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Mixed-ADC/DAC Multipair Massive MIMO Relaying Systems: Performance Analysis and Power Optimization

Jiayi Zhang, Linglong Dai, Ziyan He, Bo Ai, Octavia A. Dobre

arXiv:1809.03117v1cs.ITmath.IT

TL;DR

Practical massive-MIMO relays face high converter power consumption and hardware cost, while coarse quantization creates signal-processing challenges. The paper analyzes mixed-resolution ADC/DAC multipair relaying and reports antenna-count power scaling, rate performance, and energy-efficiency findings.

  • Problem

    High-resolution ADCs and DACs increase power consumption and hardware cost, while coarse quantization poses signal-processing challenges in practical massive-MIMO relays.

    Source: §I · p. 1, B. Contributions · p. 2

  • Method

    The paper uses AQNM to derive exact and approximate achievable-rate expressions for mixed-resolution ADC/DAC multipair relaying and proposes power allocation via geometric programming.

    Source: B. Contributions · p. 2

  • Results

    Each antenna’s transmit power can scale down by 1/M as relay antennas grow without rate loss, and the mixed-resolution system can reduce power consumption and hardware cost while maintaining considerable performance.

    Source: B. Contributions · p. 2

  • Takeaways & Limitations

    Large relay antenna arrays can support mixed-ADC/DAC relaying with high achievable rate and power saving despite low-resolution converter rate loss.

    Source: §VI · p. 9

Abstract

from arXiv · show

High power consumption and expensive hardware are two bottlenecks for practical massive multiple-input multiple-output (mMIMO) systems. One promising solution is to employ low-resolution analog-to-digital converters (ADCs) and digital-to-analog converters (DACs). In this paper, we consider a general multipair mMIMO relaying system with a mixed-ADC/DAC architecture, in which some antennas are connected to low-resolution ADCs/DACs, while the rest of the antennas are connected to high-resolution ADCs/DACs. Leveraging on the additive quantization noise model, both exact and approximate closed-form expressions for the achievable rate are derived. It is shown that the achievable rate can approach the unquantized one by using only 2-3 bits of resolutions. Moreover, a power scaling law is presented to reveal that the transmit power can be scaled down inversely proportional to the number of antennas at the relay. We further propose an efficient power allocation scheme by solving a complementary geometric programming problem. In addition, a trade-off between the achievable rate and power consumption for different numbers of low-resolution ADCs/DACs is investigated by deriving the energy efficiency. Our results reveal that the large antenna array can be exploited to enable the mixed-ADC/DAC architecture, which significantly reduces the power consumption and hardware cost for practical mMIMO systems.

I. INTRODUCTION

The paper studies mixed-resolution ADC/DAC multipair massive-MIMO relaying to address converter cost and power while retaining achievable-rate performance. It develops rate analysis, power scaling and allocation, and energy-efficiency results for this architecture.

I. INTRODUCTION

  • High-resolution converters raise power consumption and hardware cost, while coarse quantization brings signal-processing challenges in practical massive-MIMO relays.The paper frames mixed-resolution converters as a way to balance those concerns.Source: §I · p. 1

A. Related Works

  • Earlier mixed-ADC research largely concerned single-hop systems; prior low-resolution two-hop relays were rate-limited by very coarse quantization, motivating arbitrary-resolution ADCs and DACs.The paper positions its architecture as more general than one-bit ADC/DAC designs.Source: A. Related Works · p. 2, B. Contributions · p. 2

B. Contributions

  • Using AQNM, the paper derives exact and approximate closed-form achievable-rate expressions for mixed-ADC/DAC multipair relaying systems.The approximate expressions use asymptotic arguments and provide insight into effects of antenna count, transmit power, quantization bits, and high-resolution-quantizer fraction.Source: B. Contributions · p. 2
  • As the relay antenna count M grows, each antenna’s transmit power can scale down by 1/M without rate loss; the low-power rate gap from an unquantized relay is constant.The stated scaling law concerns the data-transmission phase.Source: B. Contributions · p. 2
  • A low-complexity power-allocation algorithm addresses coarse-quantization rate degradation by transforming the problem into a sequence of geometric programs.The general complementary geometric program is approximated through successive GP problems.Source: B. Contributions · p. 2
  • The energy-efficiency analysis examines high-resolution-converter fraction and quantization bits, with the optimal bit count obtained numerically.The paper reports reduced power consumption and hardware cost while maintaining considerable performance.Source: B. Contributions · p. 2

II. SYSTEM MODEL

  • The system has K source-destination pairs communicating through a half-duplex relay, with M0 high-resolution and M−M0 low-resolution ADC/DAC pairs.The relay receives in one time slot and forwards quantized signals in the next.Source: §II · p. 3

A. Quantization with Mixed-Resolution ADCs

The mixed-resolution ADC model separates high- and low-resolution received signals and represents low-resolution quantization using the additive quantization noise model.

