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MIMO Transmission with Residual Transmit-RF Impairments

Christoph Studer, Markus Wenk, Andreas Burg

arXiv:1002.0406v1cs.IT

TL;DR

Residual Tx-RF impairments can substantially reduce MIMO capacity and the performance of near-optimum detectors, even at small EVMs. The paper models these impairments as i.i.d. Gaussian Tx-noise, validates that model with 4-stream MIMO-OFDM measurements, and proposes Tx-noise whitening to mitigate the loss.

  • Problem

    Residual Tx-RF impairments are often ignored despite potentially affecting MIMO channel capacity and detection performance.

  • Method

    The paper uses an i.i.d. Gaussian Tx-noise model, validates it with real-world 4-stream MIMO-OFDM measurements, and applies Tx-noise whitening.

  • Results

    Residual Tx-RF impairments severely affect near-optimum MIMO detectors, while Tx-noise whitening considerably mitigates the associated performance loss.

  • Takeaways & Limitations

    Residual Tx-RF impairments should be included in MIMO performance analysis and can be mitigated with a practical whitening method.

Abstract

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Physical transceiver implementations for multiple-input multiple-output (MIMO) wireless communication systems suffer from transmit-RF (Tx-RF) impairments. In this paper, we study the effect on channel capacity and error-rate performance of residual Tx-RF impairments that defy proper compensation. In particular, we demonstrate that such residual distortions severely degrade the performance of (near-)optimum MIMO detection algorithms. To mitigate this performance loss, we propose an efficient algorithm, which is based on an i.i.d. Gaussian model for the distortion caused by these impairments. In order to validate this model, we provide measurement results based on a 4-stream Tx-RF chain implementation for MIMO orthogonal frequency-division multiplexing (OFDM).

I. INTRODUCTION

The paper examines residual Tx-RF impairments that remain after imperfect or impractical compensation and extends MIMO modeling to account for them. It studies their effects on capacity and detection performance using a statistical impairment model and real-world validation.

  • I. INTRODUCTION: Residual Tx-RF distortion remains because compensation is imperfect, mismatched, or too complex for economical implementation.In MIMO, the resulting distortion appears as colored noise at the receiver and is often ignored.
  • I. INTRODUCTION: The paper extends the conventional MIMO system model with a statistical model for residual Tx-RF impairments.The model is validated using a 4-stream Tx-RF chain in a MIMO-OFDM scenario.
  • I. INTRODUCTION: Using received signal power relative to thermal-noise power to define SNR enables intuitive analysis of impairment effects on capacity and MIMO detection.This definition avoids observations suggesting that linear detection improves when residual impairments are added.
  • I. INTRODUCTION: Near-optimum MIMO detection algorithms suffer substantial performance loss from residual Tx-RF impairments, even with high-quality RF chains.The paper argues that minimum impairment-quality requirements in standards may be insufficient for careless treatment of this issue.
  • II. MIMO SYSTEM MODEL WITH RESIDUAL TX-RF IMPAIRMENTS: The considered system spatially multiplexes MT-dimensional symbol vectors over MT transmit and MR ≥ MT receive antennas under coherent detection.The receiver knows the channel realization and thermal-noise variance, while the transmitter has no channel-state information.

A. Gaussian Model for Residual Tx-RF Impairments

The paper models aggregate residual Tx-RF impairments as additive i.i.d. Gaussian Tx-noise and characterizes their strength using EVM. The impairment enters the receiver as spatially colored noise.

  • A. Gaussian Model for Residual Tx-RF Impairments: Residual impairments from additive noise, amplifier nonlinearities, phase noise, and IQ imbalance are modeled as i.i.d. additive Gaussian noise.MIMO-OFDM measurements indicate that this model accurately describes the sum of such residual impairments.
  • A. Gaussian Model for Residual Tx-RF Impairments: The additive impairment vector nt is called Tx-noise throughout the paper.It is added to the transmitted symbol vector before propagation through the channel.
  • A. Gaussian Model for Residual Tx-RF Impairments: EVM is a lump-sum measure characterizing transmitted-signal quality after applicable calibration and compensation.The paper notes that EVM values reflect residual rather than fully uncompensated impairments.
  • A. Gaussian Model for Residual Tx-RF Impairments: IEEE 802.11n specifies -28 dB EVM for 64-QAM, while reported implementations achieve -22 dB to -32 dB depending on output power.These values provide practical reference points for residual RF-chain quality.
  • B. System Model with Residual Tx-RF Impairments: Replacing s with the impaired vector produces aggregate receiver noise ˜n = Hnt + nr, which is spatially colored rather than i.i.d. thermal noise.Its covariance is represented by K, and a square-root factor of K is used in subsequent processing.

