Nonlinear Distortion Noise and Linear Attenuation in MIMO Systems—Theory and Application to Multiband Transmitters

Rönnow, Daniel; Händel, Peter

doi:10.1109/tsp.2019.2935896

Cited by 11 publications

(14 citation statements)

References 36 publications

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“…The NMSE is the normalized power of the error signal of the in and output signals. We use a baseband model of the amplifier, 5 that includes the largest hardware impairment. The largest hardware impairments are the third order static nonlinearities and the additive noise.…”

Section: Theorymentioning

confidence: 99%

“…The largest hardware impairments are the third order static nonlinearities and the additive noise. Higher order nonlinearities and nonlinear memory effects are neglected as well as in‐band frequency dependence (See References 4–7 for further discussions of these assumptions). The baseband model with normalized gain used by the amplifier is given by 5

r_{l} = u_{l} + ρ_{lk} u_{l} {|u_{l}|}^{2} + ρ_{lk} u_{l} {|u_{k}|}^{2} + n_{l},

where dual‐band input signals are u 1 and u 2 , and the output signals are r 1 and r 2 .…”

Section: Theorymentioning

confidence: 99%

“…The noise n 1 and n 2 of the two bands is uncorrelated Gaussian white noise with the same power. Assuming uncorrelated signals u 1 and u 2 and using Bussgang's theorem 17 which shows that the nonlinear distortion and the signals are uncorrelated one gets for the NMSE 5

{NMSE}_{l} = 6 {|ρ_{ll}|}^{2} σ_{l}^{4} + 2 {|ρ_{lk}|}^{2} σ_{k}^{4} + 4 ℜ ([], ρ_{ll} ρ_{lk}^{*}) σ_{l}^{2} σ_{k}^{2} + \frac{σ_{n}^{2}}{σ_{l}^{2}},

where

σ_{l}^{2}

is the power of the input signal in‐band l , and

σ_{n}^{2}

is the power of additive noise, and ℜ means the real part.…”

Section: Theorymentioning

confidence: 99%

“…In fifth generation (5G) mobile technology, statistical methods for describing the effect of hardware impairments have been given attention 3 and used in studies of system performance 4 . Various types of hardware impairments, such as inter and cross‐modulation in dual‐band, 5 and multiple input multiple output transmitters 6 and in‐phase and quadrature impairments 7 have been investigated.…”

Section: Introductionmentioning

confidence: 99%

“…An amplifier was tested at 24 GHz operated in a single‐band and a dual‐band. We use analytical expressions that were recently derived to analyze the results and derive model parameters 5 …”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Evaluating nonlinear distortion of single and dual channel excitation of an amplifier at 24 GHz

Panigrahi

Rönnow

2021

Micro & Optical Tech Letters

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Experimental characterization of an amplifier's nonlinear properties at 24 GHz is presented in single and dual‐band operation using orthogonal frequency‐division multiplex signals. A test system for characterizing an amplifier's nonlinear properties at millimeter‐wave frequencies for single and dual‐band excitation is presented. The use of standard instrument enables a feasible test system. Analytical expressions based on a statistical analysis of signals and hardware impairments were used to analyze the experimental data versus power level and found to describe well the experimental results, including inter‐ and cross‐modulation distortion. Parameters are derived that could be used in system studies.

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Section: Theorymentioning

confidence: 99%

r_{l} = u_{l} + ρ_{lk} u_{l} {|u_{l}|}^{2} + ρ_{lk} u_{l} {|u_{k}|}^{2} + n_{l},

where dual‐band input signals are u 1 and u 2 , and the output signals are r 1 and r 2 .…”

Section: Theorymentioning

confidence: 99%

{NMSE}_{l} = 6 {|ρ_{ll}|}^{2} σ_{l}^{4} + 2 {|ρ_{lk}|}^{2} σ_{k}^{4} + 4 ℜ ([], ρ_{ll} ρ_{lk}^{*}) σ_{l}^{2} σ_{k}^{2} + \frac{σ_{n}^{2}}{σ_{l}^{2}},

where

σ_{l}^{2}

is the power of the input signal in‐band l , and

σ_{n}^{2}

is the power of additive noise, and ℜ means the real part.…”

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Evaluating nonlinear distortion of single and dual channel excitation of an amplifier at 24 GHz

Panigrahi

Rönnow

2021

Micro & Optical Tech Letters

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Building Trusted Startup Teams From LinkedIn Attributes: A Higher Order Probabilistic Analysis

Drakopoulos

Kafeza

Mylonas

et al. 2020

2020 IEEE 32nd International Conference on Tools With Artificial Intelligence (ICTAI)

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Channel Estimation in Massive MIMO Under Hardware Non-Linearities: Bayesian Methods Versus Deep Learning

Demir

Björnson

2020

IEEE Open J. Commun. Soc.

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This paper considers the joint impact of non-linear hardware impairments at the base station (BS) and user equipments (UEs) on the uplink performance of single-cell massive MIMO (multiple-input multiple-output) in practical Rician fading environments. First, Bussgang decomposition-based effective channels and distortion characteristics are analytically derived and the spectral efficiency (SE) achieved by several receivers are explored for third-order non-linearities. Next, two deep feedforward neural networks are designed and trained to estimate the effective channels and the distortion variance at each BS antenna, which are used in signal detection. We compare the performance of the proposed methods with state-of-the-art distortion-aware and -unaware Bayesian linear minimum mean-squared error (LMMSE) estimators. The proposed deep learning approach improves the estimation quality by exploiting impairment characteristics, while LMMSE methods treat distortion as noise. Using the data generated by the derived effective channels for general order of non-linearities at both the BS and UEs, it is shown that the deep learning-based estimator provides better estimates of the effective channels also for non-linearities more than order three.

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Nonlinear Distortion Noise and Linear Attenuation in MIMO Systems—Theory and Application to Multiband Transmitters

Cited by 11 publications

References 36 publications

Evaluating nonlinear distortion of single and dual channel excitation of an amplifier at 24 GHz

Evaluating nonlinear distortion of single and dual channel excitation of an amplifier at 24 GHz

Building Trusted Startup Teams From LinkedIn Attributes: A Higher Order Probabilistic Analysis

Channel Estimation in Massive MIMO Under Hardware Non-Linearities: Bayesian Methods Versus Deep Learning

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