A. Quantization with Mixed-Resolution ADCs

B. Maximum Ratio (MR) Processing at the Relay

The relay uses amplify-and-forward with maximum-ratio processing, while mixed-resolution DAC quantization is incorporated into the transmit model and power normalization.

B. Maximum Ratio (MR) Processing at the Relay

C. Quantization with Mixed-Resolution DACs

  • The DAC analysis assumes equal ADC and DAC resolutions for simplicity, while stating that the method extends to arbitrary resolution cases.High-resolution DAC outputs are unchanged, whereas low-resolution DACs add quantization noise uncorrelated with their input.Source: C. Quantization with Mixed-Resolution… · p. 4
  • The expected total relay transmit power is expressed in a lemma and used to obtain the normalization factor.The paper selects amplify-and-forward for lower implementation complexity than decode-and-forward.Source: C. Quantization with Mixed-Resolution… · p. 4

III. ACHIEVABLE RATE ANALYSIS

The exact achievable-rate analysis uses statistical CSI at each destination and derives a closed-form rate for the mixed-ADC/DAC multipair relay. Its effective-noise accounting includes interference and quantization effects.

A. Exact Achievable Rate Analysis

  • Destinations decode using statistical CSI because instantaneous CSI would require excessive computation for large antenna arrays.Source: A. Exact Achievable Rate Analysis · p. 4
  • The effective-noise accounting includes inter-pair interference, relay quantization noise, and DAC quantization noise.The relay-noise terms distinguish high- and low-resolution quantization.Source: A. Exact Achievable Rate Analysis · p. 4
  • Theorem 1 gives a closed-form exact achievable rate for each destination using a capacity bound.The derivation obtains the SINR from the received signal and uses the uncorrelated desired signal and effective noise.Source: A. Exact Achievable Rate Analysis · pp. 4–5

B. Asymptotic Analysis

The asymptotic analysis uses large-antenna approximations to obtain a more concise achievable-rate expression and examine how power and quantization affect it.

B. Asymptotic Analysis

  • A large-antenna approximation simplifies covariance terms before the paper derives the approximate achievable-rate expression.Theorem 2 presents the approximate rate for each destination.Source: B. Asymptotic Analysis · p. 5
  • The approximate achievable rate increases with relay transmit power and decreases with other sources’ transmit power.The system is described as interference-limited.Source: B. Asymptotic Analysis · p. 6
  • Adding more low-resolution ADCs and DACs decreases the approximate achievable rate as quantization noise increases.Source: B. Asymptotic Analysis · p. 6

C. Power Scaling Law

The section analyzes rate behavior as relay transmit power scales inversely with antenna count. Exact and approximate rates converge to a constant limit, while the low-power gap to the unquantized system remains a constant factor.

C. Power Scaling Law

  • With source and relay power scaled as ES/M and ER/M, both exact and approximate achievable rates converge to the same constant as M grows.The limiting rate depends on the fraction of high-resolution converters and the low-resolution distortion factor.Source: C. Power Scaling Law · p. 6
  • Increasing the high-resolution converter fraction κ or the low-resolution quantization quality α raises the limiting achievable rate.The rate limit improves monotonically with α.Source: C. Power Scaling Law · p. 6
  • In the low-power regime, the mixed-ADC/DAC system’s sum-rate gap from the unquantized system is a constant factor and vanishes when α = 1.The gap factor increases with α; at α = 1, the achievable rates are equal.Source: C. Power Scaling Law · p. 7

IV. POWER ALLOCATION

The section formulates sum-rate maximization as a power-allocation problem under a total transmit-power constraint. It approximates the resulting nonconvex complementary geometric program through a sequence of geometric programs.

IV. POWER ALLOCATION

  • The power-allocation problem maximizes the mixed-ADC/DAC system’s sum achievable rate subject to a total power budget PT.The source and relay powers are constrained by the given total sum power.Source: §IV · p. 7
  • The resulting complementary geometric program is generally nonconvex, so the method approximates it with a sequence of geometric programs.Standard convex optimization tools can solve the resulting GP problems.Source: §IV · p. 7
  • Algorithm 1 iteratively updates SINR-related initial values and stops when the maximum update difference falls below tolerance ε.The procedure initializes from the SINR expression and repeats the GP solve and update steps.Source: §IV · p. 7

V. NUMERICAL RESULTS

The numerical section tests the rate expressions and examines power scaling and power allocation. The reported results show close agreement among analytical and simulated rates, and a sum-rate gain from the proposed allocation scheme over the unquantized uniform-power benchmark.