III. IMPACT OF TX-NOISE ON CHANNEL CAPACITY

Residual Tx-noise changes MIMO capacity through spatially colored receiver noise while preserving the channel eigenmodes. At high SNR, capacity is bounded by a Tx-noise-dependent limit.

  • III. IMPACT OF TX-NOISE ON CHANNEL CAPACITY: Tx-noise yields the same eigenmodes as the corresponding impairment-free system because U diagonalizes both H^H H and K^-1H^H H.Thus, the impairment changes eigenmode gains rather than the eigenmode directions.
  • III. IMPACT OF TX-NOISE ON CHANNEL CAPACITY: Strong eigenmodes are more severely affected by Tx-noise than eigenmodes associated with small eigenvalues λi.The contribution of an eigenmode becomes limited when its channel strength exceeds the relevant Tx-noise scale.
  • III. IMPACT OF TX-NOISE ON CHANNEL CAPACITY: At SNR → ∞, channel capacity with Tx-noise is upper-bounded by Clim.The asymptotic limit follows from the saturation of eigenmode contributions under transmit distortion.

B. Numerical Channel-Capacity Results

With residual Tx-noise at −16 dB EVM, channel capacity approaches a finite limit, and outage performance becomes increasingly difficult near that limit. The required SNR increase rises sharply at higher transmission rates.

  • Approximately 21 bpcu is the maximum capacity Clim for MT = MR = 4 at −16 dB EVM.
  • Near Clim, outage CDFs become skewed because the upper tail disappears while low-EV channel realizations remain.
  • A 4 dB SNR increase reduces outage from 90% to 5% at 8 bpcu, whereas at 16 bpcu at least 8 dB is required.
  • Reliably achieving transmission rates close to Clim requires prohibitively high SNRs.

IV. IMPACT OF TX-NOISE ON PERFORMANCE OF MIMO DETECTION ALGORITHMS

The paper evaluates residual Tx-noise effects on practical MIMO detection under impairment-free detector assumptions. It compares ZF, ML, and soft-output max-log APP detection in a coded 4×4 MIMO simulation.

  • Residual Tx-RF impairments are studied for MIMO detection algorithms designed under the assumption of impairment-free transmitted signals.
  • The simulations use a coded 4×4 MIMO system with 16-QAM, a rate-1/2 convolutional code, block fading, and 64 symbol-vectors per frame.
  • The evaluated detectors are zero-forcing, maximum-likelihood, and soft-output max-log a posteriori probability detection.

1) ZF detection:

The section introduces ZF detection and contrasts its behavior with ML and max-log APP detection under residual Tx-RF impairments. ZF is comparatively robust, while Bayesian detectors can lose substantial performance.

  • 1) ZF detection:: ZF estimates the transmitted vector by applying the channel pseudo-inverse H† to y and quantizing each entry to the nearest constellation point.
  • 1) ZF detection:: ML and max-log APP use Bayesian estimation, with max-log APP producing soft bit log-likelihood ratios through a max-log approximation.
  • 1) ZF detection:: Without residual Tx-RF impairments, ZF performs worst, while ML is outperformed by soft-output max-log APP detection.
  • 1) ZF detection:: At −30 dB EVM, ML and max-log APP suffer substantial performance loss, whereas ZF is only slightly affected.
  • 1) ZF detection:: ML detection becomes worse than ZF in the high-SNR regime when residual Tx-RF impairments are present.

1) ZF detection:

Residual Tx-RF impairments affect detectors differently because ZF is dominated by equalized thermal noise, whereas ML and max-log APP rely on mismatched noise statistics. Noise whitening restores compatibility with conventional detectors.

  • 1) ZF detection:: ZF is only mildly degraded because equalized thermal noise is colored and noise-enhanced, dominating Tx-noise across a broad SNR range.
  • 2) ML detection:: ML assumes i.i.d. CSCG receiver noise, so mismatch with the impaired system model causes detrimental performance loss.
  • 3) Max-log APP detection:: Max-log APP behaves similarly to ML because both use Bayesian estimation and suffer from mismatched noise statistics, though its degradation is less pronounced.
  • A. Tx-Noise Whitening: The proposed mitigation whitens Tx-noise before detection, preserving established detector structures while restoring the i.i.d. CSCG noise distribution.

B. Numerical Performance Results for Tx-Noise Whitening

Tx-noise whitening substantially improves ML and max-log APP detection under residual Tx-RF impairments, while ZF remains unchanged. The QRD-based implementation avoids costly covariance inversion and decomposition steps, but residual performance loss remains.

