Modern telecommunications are moving towards (massive) multi-input multi-output systems in 5th generation (5G) technology, increasing the dimensionality of the system dramatically. In this paper, the impairments of radio frequency (RF)power amplifiers (PAs) in a 3x3 MIMO system are compensated in both time and frequency domains. A three-dimensional(3D) time-domain memory polynomial-type model is proposed as an extension of conventional 2D models. Furthermore, a 3D frequency-domain technique is formulated based on the proposed time-domain model to reduce the dimensionality of the model, while preserving the performance in terms of model errors. In the 3D frequency-domain technique, the bandwidth of a system is split into several narrow sub-bands, and the parameters of the system are estimated for each subband. This approach requires less computational complexity, and also the procedure of the parameters estimation for each sub-band can be implemented independently. The device-under-test (DUT) consists of three RF PAs including input and output cross-talk channels. The proposed techniques are evaluated in both behavioural modelling and digital pre-distortion(DPD) perspectives. The results show that the proposed DPD technique can compensate the errors of non-linearity and memory effects by about 23.5 dB and 7 dB in terms of the normalized mean square error and adjacent channel leakage ratio, respectively.

Combating the effects of mixer and power amplifier (PA) imperfections on transmitter performance is crucial for the design of wireless systems. PA compression and in-phase/quadrature imbalance are analyzed for a single-input-single-output transmitter model. The influence of the imperfection on the normalized mean squared error (NMSE) of the transmitter is studied using an analytical framework that relies on the classic Bussgang theory. The study concludes with a closed-form expression for the NMSE that provides insights into the behavior of the transmitter. © 2019 IEEE.

Nonlinear static multiple-input multiple-output (MIMO) systems are analyzed. The matrix formulation of Bussgang's theorem for complex Gaussian signals is rederived and put in the context of the multivariate cumulant series expansion. The attenuation matrix is a function of the input signals' covariance and the covariance of the input and output signals. The covariance of the distortion noise is in addition a function of the output signal's covariance. The effect of the observation bandwidth is discussed. Models of concurrent multiband transmitters are analyzed. For a transmitter with dual non-contiguous bands expressions for the normalized mean square error (NMSE) vs input signal power are derived for uncorrelated, partially correlated, and correlated input signals. A transmitter with arbitrary number of non-contiguous bands is analysed for correlated and uncorrelated signals. In an example, the NMSE is higher when the input signals are correlated than when they are uncorrelated for the same input signal power and it increases with the number of frequency bands. A concurrent dual band amplifier with contiguous bands is analyzed; in this case the NMSE depends on the bandwidth of the aggregated signal.

In this paper, a new approach is proposed to decompose the basis functions in a piece-wise modeling technique for nonlinear radio frequency (RF) power amplifiers. The proposed technique treats the discontinuity problem of the model output at the joint points between different operating points, whereas preserves the linear and nonlinear properties of the original model within each region. Experimental results show that the proposed technique outperforms the conventional piece-wise model in terms of model errors.

The 3rd-order Volterra kernels of a radio frequency (RF) power amplifier (PA) are characterized using a large-signal and a two-tone probing-signal. In this technique, the magnitude and phase asymmetries of the kernels of the PA excited by the probing-signal are analyzed in different amplitude regions of the large-signal. The device under test is a class-AB PA operating at 2.14 GHz. The maximum sweeping frequency space of the probing-signal is 20 MHz. The results indicate that the Volterra kernels of the PA show different behaviors (frequency dependency and asymmetry) in different regions.

The radio frequency transmitter is a key component in contemporary MIMO OFDM systems. A detailed study of a 2×2 MIMO transmitter subjected to correlated input data streams, nonlinear distortion, thermal noise, and crosstalk is provided by stochastic modeling. The effects of correlated input streams, crosstalk and nonlinearities are studied in detail, and exemplified both by approximate expressions and numerical simulations. Key results include exact and approximate expressions for the normalized mean-squared error (NMSE) for systems with or without digital predistortion, the relationship between NMSE and the signal-to-noise-and-distortion ratio, the properties of the distortion noise, and a novel design for power amplifier back-off for MIMO-transmitters subject to crosstalk. The theoretical derivations are illustrated by numerical examples and simulation results, and their relationship to state-of-the-art research are discussed. OAPA

This paper uses multitone signals to simplify the analysis of 3×3 multiple-input multiple-output (MIMO) Volterra systems by isolating the third-order kernel outputs from each other. Multitone signals fed to an MIMO Volterra system yield a spectrum that is a permutation of the sums of the input signal tones. This a priori knowledge is used to design multitone signals such that the third-order kernel outputs are isolated in the frequency domain. The signals are designed by deriving the conditions for the offset and spacing of the input frequency grids. The proposed technique is then validated for the six possible configurations of a 3x3 RF MIMO transmitter impaired by crosstalk effects. The proposed multitone signal design is used to extract the third-order kernel outputs, and their relative contributions are analyzed to determine the dominant crosstalk effects for each configuration.

The paper presents a 2D extended envelope memory polynomial (2D-EEMP) model for concurrent dual-band radio frequency (RF) power amplifiers (PAs). The model is derived based on the physical knowledge of a dual-band RF PA. The derived model contains cross-modulation terms not included in previously published models; these terms are found to be of importance for both behavioral modeling and digital pre-distortion (DPD). The performance of the derived model is evaluated both as the behavioral model and DPD, and the performance is compared with state-of-the-art2D-DPD and dual-band generalized memory polynomial (DB-GMP) models. Experimental result shows that the proposed model resulted in normalized mean square error (NMSE) of -51.7/-51.6dB and adjacent channel error power ratio (ACEPR) of -63.1/-63.4 dB, for channel 1/2, whereas the 2D-DPD resulted in the largest model error and DB-GMP resulted in model parameters that are 3 times more than those resulted with the proposed model with the same performance. As pre-distorter, the proposed model resulted in adjacent channel power ratio (ACPR) of -55.8/ -54.6 dB for channel 1/2 and is 7-10 dB lower than those resulted with the 2D-DPD model and2-4 dB lower compared to the DB-GMP model.

This paper presents a comparative analysis of the complexity accuracy tradeoff in state-of-the-art RF MIMO transmitter mitigation models. The complexity and accuracy of the candidate models depends on the basis functions considered in these models. Therefore, a brief description of the mitigation models is presented accompanied by derivations of the model complexities in terms of the number of FLOPs. Consequently, the complexity accuracy tradeoff in the candidate models is evaluated for a 2 × 2 RF MIMO transmitter. Furthermore, the model complexities are analyzed for increasing nonlinear orders and number of antennas.

A new block-structure behavioral model is proposed for radio frequency power amplifiers in a 2x2 multiple-input multiple-output system including input cross-talk. The proposed model forms kernels of blocks of different nonlinear order that correspond to the significant frequency response of measured frequency domain Volterra kernels. The model can therefore well describe the input-output relationships of the nonlinear dynamic behavior of PAs. The proposed model outperforms conventional models in terms of model errors.