A dual two-tone technique for the characterization of memory effects in concurrent dual-band transmitters is revisited to modify a 2D-DPD model for the linearization of concurrent dual-band transmitters. By taking into account the individual nonlinear memory effects of the self- and cross-kernels, a new 2D modified digital pre-distortion (2D-MDPD) model is proposed, which not only supersedes the linearization performance but also reduces the computational complexity compared to the 2D-DP Dmodel in terms of a number of floating point operations (FLOPs). Experimental results show an improvement of 1.7 dBin normalized mean square error (NMSE) and a 58% reduction in the number of FLOPs.

A general description of nonlinear dynamic MIMO systems, given by Volterra series, has significantly larger complexity than SISO systems. Modeling and predistortion of MIMO amplifiers consequently become unfeasible due to the large number of basis functions. We have designed digital predistorters for a MIMO amplifier using a basis pursuit method for reducing model complexity. This method reduces the numerical problems that appear in MIMO Volterra predistorters due to the large number of basis functions. The number of basis functions was reduced from 1402 to 220 in a 2x2 MIMO amplifier and from 127 to 13 in the corresponding SISO case. Reducing the number of basis functions caused an increase of approximately 1 dB of model error and adjacent channel power ratio.

This paper proposes three novel models for behavioral modeling and digital pre-distortion (DPD) of nonlinear 2$,times,$ 2 multiple-input multiple-output (MIMO) transmitters in the presence of crosstalk. The proposed models are extensions of the single-input single-output generalized memory polynomial model. Three types of crosstalk effects were studied and characterized as linear, nonlinear, and nonlinear & linear crosstalk. A comparative study was performed with previously published models for the linearization of crosstalk in a nonlinear 2 $,times,$2 MIMO transmitter. The experiments indicate that, depending on the type of crosstalk, the selection of the correct model in the transmitter is necessary for behavioral modeling and sufficient DPD performance. The effects of coherent and partially noncoherent signal generation on the performance of DPD were also studied. For crosstalk levels of ${-}{hbox{30}}$ dB, the difference in the normalized mean square error and adjacent channel power ratio was found to be 3–4 dB between coherent and partially noncoherent signal generation.

A method to characterize the memory effects in a nonlinear concurrent dual-band transmitter is presented. It is an extension of the conventional two tone test for power amplifiers to concurrent dual band transmitters. The output signal of a concurrent dual-band transmitter is affected not only by intermodulation products but also by cross-modulation products. In one frequency band, the transmitter is excited by a two tone signal which frequency separation is swept. In the second band the transmitter is concurrently excited by an other two tone signal with slightly wider frequency separation. The frequency difference of the two signals is fixed during the frequency sweep. The two tone test is made at different power levels. The upper and lower third-order inter- and cross-modulation products are measured. The asymmetry between the upper and lower third-order inter- and cross-modulation products are measures of the transmitter's memory effects. The measurement results show that the memory effects are more dominant in the third-order intermodulation products than in the cross modulation products. An error analysis and system calibration was performed and measurement results for two different devices are presented.

Multiple-input multiple-output (MIMO) frequency-domain Volterra kernels of nonlinear order 3 are experimentally determined in bandwidth-limited frequency regions. How the effect of higher nonlinear orders can be reduced and how this affects the estimated errors are discussed. The magnitude and phase of the kernels areKramers-Kronig consistent. The self- and cross-kernels have different symmetries and the kernels are therefore determined and analyzed in different regions in the 3D frequency space. By analyzing the properties along certain paths in the 3D frequency space, the block structures for the respective kernels are determined. These block structures contain the significant blocks of the general block structures for third-order kernels. The device under test is a MIMO transmitter for radio frequency signals.

Electrical anomalies due to trapping effects in Gallium Nitride (GaN) power amplifiers (PAs)give rise to long-term or strong memory effects. We propose novel models based on infinite impulse response (IIR) fixed pole expansion techniques for the behavioural modeling and digital pre-distortion of single-input-single-output (SISO) and concurrent dual-bandGaN PAs. Experimental results show that the proposed models outperform the corresponding finite impulse response (FIR) models by up to 17 dB for the same number of model parameters. For the linearization of a SISO GaN PA the proposed models give adjacent channel power ratios (ACPRs) that are 7 to 17 dBlower than the FIR models. For the concurrent dual-band case, the proposed models give ACPRs that are 9to 14 dB lower than the FIR models.

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.