Efficient and low-complexity beamforming design is an important element of satellite communication systems with mobile receivers equipped with phased arrays. In this work, we apply the simultaneous perturbation stochastic approximation (SPSA) method with successive sub-array selection for finding the optimal antenna weights that maximize the received signal power at a uniform plane array (UPA). The proposed algorithms are based on iterative gradient approximation by injecting some carefully designed perturbations on the parameters to be estimated. Additionally, the successive sub-array selection technique enhances the performance of SPSA-based algorithms and makes them less sensitive to the initial beam direction. Simulation results show that our proposed algorithms can achieve efficient and reliable performance even when the initial beam direction is not well aligned with the satellite direction.

A radio frequency (RF) power amplifier (PA) plays an important role to amplify the message signal at higher power to transmit it to a distant receiver. Due to a typical nonlinear behavior of the PA at high power transmission, digital predistortion (DPD), exploiting the preinversion of the nonlinearity, is used to linearize the PA. However, in a massive MIMO (mMIMO) transmitter, a single DPD is not sufficient to fully linearize multiple PAs. Further, for the full linearization, assigning a separate DPD to each PA is complex and not economical. In this work, we address these challenges via the proposed low-complexity DPD (LC-DPD) scheme. Initially, we describe the fully-featured DPD (FF-DPD) scheme to linearize the multiple PAs and examine its complexity. Thereafter, using it, we derive the LC-DPD scheme that can adaptively linearize the PAs as per the requirement. The coefficients in the two schemes are learned using the algorithms that adopt indirect learning architecture based recursive prediction error method (ILA-RPEM) due to its adaptive and free from matrix inversion operations. Furthermore, for the LC-DPD structure, we have proposed three algorithms based on correlation of its common coefficients with the distinct coefficients.

Implementation techniques and results for a recently proposed real-time reconfigurable low-pass equalizer (RLPE) consisting of a variable bandwidth (VBW) filter and a variable equalizer (VE) are presented. Both components utilize fixed finite-length impulse response (FIR) filters combined with a few general multipliers, resulting in lower area and power consumption compared to a general FIR filter, despite requiring more multiplications. This is because the constant multipliers in the fixed FIR filters of the RLPE can be optimized for implementation. An additional advantage is that the proposed RLPE does not require online design. Various implementation alternatives for fixed FIR filters, including ways to increase the frequency, are evaluated to optimize the implementation of the RLPE. Several versions of the proposed RLPE and a general FIR filter for comparison are implemented using a 28-nm fully depleted silicon on insulator (FD-SOI) standard cell library. The results demonstrate that the RLPE baseline design requires less power and area than the general equalizer, and although the frequency of the baseline implementation is lower, the design can reach the same frequency while still having significantly less power and area. Furthermore, an approach is introduced to break the chain in the polynomial section of the VBW filter by using fewer additional registers compared to standard pipelining. Instead, this method reformulates the constant multiplication problem to produce correct results. For the considered case, the power consumption is reduced between 49% and 70% for different frequencies, with an area decrease in the range of 64%–67%, by using the proposed RLPE compared to a general FIR filter.

A radio frequency (RF) power amplifier (PA) is crucial to enhance the signal to transmit via antenna over long distances. High-power transmission often leads to nonlinear behavior in the PA, necessitating the use of digital predistortion (DPD) signal processing to restore linearity by preinverting the nonlinearity. However, when dealing with a massive MIMO (mMIMO) transmitter with numerous PAs, a single DPD is not enough, and allocating a separate DPD for each PA is intricate and cost-inefficient. In this study, we tackle these challenges through our proposed low-complexity DPD (LC-DPD) architecture. The LC-DPD has the flexibility to choose the parameters of its architecture as per the desired tradeoff between the performance and complexity in the linearization. It employs learning of its coefficients through algorithms utilizing an indirect learning architecture based recursive prediction error method (ILA-RPEM), which is adaptive and free from matrix inversions.

This letter considers the design and properties of linear-phase finite-length impulse response (FIR) filters for equalization of the frequency responses of digital-to-analog converters (DACs). The letter derives estimates for the filter orders required, as functions of the bandwidth and equalization accuracy, for four DAC pulses that are used in DACs in multiple Nyquist bands. The estimates are derived through a large set of minimax-optimal equalizers and the use of symbolic regression followed by minimax-optimal curve fitting for further enhancement. Design examples demonstrate the accuracy of the proposed estimates. In addition, the letter discusses the appropriateness of the four types of linear-phase FIR filters, for the different equalizer cases, as well as the corresponding properties of the equalized systems.

