PaperlayerView exact revision on arXiv

Source-linked AI summary

MIMO-NOMA Design for Small Packet Transmission in the Internet of Things

Z. Ding, L. Dai, H. V. Poor

arXiv:1603.00302v1cs.IT

TL;DR

The paper addresses MIMO-NOMA operation for IoT users requiring rapid small-packet service when users have similar channel conditions. It designs precoding and power allocation to differentiate effective channels, strictly satisfy one user’s QoS, and serve the other opportunistically. Analytical and numerical results demonstrate the proposed scheme’s performance and compare its power-allocation policies.

  • Problem

    Existing MIMO-NOMA schemes rely on users having different channel conditions, an assumption that may fail when IoT users have similar channels and diversified QoS requirements.

  • Method

    The scheme jointly designs precoding and power allocation so user 1’s effective channel is degraded but its QoS is protected, while user 2’s effective channel is improved and decoded using NOMA.

  • Results

    Analytical and numerical results show that the proposed MIMO-NOMA scheme realizes NOMA with similar original channels and outperforms existing MIMO-NOMA schemes at all layers.

  • Takeaways & Limitations

    The design supports strict QoS for a rapidly served IoT user while allowing opportunistic service for another user despite similar channel conditions.

Abstract

from arXiv · show

A feature of the Internet of Things (IoT) is that some users in the system need to be served quickly for small packet transmission. To address this requirement, a new multiple-input multiple-output non-orthogonal multiple access (MIMO-NOMA) scheme is designed in this paper, where one user is served with its quality of service (QoS) requirement strictly met, and the other user is served opportunistically by using the NOMA concept. The novelty of this new scheme is that it confronts the challenge that most existing MIMO-NOMA schemes rely on the assumption that users' channel conditions are different, a strong assumption which may not be valid in practice. The developed precoding and detection strategies can effectively create a significant difference between the users' effective channel gains, and therefore the potential of NOMA can be realized even if the users' original channel conditions are similar. Analytical and numerical results are provided to demonstrate the performance of the proposed MIMO-NOMA scheme.

I. INTRODUCTION

The paper develops a MIMO-NOMA downlink for two IoT users with different QoS needs, addressing cases where their original channel conditions are similar. Precoding and power allocation create differentiated effective channels while strictly supporting user 1’s QoS and opportunistically serving user 2.

  • I. INTRODUCTION: 5G IoT connectivity is difficult because billions of devices have diversified QoS requirements under scarce bandwidth, motivating NOMA’s shared-resource access.NOMA uses shared frequency, time, or spreading resources while separating users through power-domain multiple access.
  • I. INTRODUCTION: The considered scenario serves user 1 quickly with a low targeted data rate for small packets, while user 2 receives best-effort service.An incident-warning vehicle and another vehicle downloading multimedia files illustrate the two service profiles.
  • I. INTRODUCTION: Existing MIMO-NOMA schemes commonly assume substantially different user channel conditions, although participating users may instead have similar channels.The paper focuses on two users without path loss, making their channel conditions similar; it assumes M ≥N.
  • I. INTRODUCTION: The proposed design uses precoding to degrade user 1’s effective channel and improve user 2’s, creating channel disparity for NOMA despite similar original channels.The precoding matrix is selected from user 2’s QR decomposition, with P = V2; this improves user 2 and degrades user 1.
  • I. INTRODUCTION: Power allocation is designed alongside the precoder to meet user 1’s QoS strictly while improving user 2 opportunistically.The design treats user 1 as a primary user with strict QoS and user 2 as an opportunistic user, analogous to a cognitive radio network.
  • I. INTRODUCTION: User 2 applies SIC to remove user 1’s message before decoding its own message, while user 1 uses zero forcing rather than QR-based detection.SIC addresses inter-layer and intra-layer interference at user 2; zero forcing is applied at user 1 because it does not decode user 2’s streams.

A. Impact of the Proposed Precoding Scheme

The proposed precoding strengthens user 2 while shrinking user 1’s effective channel, creating channel disparity for NOMA even when original channels are similar. Power allocation then protects user 1’s QoS while serving user 2 opportunistically.

  • Precoding impact: The reception reliability at user 2 depends on ξ_i, whose distribution shows that increasing base-station antennas improves user 2’s receive signal strength.The diagonal element has a chi-square distribution with 2(M−i+1) degrees of freedom.
  • Precoding impact: The precoding matrix shrinks user 1’s channel from an M × N Gaussian matrix to an N × N Gaussian matrix, removing dependence on M.This follows because H_1 and H_2 are independent and unitary transformation preserves Gaussian statistics.
  • Precoding impact: For N = 1, user 2’s effective channel gain strengthens with M, whereas user 1’s gain remains exponentially distributed and its reliability does not improve with more antennas.The asymmetric effect creates the intended effective-channel disparity.
  • Power allocation: Because precoding degrades user 1’s channel, the power allocation coefficients must preserve user 1’s QoS under the weakened effective channel.The paper develops long-term and instantaneous QoS policies.
  • Power allocation: The revised policy handles cases where user 1’s effective gain exceeds user 2’s, avoiding a choice that guarantees SIC failure at user 2.The paper also notes that reversing decoding order would make user 1’s outage depend on user 2’s targeted rate, so it is not considered.

