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Digital Predistortion for Hybrid MIMO Transmitters

Mahmoud Abdelaziz, Lauri Anttila, Alberto Brihuega, Fredrik Tufvesson, Mikko Valkama

arXiv:1804.02178v1eess.SP

TL;DR

Hybrid MIMO transmitters need linearization for nonlinear PA distortion, while a sub-array's single RF chain limits it to one DPD stage despite differing PA characteristics. The paper proposes a memory-aware DPD that learns from combined PA outputs using one observation receiver. It reports more than 10 dB ACLR gain over single-PA learning and well-behaved out-of-band emissions across spatial directions, with realistic feedback mismatches having negligible effect in the reported analysis.

  • Problem

    PA nonlinearities can compromise massive-MIMO spectral and energy efficiency, while hybrid transmitters use one DPD stage for multiple PAs whose characteristics can differ.

    Source: §I · p. 2

  • Method

    The proposed sub-array DPD learns from a combined feedback signal of the PA outputs and uses decorrelation-based learning to target nonlinear distortion toward the intended receiver.

    Source: §I · p. 2, §VI · p. 9

  • Results

    More than 10 dB gain in ACLR was achieved over single-PA-output learning, and out-of-band emissions in other directions were generally well-behaved, with only a few-dB excess in certain directions.

    Source: A. DPD Performance Results and Analysis · p. 8, B. Analysis of Unwanted Emissions in… · p. 9

  • Takeaways & Limitations

    The combined-output learning approach requires only one observation receiver, and realistic feedback amplitude and phase mismatches had negligible effect in the reported analysis.

    Source: §I · p. 2, §IV · p. 7, §VI · p. 9

Abstract

from arXiv · show

This article investigates digital predistortion (DPD) linearization of hybrid beamforming large-scale antenna transmitters. We propose a novel DPD processing and learning technique for an antenna sub-array, which utilizes a combined signal of the individual power amplifier (PA) outputs in conjunction with a decorrelation-based learning rule. In effect, the proposed approach results in minimizing the nonlinear distortions in the direction of the intended receiver. This feature is highly desirable, since emissions in other directions are naturally weak due to beamforming. The proposed parameter learning technique requires only a single observation receiver, and therefore supports simple hardware implementation. It is also shown to clearly outperform the current state-of-the-art technique which utilizes only a single PA for learning. Analysis of the feedback network amplitude and phase imbalances reveals that the technique is robust even to high levels of such imbalances. Finally, we also show that the array system out-of-band emissions are well-behaving in all spatial directions, and essentially below those of the corresponding single-antenna transmitter, due to the combined effects of the DPD and beamforming.

I. INTRODUCTION

Hybrid beamforming reduces the hardware burden of large arrays, but nonlinear PAs can impair spectral efficiency and produce harmful out-of-band emissions. This paper proposes sub-array DPD that learns from combined PA outputs to reduce distortion toward the intended receiver, using one observation receiver.

I. INTRODUCTION

  • PA nonlinearities can compromise spectral efficiency and energy efficiency, while out-of-band radiation can interfere with neighboring channels or violate emission limits.Prior work reported average ACLR in massive MIMO equal to the single-antenna case at the same total sum-power.Source: §I · p. 2
  • Under ideal beamforming and free-space LoS assumptions, the most harmful nonlinear emissions are in the main-beam direction toward the intended receiver.The introduction also frames high PA efficiency as important for large arrays with wide instantaneous bandwidth.Source: §I · pp. 1–2
  • Backoff requires larger PAs operating in their linear region, increasing RF-chain cost and size and reducing energy efficiency.The paper instead motivates smaller, more efficient PAs operating near saturation with low-complexity linearization.Source: §I · p. 2
  • A single DPD must linearize all sub-array PAs, an underdetermined task that can reduce individual-PA performance when their nonlinear characteristics differ.Earlier approaches relied on one PA for learning, similar PAs, or per-PA observation chains; the cited direct-learning approach used memoryless DPD and memoryless PAs.Source: §I · p. 2
  • The proposed hybrid-MIMO DPD learns from the superposition of PA outputs, uses one observation receiver, and targets distortion in the intended receiver direction.The reported approach outperforms single-PA learning and is analyzed for feedback-path imbalance and emissions across spatial directions.Source: §I · p. 2