  • Whitening substantially improves ML and max-log APP detection under −30 dB EVM, restoring their advantage over linear detection.The improvement is measured against mismatched detectors without whitening.
  • ZF performance remains unchanged because the whitening filter cancels when applied consistently to the effective channel and received vector.
  • All MIMO detectors still incur a performance penalty relative to operation without residual Tx-RF impairments.
  • Additional whitening computations are concentrated in channel preprocessing, performed only when the channel state changes.
  • The QRD-based whitening filter avoids explicit covariance computation, eigenvalue or Cholesky decomposition, and subsequent matrix inversion.This relaxes precision requirements for practical fixed-point implementations.

2) Whitening for QRD-based MIMO detectors:

The proposed Tx-noise whitening integrates with QRD-based MIMO detectors by preprocessing the channel and limiting symbol-rate operations. Measurements on a four-stream RF-chain implementation support the associated impaired-system model and performance evaluation.

  • Whitening for QRD-based MIMO detectors:: The algorithm is integrated into QRD-based detectors, including sphere decoding and other tree-search detectors.
  • Whitening for QRD-based MIMO detectors:: QRD-based whitening computes W, forms the effective channel ˜H = WH, and then applies QRD before detection.
  • Whitening for QRD-based MIMO detectors:: Only whitening, phase-noise compensation, and Q^H multiplication of received vectors are performed at symbol-rate.The detector then produces symbol estimates or LLRs.
  • Whitening for QRD-based MIMO detectors:: Most additional computations occur during preprocessing and include an economy-size QRD of an (M_R+M_T)×M_R matrix plus one matrix multiplication.Existing preprocessing arithmetic may be reusable.
  • Whitening for QRD-based MIMO detectors:: A four-stream RF-chain implementation provides real-world measurements for validating the impaired-system model and whitening-related FER results in MIMO-OFDM.

A. RF-Chain Implementation and Measurement Setup

The measurement platform uses four calibrated RF chains and oscilloscope acquisition to characterize residual Tx-RF impairments. The measured samples support the i.i.d. Gaussian assumption across streams and I/Q components for the studied MIMO-OFDM setup.

  • A. RF-Chain Implementation and Measurement Setup: Each RF chain includes a 10-bit, 80 MSPS DAC, an OFDM-oriented dual-band RF transceiver, and an auxiliary filtering and amplification module.Calibration facilities are available for carrier leakage and IQ imbalance.
  • A. RF-Chain Implementation and Measurement Setup: The setup combines MATLAB control and processing, an FPGA baseboard, four calibrated RF chains, and a high-performance oscilloscope.RF data are acquired at 2.4 GHz.
  • A. RF-Chain Implementation and Measurement Setup: Frames are generated in MATLAB, transmitted through all four RF chains, recorded simultaneously, and returned for synchronization and OFDM baseband processing.
  • A. RF-Chain Implementation and Measurement Setup: Residual impairments are isolated by subtracting the known transmitted signal; their measured EVM is −28 dB.The EVM follows IEEE 802.11n measurement practice.
  • A. RF-Chain Implementation and Measurement Setup: The quantile-quantile comparison uses real-part samples from one RF chain and one 40-symbol OFDM frame, with similar results for imaginary parts and the other chains.Four streams are transmitted simultaneously to account for crosstalk.
  • A. RF-Chain Implementation and Measurement Setup: The strongest off-diagonal covariance component is more than 19.5 dB below the diagonal, supporting the i.i.d. assumption for the studied implementation and scenario.

C. FER Performance Measurements

The paper evaluates residual Tx-RF impairments in a 4×4 MIMO-OFDM system using measured FER and simulations based on the proposed Tx-noise model. Tx-noise whitening substantially improves measured FER, while the model reproduces the measured-data performance; comparisons with earlier simulations use different assumptions.

  • Measurement setup: FER measurements use a 4×4 MIMO-OFDM setup with coded 16-QAM frames containing preambles, training symbols, and 32 OFDM data symbols.Each OFDM data symbol has 64 tones, including 48 data sub-carriers and four pilot tones.
  • Measurement setup: The receiver compares measured performance with simulations that add −32 dB i.i.d. Gaussian transmit noise, corresponding to an EVM of about −28 dB.The receiver processing used for measured and simulated FER comparisons is illustrated in Fig. 8.
  • FER results: Tx-noise whitening significantly improves FER for ZF and ML detection in the presence of real-world residual Tx-RF impairments.Fig. 9 reports measured and simulated FER and marks whitening with “comp.”
  • Scope of comparison: The measurement results and corresponding simulations differ from earlier curves because those simulations assume block fading, one OFDM symbol per frame, perfect channel estimation and synchronization, and no phase noise.These assumptions apply to the simulations in Sec. V-A.
  • FER results: The simulated residual-impairment performance matches measured-data FER, supporting the proposed Tx-noise model for MIMO-OFDM systems.The dashed curves in Fig. 9 correspond to simulations based on the Tx-noise model.
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