V. NUMERICAL RESULTS

  • The simulations use users distributed in a 1,000-meter-radius hexagonal cell, with a 100-meter minimum relay distance and pathloss exponent α = 3.8.The coherence interval is τc = 20K and the pilot sequence length is τp = K.Source: §V · pp. 7–8

A. Achievable Rate

  • Exact, approximate, and simulated rates are close; larger quantization bit counts improve rate performance, especially beyond b = 1.For a small relay array, sum rates for b = 1, 2, and ∞ match well; the approximate and simulated curves also draw closer as b increases.Source: A. Achievable Rate · p. 8
  • As relay antenna count M grows, exact and approximate rates approach a constant, and increasing κ raises the achievable rate.The comparison considers κ = 0, 1/2, and 1.Source: A. Achievable Rate · p. 8, Figure 2 · p. 8

B. Power Allocation

  • The proposed optimal power allocation significantly boosts sum rate over the unquantized system with uniform power allocation.Fig. 3 plots sum achievable rate against relay antenna count M for K = 10, κ = 1/2, and PT = 10 dB.Source: B. Power Allocation · p. 8, Figure 3 · p. 8

C. Energy Efficiency

The section examines the trade-off between achievable rate and energy efficiency in mixed-ADC/DAC multipair relaying systems. It reports that increasing the share of low-resolution converters improves energy efficiency, while mixed resolution retains spectral-efficiency and channel-estimation advantages over an all-low-resolution architecture.

C. Energy Efficiency

  • Energy efficiency is studied as a rate–power trade-off, with total power consumption including circuit-block and converter power.The rate definition assumes a transmission bandwidth of 20 MHz; converter power is expressed in terms of quantization bits and circuit parameters.Source: C. Energy Efficiency · p. 8, ADC, P H · p. 9

ADC, P H

  • Pure low-resolution ADCs/DACs attain the best energy efficiency, which increases with the proportion of low-resolution converters in the mixed architecture.Fig. 4 plots energy efficiency against low-resolution quantization bits b for pS = 10 dB, pR = 10 dB, and K = 10.Source: ADC, P H · p. 9, Figure 4 · p. 9
  • Mixed resolution offers better spectral efficiency than a pure low-resolution architecture, whose channel estimation is less tractable without partial high-resolution ADCs.The section characterizes the mixed architecture as reducing power-consumption burden considerably while achieving better spectral efficiency.Source: ADC, P H · p. 9

VI. CONCLUSIONS

  • Mixed-ADC/DAC relaying can attain considerable rate and energy efficiency simultaneously, while massive antenna arrays enable high achievable rate and power savings despite low-resolution rate loss.The conclusion also reports a user transmit-power scaling law of 1/M and an efficient power-allocation scheme that can compensate for rate degradation.Source: §VI · p. 9

APPENDIX A PROOF OF LEMMA 1

The proof breaks an expectation into constituent terms, evaluates them through substitutions and related calculations, and combines the derived expressions to conclude the lemma.

APPENDIX A PROOF OF LEMMA 1

  • The proof partitions the relevant covariance expression into four parts, Q1 through Q4, and uses associated covariance terms defined in equations (17)–(20).It then derives expectations for Q2, Q3, and Q4 in sequence.Source: Appendix A · pp. 9–10
  • The expectation of the diagonal term is decomposed and simplified through substitutions to obtain successive expressions.The proof also derives the expectation of Q4 using earlier results.Source: Appendix A · p. 10
  • Substituting the derived expressions yields RnqD, which the proof reduces to µ(M0 + αM1) before concluding.The derivation also invokes related calculations for the covariance terms.Source: Appendix A · p. 10

APPENDIX B PROOF OF THEOREM 1

The proof of Theorem 1 decomposes the log-function argument into signal, error, interference, noise, and quantization contributions, then computes its terms and combines the results.

APPENDIX B PROOF OF THEOREM 1

  • The log-function argument comprises desired signal power, estimation error, inter-pair interference, relay noise, and ADC and DAC quantization noise.These contributions are labeled Ak through Gk in the proof.Source: Appendix B · p. 10
  • The proof defines t1 through t10 as decomposed terms and includes each undefined term only when its index matches the term number.It then substitutes and simplifies expressions to obtain (29).Source: 2) Compute Bk · p. 11
  • The proof derives expressions for inter-pair interference and relay-noise terms, and computes DAC quantization noise using an earlier result.It states that combining the derived terms completes the proof.Source: 6) Compute Gk · p. 11
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