The usage of passive intelligent surface (PIS) is emerging as a low-cost green alternative to massive antenna systems for realizing high-energy beamforming (EB) gains. Considering the limited computational capability and constant-envelope precoding for PIS, we propose three novel low-complexity passive EB designs for optimizing the efficacy of PIS-assisted energy transfer (PET) from a multiantenna power beacon (PB) to a single-antenna energy harvesting (EH) user. The first EB design involves solving a univariate equation, and closed forms expressed are presented for the other two. Further, to maximize the practical utility of PET, we introduce a novel channel estimation (CE) protocol for obtaining least-squares estimators for the channels as required for EB designing. Using them, we also derive closed-form expressions for optimal PIS location and optimal time allocation between CE and PET within each coherence block to maximize the user’s net harvested energy. Numerical results verify the CE analysis and validate the novel analytical bound derived for received power during PET and proposed PIS designs’ quality against existing benchmarks. We show that the proposed jointly optimal design for PET can yield a significant improvement of about 15 dB, and a reduced active array size at PB can achieve the desired EB gain with sufficient passive elements at PIS. Finally, we also briefly discuss how the proposed CE and EB designs can be extended to the multiuser settings.

Mismatches affect the dynamic performance of time-interleaved analog-to-digital converters (TIADCs). Linear mismatches can be calibrated by many mature methods, but if higher performance is required, nonlinearity mismatches have to be suppressed. The background calibration method based on input-free band (IFB) functions poorly for narrow-band signals. This paper proposes a correlation-based calibration method for nonlinearity mismatches in dual-channel TIADCs which behaves well for both wide-band and narrow-band signals. The output samples are calibrated by reducing the residual distortions which are approximated by multiplying the pseudo distortions and the estimated mismatch coefficients. The pseudo distortions are acquired by using a frequency-shifter, a differentiator, and multipliers. The coefficients which indicate the mismatch strength are estimated by eliminating the cross-correlation of the calibrated output samples and the calibrated pseudo distortions at zero lag. Simulations show that the proposed method can improve the SFDR by dozens of dBc for narrow-band input signals, compared with the input-free band method. For the 16-QAM signal, the EVM improvement over the IFB method is 35.48 dB.

In this paper, two first-order compensation strategies for timing mismatch in two-channel time-interleaved analog-to-digital converters (TIADCs) are analyzed, and expressions for the spurious-free dynamic range (SFDR) after compensation are derived. The derived expressions reveal that the strategy where both channels are compensated to match each other, using half the value of the mismatch with different signs, achieves a substantially greater SFDR than the strategy where only one channel is compensated to match the other (reference) channel. This is because, after compensation, the remaining aliasing distortion is shown to be of third order in the former strategy whereas it is of second order in the latter. Simulations included demonstrate the validity of the derived expressions.

Massive multiple-input multiple-output (MIMO) systems have attracted much attention lately due to the many advantages they provide over single-antenna systems. Owing to the many antennas, low-cost implementation and low power consumption per antenna are desired. To that end, massive MIMO structures with low-resolution analog-to-digital converters (ADC) have been investigated in many studies. However, the effect of a strong interferer in the adjacent band on quantized massive MIMO systems have not been examined yet. In this study, we analyze the performance of uplink massive MIMO with low-resolution ADCs under frequency selective fading with orthogonal frequency division multiplexing (OFDM) in the perfect and imperfect receiver channel state information cases. We derive analytical expressions for the bit error rate and ergodic capacity. We show that the interfering band can be suppressed by increasing the number of antennas or the oversampling rate when a zero-forcing receiver is employed.

Massive multiple-input multiple-output (MIMO) systems have attracted much attention lately due to the many advantages they provide over single- antenna systems. Owing to the many antennas, low- cost implementation and low power consumption per antenna are desired. To that end, massive MIMO structures with one-bit analog-to-digital converters (ADC) have been investigated in many studies. However, the effect of a strong interferer in the adjacent band on one-bit quantized massive MIMO systems have not been examined yet. In this study, we analyze the performance of uplink massive MIMO with one-bit ADCs under frequency selective fading with orthogonal frequency division multiplexing (OFDM) in the perfect and imperfect receiver channel state information cases. We derive analytical expressions for the bit error rate and ergodic rate. We show that the interfering band can be suppressed by increasing the number of antennas or the oversampling rate when a zero-forcing receiver is employed.

