PaperlayerView exact revision on arXiv

Source-linked AI summary

Low Power Analog-to-Digital Conversion in Millimeter Wave Systems: Impact of Resolution and Bandwidth on Performance

Oner Orhan, Elza Erkip, Sundeep Rangan

arXiv:1502.01980v1cs.IT

TL;DR

Wide bandwidths and many antennas make ADC power a central constraint in mmWave receivers. The paper uses an AQNM to study how ADC bandwidth and resolution affect achievable rate under receiver power limits, comparing analog and digital combining. It finds that rate-optimal bandwidth exists, analog combining can outperform digital combining under ADC-only constraints in some regimes, while digital combining can lead when total front-end power is counted.

  • Problem

    The paper asks how ADC power constraints affect information-theoretic communication limits and receiver design in wideband, multi-antenna mmWave systems.

  • Method

    Using an additive quantization noise model, the paper derives achievable rates for SISO and MIMO systems while varying ADC bandwidth, resolution, antenna count, combining architecture, and receiver power constraint.

  • Results

    There is a maximum useful bandwidth for both combining architectures; with ADC-only power, analog combining can have higher rate while digital combining uses less bandwidth, whereas total front-end accounting may favor digital combining.

  • Takeaways & Limitations

    Receiver architecture and ADC operating point should be evaluated jointly with the applicable power budget rather than by bandwidth or resolution alone.

Abstract

from arXiv · show

The wide bandwidth and large number of antennas used in millimeter wave systems put a heavy burden on the power consumption at the receiver. In this paper, using an additive quantization noise model, the effect of analog-digital conversion (ADC) resolution and bandwidth on the achievable rate is investigated for a multi-antenna system under a receiver power constraint. Two receiver architectures, analog and digital combining, are compared in terms of performance. Results demonstrate that: (i) For both analog and digital combining, there is a maximum bandwidth beyond which the achievable rate decreases; (ii) Depending on the operating regime of the system, analog combiner may have higher rate but digital combining uses less bandwidth when only ADC power consumption is considered, (iii) digital combining may have higher rate when power consumption of all the components in the receiver front-end are taken into account.

I. INTRODUCTION

The paper studies ADC power constraints in wideband mmWave MIMO receivers, comparing analog and digital combining while optimizing bandwidth and resolution for achievable rate.

  • Motivation: MmWave systems offer vast spectrum and very high-dimensional antenna arrays, but ADCs consume substantial power when processing many antenna outputs over wide bandwidths.ADC power is an important receiver concern alongside baseband processing, particularly in handheld devices.
  • Scope: The paper investigates achievable rates under either total front-end receiver-power constraints or ADC-only power constraints.It studies SISO and MIMO systems, including spatial multiplexing and beamforming.
  • Main results: An optimal ADC bandwidth and resolution exists for wideband SISO systems, so operating over the full available bandwidth may be undesirable.The optimization targets the achievable rate under a receiver power constraint.
  • Scope: The analysis leaves detailed hybrid analog/digital combining for future work, expecting its simulation results to lie between the analog and digital cases.This scope boundary limits the paper’s direct architectural comparison.
  • Main results: With ADC power alone constrained, analog combining can achieve a higher maximum rate in some MIMO regimes, while digital combining reaches its maximum rate at less bandwidth.The utilized bandwidth decreases as the number of transmit and receive antennas increases.
  • Main results: When all receiver-front-end components are included in the power constraint, digital combining may achieve a higher rate when channel state information is available at the transmitter.The comparison differs from the ADC-only case because analog-combiner power also increases with antenna count.

II. SYSTEM MODEL

The system model considers point-to-point frequency-selective mmWave MIMO channels with separate digital-combining and analog-combining receiver architectures under standard power and channel-knowledge assumptions.

