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arxiv: 1907.00482 · v1 · pith:XNGEFIWZnew · submitted 2019-06-30 · 📡 eess.SP · cs.IT· math.IT

Base Station Antenna Selection for Low-Resolution ADC Systems

Jinseok Choi , Junmo Sung , Narayan Prasad , Xiao-Feng Qi , Brian L. Evans , Alan Gatherer This is my paper

Pith reviewed 2026-05-25 12:21 UTC · model grok-4.3

classification 📡 eess.SP cs.ITmath.IT
keywords antenna selectionlow-resolution ADCzero-forcing precodingsum ratequantization noisebase stationOFDM
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The pith

For low-resolution ADCs, the downlink antenna selection criterion that maximizes sum rate under zero-forcing precoding is identical to the perfect quantization case.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper studies transmit and receive antenna selection at base stations that use large arrays paired with low-resolution ADCs. For downlink narrowband transmission with zero-forcing precoding, it shows that the sum-rate-maximizing selection rule does not change when the ADCs become coarse. It also derives the exact sum-rate loss incurred by choosing a subset of antennas and proves that this loss, unlike the high-resolution case, reaches a peak at finite transmit power and then falls back to zero. For uplink reception the work supplies a quantization-aware greedy selection rule together with a submodular lower bound on the resulting sum rate. The same conclusions hold for wideband OFDM provided the identical antenna subset is retained across all subcarriers.

Core claim

The central claim is that, under zero-forcing precoding, the antenna subset that maximizes downlink sum rate with low-resolution ADCs is the same subset that would be chosen if the ADCs were ideal; the sum-rate penalty from using fewer antennas is a unimodal function of total transmit power that attains a maximum and thereafter declines to zero.

What carries the argument

The sum-rate loss expression obtained by subtracting the subset sum rate from the full-array sum rate under the additive quantization noise model.

If this is right

  • Maximum achievable sum rate continues to rise as more antennas are selected from the array.
  • At sufficiently high transmit power the performance gap between the selected subset and the full array vanishes.
  • The uplink greedy algorithm yields a sum rate that is at least as large as the submodular lower bound supplied in the paper.
  • All stated results carry over to OFDM when the antenna subset is identical on every subcarrier.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Existing high-resolution antenna-selection code can be reused without modification in low-resolution ADC base stations that employ zero-forcing.
  • Power-control policies may be adjusted to operate near the peak-loss point if that point lies inside the practical transmit-power range.
  • The submodular lower bound offers a route to polynomial-time approximation guarantees for larger antenna-selection problems.

Load-bearing premise

The analysis assumes either narrowband flat fading or that the same antenna subset is held fixed across every subcarrier in wideband OFDM, and that the additive quantization noise model remains accurate under the chosen precoding and detection.

What would settle it

A plot of measured or simulated sum-rate loss versus increasing total transmit power that fails to show a single peak followed by monotonic decline to zero in a low-resolution ADC downlink with zero-forcing precoding.

Figures

Figures reproduced from arXiv: 1907.00482 by Alan Gatherer, Brian L. Evans, Jinseok Choi, Junmo Sung, Narayan Prasad, Xiao-Feng Qi.

