T F Torrence (ed) 1982 Edinburgh: Scottish Academic Press xiii + 103 pp price £7.50 In 1865 James Clerk Maxwell published in the Philosophical Transactions a long paper entitled 'A dynamical theory of the electromagnetic field'. In this work, about which he wrote to a relative, 'I have a paper afloat, with an electromagnetic theory of light, which, till I am convinced of the contrary, Ihold to be great guns', he set up the electromagnetic field equations unifying electricity and magnetism, and identified light as 'an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws'.

A Dynamical Theory of the Electromagnetic Field

In this paper, we propose a beam-oriented digital predistortion (BO-DPD) technique for power amplifiers (PAs) in hybrid beamforming massive multiple-input multiple-output (MIMO) transmitters, which can achieve linearization of the transmitted signal in the main beam direction and address the DPD implementation issue in the hybrid beamforming array. In massive MIMO hybrid beamforming transmitters, the conventional DPD to linearize each PA is impractical to implement for that the number of digital chains is less than the number of PAs; however, the BO-DPD can resolve this issue by constructing and linearizing the “virtual” main beam signal rather than single PAs. According to the beamforming weights for array elements, the feedback path combines all PA’s outputs to estimate the main beam signal for DPD processing. In addition, an average estimation method is also presented to broaden the linearized angle range around the main beam direction. A $4 \times 16$ (four subarrays and 16 antennas in each subarray) uniform linear array (ULA) simulation along with a $1 \times 2$ ULA at 2.5 GHz and a $2 \times 2$ ULA at 3.5-GHz experimental tests was performed. The experimental results show that the proposed technique and linearization angle range broadening method achieve up to 15-dB adjacent channel power ratio improvement and 10° linearization angle range in the main beam direction.

Beam-Oriented Digital Predistortion for 5G Massive MIMO Hybrid Beamforming Transmitters

Every new generation of mobile systems should provide higher capacity, serve more users, be more energy efficient, and have lower cost. Radio-access hardware constitutes a major bottleneck for reaching these goals, which is a particularly noticeable issue now that 5G communication systems are being developed. A combination of breakthroughs in communication theory-as in massive multiple input/multiple output (MIMO) [1], highly integrated semiconductor and packaging technologies, and extended spectrum allocations- has enabled a paradigm shift in the way radio hardware will be realized. Today's high-power, fewantenna, sectorized systems will soon be replaced with highly integrated active antenna systems having up to hundreds of individually driven low-power radios operating with very wideband signals.

Linearity and Efficiency in 5G Transmitters: New Techniques for Analyzing Efficiency, Linearity, and Linearization in a 5G Active Antenna Transmitter Context

A simple and flexible technique for improving the modeling and predistortion of power amplifiers is presented. The technique, which relies on the sparsity assumption for the kernel coefficients of the full Volterra (FV) behavioral model, combines a greedy algorithm for the selection of the active coefficients, a maximum likelihood method for their estimation and an information criterion for determining the best model. The approach has been applied to the design of reduced-parameters FV-based digital predistorters for three power amplifiers driven with orthogonal frequency division multiplexing signals, following the LTE and DVB-T2 standards, and a multichannel wideband code-division multiple access signal. Results show that the proposed linearizers meet the spectral masks and error vector magnitude constraints of the referred standards and provide a reduction better than 45% in the number of parameters, compared to the FV predistorters.

Behavioral Modeling and Predistortion of Power Amplifiers Under Sparsity Hypothesis

This paper proposes three novel models for behavioral modeling and digital pre-distortion (DPD) of nonlinear 2 × 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 × 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 -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.

Behavioral Modeling and Linearization of Crosstalk and Memory Effects in RF MIMO Transmitters

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 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.

Measurement and Analysis of Frequency-Domain Volterra Kernels of Nonlinear Dynamic $3 \times 3$ MIMO Systems

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 ...

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Combating the dimensionality of nonlinear MIMO amplifier predistortion by basis pursuit

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 (IM) products but also by cross-modulation (CM) 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 another 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 IM and CM products are measured. The asymmetry between the upper and lower third-order IM and CM products are measures of the transmitter’s memory effects. The measurement results show that the memory effects are more dominant in the third-order IM products than in the CM products. An error analysis and system calibration was performed and measurement results for two different devices are presented.

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Characterization of Concurrent Dual-Band Power Amplifiers Using a Dual Two-Tone Excitation Signal

The indirect learning architecture (ILA) is the most used methodology for the identification of Digital Predistorter (DPD) functions for nonlinear systems, particularly for high power amplifiers. The ILA principle works in black box modeling relying on the inversion of input and output signals of the nonlinear system, such that the inverse is estimated. This paper presents the impact of disturbances, such as noise in the DPD identification. Experiments were performed with a state-of-art Doherty power amplifier intended for base station operation in current telecommunication wireless networks. As expected, a degradation in the performance of the DPD (measured in normalized mean square error (NMSE)) is found in our experiments. However, adjacent channel power ratio (ACPR) can be a misleading figure of merit showing improvement in the performance for wrongly estimated DPD functions.

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Shoaib Amin

Papers

Behavioral Modeling and Linearization of Crosstalk and Memory Effects in RF MIMO Transmitters

Measurement and Analysis of Frequency-Domain Volterra Kernels of Nonlinear Dynamic $3 \times 3$ MIMO Systems

Combating the dimensionality of nonlinear MIMO amplifier predistortion by basis pursuit

Characterization of Concurrent Dual-Band Power Amplifiers Using a Dual Two-Tone Excitation Signal

Noise impact on the identification of digital predistorter parameters in the indirect learning architecture