  • Channel model: The model uses Nt transmit antennas, Nr receive antennas, total bandwidth Wtot, AWGN with power spectral density N0, and transmit-power constraint P.Fading is independent across frequency and antennas, and instantaneous fading is known at the receiver.
  • Receiver architectures: Digital combining quantizes each antenna output before baseband combining, with separate I/Q ADCs operating at the Nyquist rate.Each I/Q ADC represents two ADCs for in-phase and quadrature components.
  • Receiver architectures: Analog combining combines antenna signals with phase shifters before digitization, requiring one I/Q ADC per stream.The RF analog architecture includes Nr LNAs, Nr phase shifters, one combiner, one mixer, and one I/Q ADC.
  • Quantization model: Each ADC is modeled as a b-bin scalar quantizer, and the analysis uses an AQNM-based lower bound with Gaussian inputs and Gaussian quantization noise.The AQNM is used because optimal input distributions for arbitrary multi-bit quantizers are difficult to obtain.

A. Additive Quantization Noise Model (AQNM)

The AQNM represents quantization through an additive noise term, with quantization quality characterized by a coding-gain parameter that decreases as resolution increases.

  • Quantizer representation: The quantizer maps input z to output zq = Q(z), chosen as the conditional mean E[z|zq].This defines the quantized output used in the AQNM representation.
  • Additive noise model: The AQNM models the quantized signal using additive quantization noise nq that is uncorrelated with the input z.The model also characterizes the variance of the additive quantization noise and the quantization error.
  • Model parameters: The quantization-error variance eq and input variance σ_z^2 determine the AQNM parameter α through the model’s variance relation.The supplied formulation identifies eq as the variance of z − zq and σ_z^2 as the quantizer-input variance.
  • Coding gain: For a non-uniform scalar MMSE quantizer, the coding gain β is approximated by a resolution-dependent expression and modeled as β = ab^-2 ≤ 1.Here b is the number of quantization bins, a > 0 is constant, and β approaches zero as b increases.

B. Power Consumption of the Receiver

The receiver power model accounts for front-end components and ADC conversion costs, with ADC power increasing with sampling rate and quantization resolution. The analysis evaluates achievable rates under either total receiver-power or ADC-only constraints, using AQNM-based SISO comparisons.

  • Total receiver power includes LNA, phase shifter, combiner, mixer, and ADC consumption.
  • ADC power scales linearly with sampling rate and exponentially with the number of bits per sample.The model assumes Nyquist-rate sampling and uses c as the energy per conversion step.
  • The ADC-only scenario constrains total ADC power while avoiding direct comparison of differently designed front-end components.The authors caution that this scenario may provide only a partial indication of practical behavior.
  • For the SISO channel, AQNM with Gaussian inputs provides an achievable rate that lower bounds capacity.The rate is monotonically increasing and concave in transmit power for fixed bandwidth and resolution.
  • At −10dB SNR, AQNM rates are 96% and 99% of capacity for 2-bin and 8-bin quantization, respectively.
  • At 20dB SNR, AQNM rates are 72% and 77% of capacity for 2-bin and 8-bin quantization, respectively.The gap increases at high SNR, while equiprobable b-point inputs approach capacity.

IV. THE OPTIMAL BANDWIDTH AND RESOLUTION OF ADC FOR SISO SYSTEMS

The SISO analysis optimizes ADC bandwidth and quantization resolution under a total receiver-power constraint. It shows that finite optimal bandwidth and resolution can arise because ADC power consumes more of the available budget as bandwidth increases.

  • The SISO optimization chooses bandwidth W and quantization bins b to maximize achievable rate under total receiver power Ptot.
  • ADC power feasibility imposes PLNA + PM + 2cWb ≤ Ptot, with bandwidth bounded by Wtot.
  • When Wtot is large, an optimal bandwidth exists beyond which the achievable rate decreases.
  • When ab^-2 < 1, a finite bandwidth W* maximizes the constrained achievable rate.
  • Under receiver power constraints, larger bandwidth is not always preferable, and an optimal number of quantization levels also exists.
  • At low SNR, the optimum uses lower bandwidth and more quantization bins under the stated 20mW ADC budget and 7GHz total bandwidth.Reducing bandwidth allows available transmit power to be spread over a smaller band, increasing effective SNR.

V. MIMO SYSTEM

The MIMO analysis compares digital and analog combining under perfect CSIT and no CSIT. These scenarios distinguish transmitter knowledge of instantaneous channel realizations from knowledge only of channel state.

  • The MIMO achievable-rate analysis considers both digital and analog receiver combining.
  • Each architecture is evaluated with perfect CSIT, where instantaneous channel realizations are known, and no CSIT, where only channel state is known.