Figure 1
Figure 1. Figure 1: A multiuser communication system in which a base station (BS) serves [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Average sum rate Rdl,ofdm (a) with respect to the number of selected antennas Nt for NBS = 64 BS antennas, NMS = 8 MSs, P = 30 dBm total power constraint, and b ∈ {3, 4, 5} ADC bits, and (b) with respect to the total transmit power constraint P for NBS = 128 BS antennas, NMS = 12 MSs, Nt = 16 selected antennas, and b = 3 ADC bits. To find an approximated optimal solution, we can also use the adaptive MCMC … view at source ↗
Figure 3
Figure 3. Figure 3: Average capacity Rul with respect to transmit power ρ for (a) NBS = 32 BS antennas, NMS = 8 MSs, Nr = 8 selected antennas, and b = 3 quantization bits, and for (b) NBS = 128 BS antennas, NMS = 12 MSs, Nr = 16 selected antennas, and b = 3 ADC bits. A. Downlink Transmit Antenna Selection We consider the DL ODFM system with Nsc = 64 subcarriers for channels with L = 4 taps. To validate the analysis, we use th… view at source ↗
Figure 4
Figure 4. Figure 4: Average capacity Rul with respect to the number of ADC bits b for NBS = 128 BS antennas, NMS = 8 MSs, Nr = 16 selected antennas, and ρ = 10 dBm transmit power. quantization. Although the NBS method presents low performance improvement, because of its low complexity O(NMSNr), it is considered as a reasonable antenna selection method for high￾resolution ADC systems [23]. A random selection is simulated to of… view at source ↗
Figure 5
Figure 5. Figure 5: Average capacity Rul (a) with respect to the number of BS antennas NBS for NMS = 12 MSs, Nr = 16 selected antennas, ρ = 20 dBm transmit power, and b = 3 ADC bits, and (b) with respect to the number of MSs NMS for NBS = 128 BS antennas, Nr = 16 selected antennas, ρ = 20 dBm transmit power, and b = 3 ADC bits. addition, the results in [PITH_FULL_IMAGE:figures/full_fig_p026_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Average sum capacity 1 Nsc P n Rul n with respect to transmit power ρ for NBS = 32 BS antennas, NMS = 8 MSs, Nr = 8 selected antennas, b = 3 quantization bits, and Nsc = 64 subcarriers with L = 4-tap channels. NMS, which is desirable in term of maximizing the sum rate. Overall, performance improvement with the proposed QFAS becomes larger as more users are served and more antennas are deployed for the fixe… view at source ↗
Figure 7
Figure 7. Figure 7: Average sum capacity 1 Nsc P n Rul n with respect to the number of selected antennas Nr for NBS = 128 BS antennas, NMS = 12 MSs, b = 3 quantization bits, Nsc = 64 subcarriers with L = 4-tab channels, and ρ = 20 dBm. VII. CONCLUSION In this paper, we investigate antenna selection at a BS in low-resolution ADC systems to achieve power-efficient wireless communication systems. For downlink narrowband and wide… view at source ↗
read the original abstract

This paper investigates antenna selection at a base station with large antenna arrays and low-resolution analog-to-digital converters. For downlink transmit antenna selection for narrowband channels, we show (1) a selection criterion that maximizes sum rate with zero-forcing precoding equivalent to that of a perfect quantization system; (2) maximum sum rate increases with number of selected antennas; (3) derivation of the sum rate loss function from using a subset of antennas; and (4) unlike high-resolution converter systems, sum rate loss reaches a maximum at a point of total transmit power and decreases beyond that point to converge to zero. For wideband orthogonal-frequency-division-multiplexing (OFDM) systems, our results hold when entire subcarriers share a common subset of antennas. For uplink receive antenna selection for narrowband channels, we (1) generalize a greedy antenna selection criterion to capture tradeoffs between channel gain and quantization error; (2) propose a quantization-aware fast antenna selection algorithm using the criterion; and (3) derive a lower bound on sum rate achieved by the proposed algorithm based on submodular functions. For wideband OFDM systems, we extend our algorithm and derive a lower bound on its sum rate. Simulation results validate theoretical analyses and show increases in sum rate over conventional algorithms.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript examines base station antenna selection in systems with low-resolution ADCs. For downlink transmit antenna selection with zero-forcing precoding in narrowband channels, it claims equivalence of the sum-rate maximizing selection criterion to the perfect quantization case, that the maximum sum rate increases with the number of selected antennas, derives the sum rate loss due to using a subset, and shows that unlike high-resolution systems the sum rate loss peaks at a certain transmit power and then decreases to zero. Similar results for wideband OFDM when using common subset. For uplink receive antenna selection, it generalizes a greedy criterion, proposes a quantization-aware fast algorithm, and derives a submodular lower bound on the sum rate. Simulations support the claims.

Significance. If the derivations hold under the modeling assumptions, the paper provides valuable insights into how low-resolution ADCs affect antenna selection strategies in massive MIMO systems, particularly the distinct behavior of sum-rate loss with transmit power and the applicability of submodular optimization for algorithm design. The submodular lower bound is a strength providing theoretical performance guarantee.

