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.

The World today is deeply transformed by the advancement in wireless technology. The envision of a smart society where interactions between physical and virtual dimensions of life are intertwined and where human interaction is mediated by machines, e.g., smart phones, demands increasingly more data traffic. This continual increase in data traffic requires re-designing of the wireless technologies for increased system capacity and flexibility. In this thesis, aspects related to behavioral modeling, characterization, and linearization of multi-channel/band power amplifiers (PAs) are discussed.

When building a model of any system, it is advantageous to take into account the knowledge of the physics of the system and include into the model. This approach could help to improve the model performance. In this context, three novel behavioral models and DPD schemes for nonlinear MIMO transmitters are proposed.

To model and compensate distortions in GaN based RF PAs in presence of long-term memory effects, novel models for SISO and concurrent dual-band PAs are proposed. These models are based on a fixed pole expansion technique and have infinite impulse response. They show substantial performance improvement. A behavioral model based on the physical knowledge of the concurrent dual-band PA is derived, and its performance is investigated both for behavioral modeling and compensation of nonlinear distortions.

Two-tone characterization is a fingerprint method for the characterization of memory effects in dynamic nonlinear systems. In this context, two novel techniques are proposed. The first technique is a dual two-tone characterization technique to characterize the memory effects of self- and cross-modulation products in concurrent dual-band transmitter. The second technique is for the characterization and analysis of self- and cross-Volterra kernels of nonlinear 3x3 MIMO systems using three-tone signals.

Världen av idag har omvandlats starkt av framsteg inom trådlos teknik. Framtidens smarta samhalle där samspelet mellan fysiska och virtuella dimensioner i livet är sammanflätade och där mansklig växelverkan mer ofta än inte sker med eller formedlas av maskiner - exempelvis smarta telefoner - kräver allt mer datatrafik. Denna ständigt ökande datatrafik kraver i sin tur utformning av trådlös teknik som kan rymma flera kanaler och flera frekvensband för att öka systements kapactitet och flexibilitet. I denna avhandling diskuteras aspekter relaterade till beteendemodellering, karakterisering, och kompensering av ickelinjär distortion i radiofrekvens (RF) effektforstarkare (PA) för multipla-insignaler-multipla-utsignaler (MIMO) och samtidiga signaler i dubbla frekvensband.

När man gör en modell av ett system är det fordelaktigt att ta hänsyn till kunskap om det fysikaliska systemet och använda denna information i modellen. Denna strategi skulle kunna bidra till att forbattra modellens prestanda och minska antalet modellparametrar. I detta sammanhang föreslås tre nya beteende- och DPD-modeller för ickelinjära MIMO sändare. Olika typer av överhörning i MIMO-sändare undersöks för att härleda enkla och kraftfulla modeller. Effekter av koherent och partiellt koherent signalgenerering på DPD-prestanda utvärderas också. För att modellera och kompensera ickelinjär distortion i galliumnitridbaserade (GaN) RF PA med langtidsminneseffekter föreslås två nya modeller for RF PA med en in- och en utsignal (SISO) tre nya modeller för RF PA för samtidiga signaler i olika frekvensband. Dessa modeller är baserade på teknik med expansion runt fasta polvärden och har oändligt minnesdjup. Modellerna visar betydande resultatförbättring i jämforelse med dem med ändliga impulssvar. En beteendemodell baserad på en fysikalisk modell av förstärkaren föreslås för en PA för samtidiga signaler i olika frekvensband. Dess prestanda undersöks som beteendemodell och för utjämning av ickelinjär distortion.

Tvåtonskarakterisering är som ett fingeravtryck vid karakterisering av minneseffekter i dynamiska ickelinjära system. I detta sammanhang föreslås två nya tekniker för karakterisering av sändare för samtidiga signaler med olika frekvens och och MIMO-sändare. Den första tekniken är en dubbel tvåtonskarakterisering för de individuella minneseffekterna i egen- och korsmoduleringsprodukter i sändare med samtidiga signaler i olika frekvensband. Den andra tekniken är för karakterisering och analys av egen- och korsvolterrakärnor hos ett ickelinjärt 3×3 MIMO-system med hjalp av tre-tonssignaler. I den föreslagna tekniken analyseras egen- och korskänor längs linjer i en frekvensrymd för att fastställa blockstrukturer hos det underliggande systemet. Den kunskap som erhållits med hjälp av denna karakeriseringsteknik har kunnat användas för att modifiera tidigare publicerade beteendemodeller.

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.

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.

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.

This rebuttal is to "€œOn dual-band amplifications using dual two-tone: Clarifications and discussion". In the following, we provide our reply.

A characterization technique for RF PAs excited with multiple signals is presented. The technique can be used for characterization of memory effects in IM/CM products. The extracted information can in return be of use for modifying behavioral models to better capture memory in IM/CM products.

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.

The demands for high data rates and broadband wireless access requirethe development of wireless systems that can support wide and multi-bandsignals. To deploy these signals, new radio frequency (RF) front-ends are requiredwhich impose new challenges in terms of power consumption efficiencyand sources of distortion e.g., nonlinearity. These challenges are more pronouncedin power amplifiers (PAs) that degrade the overall performance ofthe RF transmitter.Since it is difficult to optimize the linearity and efficiency characteristicsof a PA simultaneously, a trade-off is needed. At high input power, a PAexhibits high efficiency at the expense of linearity. On the other hand, atlow input power, a PA is linear at the expense of the efficiency. To achievelinearity and efficiency at the same time, digital pre-distortion (DPD) is oftenused to compensate for the PA nonlinearity at high input power. In case ofmulti-channel PAs, input and output signals of different channels interactwith each other due to cross-talk. Therefore, these PAs exhibit differentnonlinear behavior than the single-input single-output (SISO) PAs. The DPDtechniques developed for SISO PAs do not result in adequate performancewhen used for multi-channel PAs. Hence, an accurate behavioral modeling isessential for the development of DPD for multi-channel RF PAs.In this thesis, we propose three novel behavioral models and DPD schemesfor nonlinear multiple-input multiple-output (MIMO) transmitters in presenceof cross-talk. A study of the source of cross-talk in MIMO transmittershave been investigated to derive simple and powerful modeling schemes.These models are extensions of a SISO generalized memory polynomial model.A comparative study with a previously published MIMO model is also presented.The effect of coherent and partially non-coherent signal generationon DPD performance is also highlighted. It is shown experimentally thatwith partially non-coherent signal generation, the performance of the DPDdegrades compared to coherent signal generation.In context of multi-channel RF transmitters, PA behavioral models andDPD schemes suffer from a large number of model parameters with the increasein nonlinear order and memory depth. This growth leads to highcomplexity model identification and implementation. We have designed aDPD scheme for MIMO PAs using a sparse estimation technique for reducingmodel complexity. This technique also increases the numerical stability whenlinear least square estimation model identification is used.A method to characterize the memory effects in a nonlinear concurrentdual-band PAs is also presented. Compared to the SISO PAs, concurrentdual-band PAs are not only affected by intermodulation distortions but alsoby cross-modulation distortions. The characterization of memory effects inconcurrent dual-band transmitter is performed by injecting a two-tone testsignal in each input channel of the transmitter. Asymmetric energy surfacesare introduced for the intermodulation and cross-modulation products, whichcan be used to identify the power and frequency regions where the memory effects are dominant.

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.