II. MODELING AND MEASURING NONLINEAR DISTORTION IN HYBRID MIMO TX SUB-ARRAYS

The section models a sub-array's PA outputs and examines the effective signal radiated toward the intended receiver. Under ideal beamforming and free-space LoS assumptions, that signal is the coherent superposition of the antenna outputs.

II. MODELING AND MEASURING NONLINEAR DISTORTION IN HYBRID MIMO TX SUB-ARRAYS

  • The PA outputs are modeled with parallel Hammerstein branch filters, and the model includes filter memory.The input x(n), branch input and output signals, beamforming coefficient, filter response, and convolution operation are introduced in the model description.Source: §II · p. 3
  • Under ideal beamforming and free-space LoS conditions, the effective received signal y(n) is the coherent sum of individual antenna outputs.The analysis assumes phase-only analog beamforming, with |w_m| = 1, and focuses on radiation toward the intended receiver.Source: §II · p. 3
  • The section evaluates out-of-band emissions in the worst case where a victim receiver lies in the intended receiver direction, using ACLR on the combined signal y(n).In-band distortion is quantified with EVM; the text notes that ACLR evaluation for large-array transmitters had not been decided in 3GPP standardization.Source: §II · p. 3

III. PROPOSED DPD STRUCTURE AND PARAMETER LEARNING SOLUTION

A hybrid-MIMO sub-array has one RF upconversion chain and therefore uses one DPD stage. This reduces DPD processing complexity but makes linearization harder because the parallel PAs can have different characteristics.

III. PROPOSED DPD STRUCTURE AND PARAMETER LEARNING SOLUTION

  • Each hybrid-MIMO sub-array is fed by one RF upconversion chain, so it can use only one DPD stage.This lowers overall DPD processing complexity while complicating the main-path structure and parameter learning when the parallel PAs differ.Source: §III · p. 3
  • The single-stage constraint makes linearization challenging because the characteristics of the sub-array's M parallel PAs are generally different.The challenge affects both DPD main-path processing and parameter learning.Source: §III · p. 3
  • Using one DPD stage per sub-array reduces the complexity of transmitter DPD processing compared with a separate stage for each PA.The passage states the reduction in overall DPD processing complexity without quantifying it.Source: §III · p. 3

A. Proposed DPD Structure

The proposed DPD injects a filtered nonlinear cancellation signal at the sub-array input to reduce nonlinear distortion in the effective signal toward the intended receiver. Its structure uses nonlinear basis functions and memory filters.

A. Proposed DPD Structure

  • The DPD targets in-band and out-of-band nonlinear distortion in the effective combined signal y(n) toward the intended receiver.The design objective is to minimize harmful emissions in that direction.Source: A. Proposed DPD Structure · p. 4
  • The combined-signal nonlinear term is a linear combination of static nonlinear basis functions and delayed replicas, with effective branch filters depending on sums of individual PA filters.The linear distortion term is treated as typically equalized at the receiver.Source: A. Proposed DPD Structure · p. 4
  • The proposed structure injects a low-power cancellation signal, structurally similar to the nonlinear terms, at the PA inputs to reduce radiated in-band and out-of-band distortion.The injection uses static nonlinear basis functions filtered by a bank of DPD filters with memory; the coefficients determine achievable suppression.Source: A. Proposed DPD Structure · p. 4

B. Proposed Combined Feedback based DPD Learning

The proposed learner combines the sub-array’s PA outputs into one feedback observation and uses decorrelation to reduce residual nonlinear distortion. Its block-adaptive updates use orthogonalized basis functions and can run during calibration or continuously.