major comments (3)
  1. [Downlink ZF analysis (abstract points 1,4)] The equivalence of the selection criterion to the perfect-quantization case and the sum-rate loss peaking then converging to zero (abstract claims 1 and 4) both follow directly from the AQNM property that quantization noise variance scales linearly with received signal power and is independent of the chosen antenna subset in the ZF sum-rate expression. The manuscript should explicitly identify the AQNM equations used and discuss whether this independence holds for actual (non-linear) quantizers where error statistics may depend on precoded signal amplitudes in a subset-dependent manner.
  2. [Uplink algorithm and bound derivation] The submodular lower bound on sum rate for the proposed uplink algorithm is load-bearing for the theoretical guarantee (abstract uplink point 3). The specific function shown to be submodular, the proof of submodularity, and the tightness of the bound should be stated with equation numbers; without these the bound's utility is unclear.
  3. [OFDM extensions] The wideband OFDM claims (both downlink and uplink) require that the same antenna subset is used across all subcarriers. This assumption's impact when frequency selectivity makes per-subcarrier optimal subsets differ should be quantified or bounded, as it is central to the practical extension.
minor comments (2)
  1. Simulation parameters (SNR ranges, ADC bit resolutions, channel models, number of Monte Carlo runs) should be listed in a dedicated table or subsection for reproducibility.
  2. Notation for the AQNM parameters (e.g., quantization noise variance factor) should be introduced once and used consistently across downlink and uplink sections.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment below and will revise the manuscript accordingly to improve clarity and address the raised points.

read point-by-point responses

  1. Referee: [Downlink ZF analysis (abstract points 1,4)] The equivalence of the selection criterion to the perfect-quantization case and the sum-rate loss peaking then converging to zero (abstract claims 1 and 4) both follow directly from the AQNM property that quantization noise variance scales linearly with received signal power and is independent of the chosen antenna subset in the ZF sum-rate expression. The manuscript should explicitly identify the AQNM equations used and discuss whether this independence holds for actual (non-linear) quantizers where error statistics may depend on precoded signal amplitudes in a subset-dependent manner.

    Authors: We agree that the downlink results rely on the additive quantization noise model (AQNM). In the revision, we will explicitly cite and identify the AQNM equations (quantization noise variance proportional to signal power, independent of subset under ZF) in the relevant analysis section. We will also add a discussion noting that AQNM is an approximation; for actual non-linear quantizers, error statistics could depend on precoded amplitudes and thus on the subset, potentially violating independence—this is a modeling limitation of the work. revision: yes

  2. Referee: [Uplink algorithm and bound derivation] The submodular lower bound on sum rate for the proposed uplink algorithm is load-bearing for the theoretical guarantee (abstract uplink point 3). The specific function shown to be submodular, the proof of submodularity, and the tightness of the bound should be stated with equation numbers; without these the bound's utility is unclear.

    Authors: We will revise the uplink section to explicitly identify the submodular function (the quantization-aware greedy criterion) with its equation number, include the proof of submodularity (leveraging the diminishing-returns property), and add analysis or numerical results on bound tightness to clarify its utility and performance guarantee. revision: yes

  3. Referee: [OFDM extensions] The wideband OFDM claims (both downlink and uplink) require that the same antenna subset is used across all subcarriers. This assumption's impact when frequency selectivity makes per-subcarrier optimal subsets differ should be quantified or bounded, as it is central to the practical extension.

    Authors: The manuscript assumes a common subset across subcarriers for practical implementation. We will add a discussion in the OFDM sections quantifying the impact of this assumption under frequency selectivity, including simulation comparisons to per-subcarrier selection or a derived bound on the resulting sum-rate gap. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivations self-contained under AQNM

full rationale

The paper derives the downlink selection criterion equivalence and sum-rate loss peaking-then-converging behavior directly from the additive quantization noise model (AQNM) properties, where quantization noise variance scales linearly with received signal power. This leads to high-SNR effective rates becoming independent of specific channel gains (hence of subset choice) as an analytical consequence, not by redefinition or fitting. The uplink greedy criterion generalization and submodular lower bound rely on standard submodular set function properties applied to the quantization-aware metric; these are external mathematical facts, not imported via self-citation chains or ansatzes. No equations reduce to inputs by construction, no fitted parameters are relabeled as predictions, and no load-bearing uniqueness theorems from overlapping authors are invoked. The narrowband/wideband assumptions and AQNM applicability are stated as modeling choices, not derived results. The central claims therefore retain independent analytical content.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no free parameters, axioms, or invented entities can be identified from the provided text.

pith-pipeline@v0.9.0 · 5773 in / 1166 out tokens · 40901 ms · 2026-05-25T12:21:58.993344+00:00 · methodology

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