III. OUTAGE PERFORMANCE AT USER 1

Power allocation policy I targets user 1’s QoS statistically over the long term rather than for every instantaneous channel realization. Its feasibility requires a constraint on the targeted outage probability.

  • Long-term QoS: Policy I chooses α_i and β_i independently of instantaneous channel gains to satisfy user 1’s QoS in the long term.The coefficients are designed so user 1’s outage probability does not exceed its targeted value.
  • Feasibility: The targeted outage probability must obey a feasibility constraint ensuring the resulting allocation coefficient remains valid.The paper excludes P_1,i,target = 1 and identifies a lower bound achieved when all power is assigned to user 1.

B. Power Allocation Policy II

Power allocation policy II enforces user 1’s target rate instantaneously, while admitting user 2 only when SIC and the primary user’s QoS can be maintained. Under this policy, user 1 retains the benchmark outage performance.

  • Instantaneous QoS: Policy II designs the allocation coefficients to ensure log(1+SINR_1,i) ≥ R_1,i instantaneously, subject to channel conditions.Deep fading can still make the ideal allocation infeasible by forcing β_i = 0.
  • Outage performance: User 1’s diversity gain for decoding s_i is one under policy II.The outage analysis attributes remaining outage to infeasible allocation under deep fading.
  • Benchmark comparison: Policy II gives user 1 the same outage probability as the benchmark serving user 1 alone with β_i = 0.User 2 is served only while user 1’s outage probability is not degraded relative to that benchmark.
  • Benchmark comparison: A benchmark precoder designed for user 1 achieves diversity gain M−N+1 per stream, whereas the proposed precoder intentionally shrinks user 1’s channel to create channel disparity.The diversity loss is therefore linked to the proposed NOMA-oriented precoding choice.

C. When User 1 Adopts the QR Based Approach

The QR-based detection approach is analyzed for user 1, but its outage probability remains bounded away from zero at high SNR. Consequently, the paper uses zero-forcing detection instead.

  • Detection structure: QR decomposition yields an upper-triangular effective channel matrix, requiring user 1 to decode stream i before stream j for N ≥ i > j ≥ 1.User 1 does not decode messages intended for user 2, and its i-th-stream model is rewritten accordingly.
  • Outage behavior: Under the QR approach, user 1’s outage probability becomes a non-zero constant regardless of how large the SNR is.The analysis uses the distributions of the diagonal and off-diagonal entries of the QR factor under the stated power-allocation assumption.
  • Detection choice: User 1’s outage probability never goes to zero under QR detection, even when transmission power becomes infinite.Zero forcing can cancel inter-layer interference at user 1, so only zero-forcing detection is considered.
  • Power allocation: The two power-allocation policies lead to separate analyses for user 2 because user 2 experiences them differently.This distinction motivates separate subsections for the two scenarios.

A. Power Allocation Policy I

Power allocation policy I uses coefficients independent of instantaneous channel gains and analyzes user 2’s outage through layer-wise decoding events. At high SNR, user 2 achieves diversity gain M − i + 1 for decoding w_i.

  • Outage decomposition: Policy I decomposes user 2’s outage into disjoint events according to which message at layer m fails while previous-layer messages decode successfully.The events distinguish failure to decode s_m from failure to decode w_m after decoding s_m.
  • Policy structure: Under policy I, power coefficients do not depend on instantaneous channel gains, enabling a layer-wise outage analysis based on independent diagonal entries of R_2.The chosen β_i can ensure the targeted outage-probability constraint for user 1.
  • High-SNR analysis: At high SNR, ξ_m and ε_2,m/(ρβ_2m) approach zero for fixed targeted user-1 outage probability, yielding the high-SNR outage approximation.The targeted outage probability is constrained as in (22) and is not a function of ρ in this analysis.
  • Diversity gain: The resulting diversity gain for user 2 to decode w_i is M − i + 1.The same diversity-order conclusion also applies when the targeted outage probability varies with ρ as 1 − e^(−x/ρ), for x > 1.

B. Power Allocation Policy II

Power allocation policy II makes user 2’s coefficients functions of instantaneous channel gains, complicating the outage analysis. The paper therefore derives bounds using the joint distribution of inverse-Wishart diagonal elements.

  • Policy structure: Under policy II, the power allocation coefficients depend on instantaneous channel gains, making the outage probability difficult to evaluate.This dependence contrasts with policy I, whose coefficients are not functions of instantaneous channel gains.
  • Outage formulation: The outage probability is formulated by integrating over the joint probability density of diagonal elements y_11, …, y_ii of an inverse Wishart matrix.The variables are associated with W^−1, where W is formed from the effective channel matrices.
  • Analytical limitation: Because the inverse-Wishart diagonal elements are correlated and the coefficients have a complicated form, no closed-form outage expression for user 2 can be found.The analysis consequently focuses on upper and lower outage-probability bounds for diversity-gain analysis.

