Multiple-input multiple-output (MIMO) frequencydomain 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 the phase of the kernels are Kramers-Kronig consistent. The self-kernels and cross-kernels have different symmetries, and the kernels are therefore determined and analyzed in different regions in the 3-D frequency space. By analyzing the properties along certain paths in the 3-D frequency space, the block structures for the respective kernels are determined. These block structures contain the significant blocks of the general block structures for the third-order kernels. The device under test is an MIMO transmitter for radio frequency signals.

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.

Modern telecommunications are moving towards (massive) multi-input multi-output (MIMO) systems in 5th generation (5G) technology, increasing the dimensionality of the systems dramatically. In this paper, the impairments of radio frequency (RF) power amplifiers (PAs) in a 3 x 3 MIMO system are compensated in both the time and the 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 the system is split into several narrow sub-bands, and the parameters of the model are estimated for each sub-band. 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 consists of three RF PAs including input and output cross-talk channels. The proposed techniques are evaluated in both behavioral modeling and digital pre-distortion (DPD) perspectives. The experimental results show that the proposed DPD technique can compensate the errors of non-linearity and memory effects in the both time and frequency domains.

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.

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.

 A new two-tone test method for radio frequency power amplifiers is presented. The test signal is a two-tone probing-signal superimposed on large-signals of different amplitude. The amplifier is, thus, excited in different amplitude regions. The amplitude and phase of the 3rd order intermodulation (IM) products are measured vs. frequency spacing and probing-signal amplitude in each region. The IM magnitude is a measure of the nonlinearity, while the frequency dependence and asymmetry are measures of the memory effects in the different regions. A Doherty and a class-AB amplifier were tested. For both amplifiers the IM magnitude increased by ~15 dB from the lowest to the highest amplitude region. For the Doherty amplifier the behavior of the IM products vs. frequency spacing was similar in all regions, indicating similar memory effects. For the class-AB amplifier the IM vs. frequency spacing was significantly different in the different regions, which indicates different memory effects.

A new block-structure behavioral model is proposed for radio frequency power amplifiers in a 2×2 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.

A method is proposed for determining the correlated and uncorrelated parts of phase noise spectra (PNS) of two continuous wave radio signals of different frequencies, ω1 and ω2. The PNS of the two signals and of mixed signals are measured. The PNS are modelled as having a correlated part that is the same for both signals, except for a multiplicative factor, and uncorrelated parts, that are different for the two signals. A property of the model that the PNS of some mixing products are linear combinations of the PNS of the signals at ω1, ω2, and ω1 - ω2 is experimentally verified. The difference of the PNS at ω1 + ω2 and ω1 - ω2 is proportional to the correlated part of the PNS and is a part of auxiliary functions that are used for finding the multiplicative factor and the correlated, partly correlated, and uncorrelated phase noise at different offset frequencies. A conventional spectrum analyser was used to characterise two signal generators, a phase-coherent and a non-phase-coherent one. For the phase-coherent generator the phase noise of two signals was found to be correlated for offset frequencies below 10 Hz, partly correlated for 10 Hz-1 kHz and uncorrelated above 1 kHz.