B. Proposed Combined Feedback based DPD Learning

  • A single observation receiver captures the combined PA outputs after anti-beamforming cancels the transmitter’s beamforming weights.Alternatively, setting all beamforming weights to one during learning and summing the PA outputs yields essentially the same observation waveform.Source: B. Proposed Combined Feedback based… · p. 4
  • The learning error compares the observed combined signal with the ideal input after estimating the effective linear gain.A multitap estimate can be used when the effective linear response is substantially frequency-selective.Source: B. Proposed Combined Feedback based… · pp. 4–5
  • Block-adaptive updates minimize correlation between residual distortion and orthogonalized basis functions, yielding convergence to an uncorrelated residual.The basis functions are orthogonalized because the original nonlinear basis functions and delayed replicas are strongly correlated.Source: B. Proposed Combined Feedback based… · pp. 4–5
  • Learning may run during calibration or continuously because anti-beamforming makes the feedback independent of the intended receiver direction.Continuous operation can track changes in PA characteristics as accurately as possible.Source: B. Proposed Combined Feedback based… · p. 5

IV. IMPACT OF MISMATCHES BETWEEN THE FEEDBACK BRANCHES

The paper analyzes feedback-path amplitude and phase mismatches using a third-order, memoryless PA and DPD example. Under the stated large-sub-array and zero-mean, independent mismatch assumptions, the analysis finds little effect on learning performance.

IV. IMPACT OF MISMATCHES BETWEEN THE FEEDBACK BRANCHES

  • As feedback gain and phase mismatches increase, the combined observation gradually degrades, although it remains expressible using nonlinear basis functions and delayed replicas.The signal is formed by combining individual PA outputs after extracting them through feedback couplers.Source: §IV · p. 5
  • The closed-form mismatch analysis assumes third-order memoryless processing in both the PA and DPD models to assess coefficient bias.The feedback deviations are represented as complex gain deviations with separate amplitude and phase mismatches.Source: §IV · p. 5
  • The analysis finds feedback-branch mismatches have very little effect on DPD learning and performance under its stated assumptions.For a relatively large sub-array with zero-mean mismatches independent of the PA coefficients, the mismatched optimum approaches the ideal one; numerical experiments also reconfirm robustness.Source: §IV · pp. 6–7

V. NUMERICAL EXPERIMENTS

The numerical evaluation uses measured PA models with memory from the Lund University massive MIMO test-bed to compare combined-feedback DPD against learning from a single PA output.

V. NUMERICAL EXPERIMENTS

  • The proposed combined-feedback DPD is compared with a classical approach that learns from only one PA output using measured PA models with memory.The models are 11th-order parallel Hammerstein models from individual USRP modules in a 100-PA test-bed, measured at 2 GHz with a 120 MHz sample rate.Source: §V · p. 7
  • The simulations use a 20 MHz OFDM signal with 16-QAM and iterative clipping and filtering that limits PAPR to approximately 8.3 dB.The measured models represent 16 PAs selected as representative examples, with their output power spectra shown in Fig. 4.Source: §V · p. 7
  • The evaluation uses practical measured PA models with memory rather than assuming memoryless or identical PAs.The paper presents this setup as more realistic than prior hybrid-MIMO DPD studies using those simplifying assumptions.Source: §V · p. 7

A. DPD Performance Results and Analysis

The proposed DPD is evaluated on measured PA models using in-band EVM and adjacent-channel ACLR in the intended receiver direction. It achieves more than 10 dB ACLR gain over single-PA-output learning, despite substantial feedback-path mismatches.