A. Digital Combining

For digital combining, AQNM yields an equivalent channel and achievable rate over bandwidth W ≤ Wtot. The analysis uses covariance assumptions, SVD-based combining, and power allocation across channel eigenmodes.

  • AQNM produces an equivalent per-frequency-band channel whose quantization-noise covariance depends on H, Rxx, and Rnn.
  • Under no CSIT, the input covariance is chosen as Rxx = P/Nt I for identically distributed fading across antennas and frequency bands.
  • Under CSIT, SVD of the channel determines the transmit covariance and digital combiner, providing a further lower bound to achievable rate.
  • The received signal after SVD-based combining separates into eigenmode gain and combined thermal and quantization-noise terms.
  • Power is allocated across channel eigenvalues using waterfilling to obtain the digital-combining achievable rate.The strategy is optimal without quantization when the power-dependent quantization-noise term is zero.

B. Analog Combining:

The analog-combining analysis expresses an equivalent channel per frequency band and maximizes achievable rate by maximizing received power through the combining vector.

  • The AQNM analysis obtains an equivalent analog-combining channel for each frequency band.
  • Achievable rate is optimized by maximizing the received-power term |w_r^H H w_t|^2.
  • The maximum achievable received power depends on whether channel state information at the transmitter is available.
  • Without CSIT and with a symmetric channel, the optimal transmit beamforming vector uses equal components.

1) Analog Combining without CSIT:

For analog combining without CSIT, the receiver phases are selected to align the channel contributions, while maximum-ratio transmission at the transmitter maximizes received power.

  • The analog combiner phase φ_i is chosen to match the phase of the corresponding channel sum, attaining equality in the received-power bound.
  • Maximum-ratio transmission maximizes received power for a given analog combining vector.

2) Analog Combining with CSIT:

The paper evaluates analog-combining performance across ADC settings, antenna counts, architectures, and receiver power budgets. Under ADC-only constraints analog combining can outperform digital combining, whereas accounting for all front-end components can favor digital combining.

  • Numerical results vary ADC bandwidth, resolution, antenna count, receiver architecture, and power consumption under independent Rayleigh fading.The maximum available bandwidth is W_tot = 7 GHz, and the conversion-step energy is c = 494 fJ.
  • With total ADC power fixed at 20 mW, analog combining achieves higher rates than digital combining in the studied SIMO and MIMO cases.The best resolution is generally 3-bin quantization, except for digital-combining SIMO, where 2-bin quantization is optimal.
  • Under the same ADC-only budget, digital MIMO uses one-third of the bandwidth used by analog combining.The digital-combining result reflects its spatial-multiplexing advantage despite its lower rate in these cases.
  • As antenna count increases, MIMO rates rise for both combining architectures, while digital combining’s optimal bandwidth scales as 1/N and analog combining’s remains constant.
  • When total front-end power is constrained, digital combining with CSIT achieves higher rate than analog combining with CSIT, with the gap increasing as the power budget grows.Without CSIT, analog combining is better only above 350 mW, and the improvement is very small.
  • Under total receiver-power optimization, the optimal digital-combining resolution is lower than the analog-combining resolution except at P_tot = 100 mW.The optimal antenna count generally increases with P_tot, while optimal bandwidth can fluctuate as power is reallocated among antennas, resolution, and bandwidth.

VII. CONCLUSIONS

The paper finds that ADC bandwidth, resolution, antenna count, and receiver architecture jointly determine achievable rate under power constraints. Analog combining can outperform digital combining under ADC-only constraints in some regimes, whereas digital combining may prevail when total front-end power is counted.

  • An optimal ADC bandwidth and resolution exist for the SISO channel under a receiver power constraint.The analysis uses the additive quantization noise model and considers both total front-end power and ADC-only budgets.
  • Under an ADC-only power budget, analog combining may provide higher rate in some operating regimes, while digital combining uses less bandwidth.The comparison depends on the system operating regime.
  • When all receiver-component power is constrained, digital combining may achieve the higher rate.In some cases, increasing the number of receiver antennas can be optimal under this broader power model.
Loading 1502.01980v1…