly correlated users can enable complete inter-cluster-interference cancellation, making throughput unaffected by the number of transmit antennas and favoring higher-order clusters.The correlation sweep covers ρ = 0 to 1, with cluster-heads near the BS and other users near the cell edge.

VII. CONCLUSION

The paper studies downlink MIMO-NOMA when UE receive antennas outnumber BS transmit antennas, addressing interference that grows with the number of beams. It introduces zero-forcing beamforming, dynamic power allocation, and clustering, while leaving multicell evaluation for future work.

  • The proposed system groups UE receive antennas into clusters, with each cluster served by a single beam orthogonal to other clusters’ beams.
  • Inter-cluster interference increases with the number of beams, corresponding to the number of BS transmit antennas.
  • The proposed inter-cluster zero-forcing beamforming can significantly eliminate interference when clusters contain users with more distinctive channel gains.
  • Dynamic power allocation is provided for both inter-cluster and intra-cluster power allocation in the downlink MIMO-NOMA system.
  • Evaluation is limited to a single-cell scenario; multicell investigation is left for future work because inter-cell interference may affect performance.
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