A. DPD Performance Results and Analysis

  • EVM and ACLR quantify in-band waveform error and adjacent-channel interference, respectively, for the effective combined signal toward the intended receiver.The wanted-signal bandwidth contains 99% of total emitted power in the main-beam direction, and the adjacent-channel measurement bandwidth is equal to it.Source: A. DPD Performance Results and Analysis · p. 7
  • The proposed DPD and single-PA-learning reference use nonlinearity order 9, memory depth N = 3, 100k-sample learning blocks, and 24 adaptive iterations for a sub-array of size M = 16.The effective linear gain is estimated using ordinary block least squares per block iteration.Source: A. DPD Performance Results and Analysis · p. 7
  • The proposed DPD achieves more than 10 dB gain in ACLR compared with using a single PA output for learning, despite random feedback-path amplitude mismatches uniformly distributed from −10 to 10% and phase mismatches from −10 to 10o.Source: A. DPD Performance Results and Analysis · p. 8
  • The proposed DPD coefficients converge reliably and relatively quickly under the tested feedback mismatches.The example tracks the first two of four memory taps per basis function; basis-function orthogonalization partly accounts for the convergence behavior.Source: A. DPD Performance Results and Analysis · p. 8, Figure 6 · p. 8

B. Analysis of Unwanted Emissions in Spatial Domain

The spatial analysis compares in-band and out-of-band power patterns for single-antenna and array transmitters after DPD. For 16 antennas, OOB emissions remain essentially at or below the single-antenna reference, with only small exceptions; a 32-antenna array stays below that reference in every direction.

B. Analysis of Unwanted Emissions in Spatial Domain

  • The analysis examines spatial OOB behavior after DPD because the algorithm primarily learns coefficients for emissions toward the intended receiver.The figure’s OOB levels span the adjacent channel, while in-band levels span the allocated channel.Source: B. Analysis of Unwanted Emissions in… · p. 8
  • The spatial patterns compare in-band and adjacent-channel power from a single antenna with a 16-antenna array over directions from −90 to 90 degrees.The intended receiver is at the main beam, 30 degrees in the example; received passband power is normalized to 0 dB in both cases.Source: B. Analysis of Unwanted Emissions in… · p. 8, Figure 7 · p. 9
  • In one reported example, OOB emission level is −40.48 dB without predistortion and −61.42 dB with predistortion, corresponding to ACLRs of 40.48 dBc and 61.42 dBc, respectively.At the other example direction of −30 degrees, the ACLR values are 63.12 dBc and 60.51 dBc, respectively.Source: B. Analysis of Unwanted Emissions in… · p. 9
  • After applying the proposed DPD, a 32-antenna array’s higher spatial selectivity reduces OOB emissions so they no longer exceed the single-antenna emissions in any spatial direction.In certain directions, OOB emissions can exceed the reference by a few dBs at most, while remaining at a sufficiently low level.Source: B. Analysis of Unwanted Emissions in… · p. 9

VI. CONCLUSIONS

The paper concludes that its reduced-complexity sub-array DPD improves ACLR over single-PA-output learning using combined PA feedback and decorrelation-based learning. It also reports well-behaved spatial out-of-band emissions and negligible effects from realistic branch mismatches.

VI. CONCLUSIONS

  • More than 10 dB gain in ACLR was achieved with the proposed DPD compared with using a single PA output for learning.The comparison is reported for practical simulations based on measured PA models.Source: §VI · p. 9
  • The array’s out-of-band emissions were well-behaved across spatial directions and essentially at or below the reference single-antenna levels.Fig. 8 covers directions from −90 to 90 degrees, with received passband power normalized to 0 dB at the intended receiver direction.Source: §VI · p. 9, Figure 8 · p. 9
  • The reduced-complexity sub-array DPD combines PA feedback and decorrelation-based learning to target nonlinear distortion toward the intended receiver using one observation receiver chain.Memory effects were considered in both the DPD structure and learning.Source: §VI · p. 9
  • Amplitude and phase mismatches between PA branches had negligible effects under realistic assumptions.Source: §VI · p. 9
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