The paper presents a method for modeling strongnonlinear effects in power amplifiers based on the principlesof density estimation. The static nonlinear transfer function isobtained by averaging measured data. The performance obtainedwith density estimation is similar to the one using high ordernonlinear static polynomial models. The benefit of consideredmethod over the ones using polynomial models is that the formerestimates blindly the structure of the transfer function and doesnot suffer from numerical instabilities.

An instrumentation, measurement and post-processing technique is presented to characterize transmitters by multiple input multiple output (MIMO) Volterra series. The MIMO Volterra series is decomposed as the sum of nonlinear single-variable self-kernels and a multi-variable cross-kernel. These kernels are identified by sample averages of the outputs using inputs of different sample periodicity. This technique is used to study the HW effects in a RF MIMO transmitter composed by input and output coupling filters (cross-talk) sandwiching a non-linear amplification stage. The proposed technique has shown to be useful in identifying the dominant effects in the transmitter structure and it can be used to design behavioral models and compensation techniques.

A non-parametric technique for modeling the behavior of power amplifiers is presented. The proposed technique relies on the principles of density estimation using the kernel method and is suited for use in power amplifier modeling. The proposed methodology transforms the input domain into an orthogonal memory domain. In this domain, non-parametric static functions are discovered using the kernel estimator. These orthogonal, non-parametric functions can be fitted with any desired mathematical structure, thus facilitating its implementation. Furthermore, due to the orthogonality, the non-parametric functions can be analyzed and discarded individually, which simplifies pruning basis functions and provides a tradeoff between complexity and performance. The results show that the methodology can be employed to model power amplifiers, therein yielding error performance similar to state-of-the-art parametric models. Furthermore, a parameter-efficient model structure with 6 coefficients was derived for a Doherty power amplifier, therein significantly reducing the deployment’s computational complexity. Finally, the methodology can also be well exploited in digital linearization techniques.

This paper analyzes the joint effects of in-phase and quadrature (I/Q) imbalance and power amplifier (PA) distortion for RF multiple input multiple output (MIMO) transmitters in the presence of crosstalk. This paper proposes candidate models for the digital predistortion of static I/Q imbalanced sources exciting a dynamic MIMO Volterra system. The proposed models are enhanced using a novel technique based on subsample resolution to account for dynamic I/Q imbalance distortions. Finally, the computational complexity of the proposed models is analyzed for implementation suitability in digital platforms. It is shown that the error spectrum for the proposed models in subsample resolution reaches the noise floor of the measurements. The proposed models achieve a normalized mean squared error of -50 dB and an adjacent channel power ratio of -57 dB for signal bandwidths upto 65 MHz and crosstalk levels ranging to -10 dB. These results demonstrate the effectiveness of the proposed techniques in the joint mitigation of I/Q imbalance and PA distortion with crosstalk for a typical 2x2 MIMO telecommunication setup.

This paper proposes a technique for designing multitone signals that can separate the third order multiple input multiple output (MIMO) Volterra kernels. Multitone signals fed to a 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 output from the MIMO Volterra kernels does not overlap in the frequency domain, hence making it possible to separate these kernels from the output of the MIMO Volterra system. The proposed technique is applied to a 2×2 RF MIMO transmitter to determine its dominant hardware impairments. For input crosstalk, the proposed method reveals the dominant self and cross kernels whereas for output crosstalk, the proposed method reveals that only the self kernels are dominant.

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.