1) Upper and lower bounds on the outage probability:

For policy II, the paper develops upper and lower bounds on user 2’s outage probability by partitioning decoding events and analyzing the relevant channel-variable cases. The bounds establish diversity gain one.

  • Upper bound: When x_m exceeds the relevant threshold, user 2 can decode s_m for sure under the stated condition.This property is used to bound factors in the outage analysis.
  • Diversity result: Combining the derived bounds gives a lower bound of 1 on the diversity gain at user 2.This lower bound is obtained from the upper bound on the outage probability.
  • Diversity result: When power allocation policy II is used, the upper and lower bounds converge, so user 2’s diversity gain for decoding w_i is one.The paper notes that this equals user 1’s diversity gain under the same policy.

V. NUMERICAL STUDIES

The numerical studies compare the proposed scheme with MIMO-NOMA and MIMO-OMA benchmarks, then examine system-parameter effects and verify analytical results.

  • Simulations compare the proposed scheme with existing MIMO-NOMA and MIMO-OMA schemes.Additional results assess system-parameter choices and verify the paper’s analytical results.

A. Comparison to Benchmark Schemes

The proposed scheme is evaluated against existing MIMO-NOMA and MIMO-OMA benchmarks. It outperforms existing MIMO-NOMA schemes and achieves better outage performance than the considered MIMO-OMA scheme.

  • Comparison setup: The benchmark comparison uses power allocation policy I with targeted rates R1,i = 1 BPCU and R2,i = 4 BPCU.The targeted outage probabilities determine the power allocation coefficients, while user 1’s QoS is guaranteed in the long term.
  • MIMO-NOMA benchmarks: The comparison with ZF-NOMA and SA-NOMA focuses on M = N because their original system requirements must be adapted to the addressed scenario.The proposed scheme remains applicable when N is small.
  • MIMO-NOMA benchmarks: For M = N, SA-NOMA and ZF-NOMA achieve the same outage performance in the addressed scenario.Signal alignment gives the two users the same effective channel matrices in this case.
  • MIMO-NOMA benchmarks: At all layers, the proposed scheme outperforms the existing MIMO-NOMA schemes.Its outage curves have changing slopes, indicating changing diversity gains, whereas the existing schemes have the same slope because of correlated effective channel gains.
  • MIMO-OMA benchmark: The proposed MIMO-NOMA scheme achieves better outage performance than the considered MIMO-OMA scheme, with a larger gap when M increases.Both schemes achieve the same diversity gains because their outage probabilities are determined by the same underlying mechanism.

B. Impact of Different System Parameters on Users’ Outage Performance

The parameter studies verify QoS guarantees for user 1 and analytical outage expressions, while showing how antennas, target rates, layers, and power policies affect user 2’s outage performance.

  • User 1 outage performance: Under power allocation policy I, user 1’s simulated outage curves match the targeted outage probabilities, demonstrating long-term QoS guarantees.This evaluates the proposed scheme with different targeted data rates.
  • User 1 outage performance: Under power allocation policy II, user 1’s results match the analytical results, supporting instantaneous QoS satisfaction.Policy II defines coefficients to ensure user 1’s targeted data rate is met instantaneously.
  • User 2 outage performance: Simulation results for user 2 match the exact analytical outage expression, while the high-SNR approximation matches only at high SNR.The approximation’s limitation follows from its high-SNR assumption.
  • User 2 outage performance: User 2’s outage curve has a larger slope at layer i than at layer j for i < j, reflecting a larger diversity gain at the earlier layer.This layer dependence is reported for power allocation policy I.
  • User 2 outage performance: With power allocation policy II, user 2’s outage performance improves with more base-station antennas or lower targeted data rates.At high SNR, all layers have the same slope and therefore the same diversity gain, which is one.
  • Power allocation policies: Policy I gives user 2 better outage performance, whereas policy II satisfies user 1’s QoS instantaneously and policy I satisfies it only in the long term.The policies therefore expose a performance-versus-QoS-timing distinction.

VI. CONCLUSIONS

The paper proposes a MIMO-NOMA strategy that realizes NOMA with similar user channel conditions by shaping effective gains and using two QoS-oriented power allocation policies.

  • The precoding matrix degrades user 1’s effective channel gains while improving user 2’s signal strength, creating sufficiently different effective channel conditions.
  • Two power allocation policies meet user 1’s QoS requirement over the long term or instantaneously, respectively.
  • Analytical and numerical results demonstrate the advantages and disadvantages of the two power allocation policies.
  • The outage performance at user 2 is analyzed using bounding techniques, while a closed-form expression based on inverse Wishart order statistics remains future work.
Loading 1603.00302v1…