Usage of passive intelligent surface (PIS) is emerging as a low-cost green alternative to massive antenna systems for realizing high energy beamforming (EB) gains. To maximize its realistic utility, we present a novel channel estimation (CE) protocol for PIS-assisted energy transfer (PET) from a multiantenna power beacon (PB) to a single-antenna energy harvesting (EH) user. Noting the practical limitations of PIS and EH user, all computations are carried out at PB having required active components and radio resources. Using these estimates, near-optimal analytical active and passive EB designs are respectively derived for PB and PIS, that enable efficient PET over a longer duration of coherence block. Nontrivial design insights on relative significance of array size at PIS and PB are also provided. Numerical results validating theoretical claims against the existing benchmarks demonstrate that with sufficient passive elements at PIS, we can achieve desired EB gain with reduced active array size at PB.

Hybrid energy beamforming (HEB) can reduce the hardware cost, energy consumption, and space constraints associated with massive antenna array transmitter (TX). With a single radio frequency chain having N digitally controlled phase shifter pairs, one per antenna element, theoretically achieving the same performance as a fully digital beamforming architecture with N RF chains, this letter investigates the practical efficacy of the HEB. First adopting the proposed analog phase shifter impairments model and exploiting the channel reciprocity along with the available statistical information, we present a novel approach to obtain an accurate minimum mean-square error estimate for the wireless channel between TX and energy receiver (RX). Then, tight analytical approximation for the global optimal time allocation between uplink channel estimation and downlink energy transfer operations is derived to maximize the mean net harvested energy at RX. Numerical results, validating the analysis and presenting key design insights, show that with an average improvement of 58% over the benchmark scheme, the optimized HEB can help in practically realizing the fully digital array gains.

Usage of low-cost hardware in large antenna arrays and low-power wireless devices in Internet of Things (IoT) has led to the degradation of practical beamforming gains due to the underlying hardware impairments, such as in-phase and quadrature-phase imbalance (IQI). To address this timely concern, we present a new nontrivial closed-form expression for the globally optimal least squares estimator (LSE) for the IQI-influenced channel between a multiantenna transmitter and single-antenna IoT device. Thereafter, to maximize the realistic transmit beamforming gains, a novel precoder design is derived that accounts for the underlying IQI for maximizing received power in both single and multiuser settings. Finally, the simulation results, demonstrating a significant -8 dB improvement in the mean squared error of the proposed LSE over existing benchmarks, show that the optimal precoder designing is more critical than accurately estimating IQI-impaired channels. Also, the proposed jointly optimal LSE and beamformer outperforms the existing designs by providing 24% enhancement in mean signal power received under IQI.

Smart multiantenna wireless power transmission can enable perpetual operation of energy harvesting (EH) nodes in the Internet-of-Things. Moreover, to overcome the increased hardware cost and space constraints associated with having large antenna arrays at the radio frequency (RF) energy source, the hybrid energy beamforming (EBF) architecture with single RF chain can be adopted. Using the recently proposed hybrid EBF architecture modeling the practical analog phase shifter impairments (API), we derive the optimal least-squares estimator for the energy source to an EH user channel. Next, the average harvested power at the user is derived while considering the nonlinear RF EH model and a tight analytical approximation for it is also presented by exploring the practical limits on the API. Using these developments, the jointly global optimal transmit power and time allocation for channel estimation (CE) and EBF phases, that maximizes the average energy stored at the EH user is derived in closed form. Numerical results validate the proposed analysis and present nontrivial design insights on the impact of API and CE errors on the achievable EBF performance. It is shown that the optimized hybrid EBF protocol with joint resource allocation yields an average performance improvement of 37% over benchmark fixed allocation scheme.

We investigate the practical realization of energy beamforming gains in the downlink wireless power transfer from a massive antenna radio frequency (RF) source to multiple single antenna energy harvesting (EH) users. Assuming channel reciprocity for the uplink and downlink channels undergoing Rician fading, we first obtain the least-squares and linear-minimum-mean-square-error channel estimates using the energy-constrained pilot signal transmission from EH users. Due to the usage of low cost hardware at the users and for realizing massive antenna system at the RF source, these estimates are strongly influenced by the transmitter and receiver in-phase-and-quadrature-phase imbalance (IQI). Using these channel estimates, we next derive the harvested power at each user by applying the source transmit precoding that maximizes the sum harvested power among the users. Selected results generated considering practical RF EH system parameters show that IQI and channel estimation errors can lead to about 30% degradation in the sum EH performance.

This paper derives lower bounds on the L2-norms of digital resampling filters with zero-valued input samples. This emanates from uniform-grid sampling but where some of the samples are missing. One application is found in time-interleaved analog-to-digital converters with missing samples due to calibration at certain time instances. The square of the L2-norms correspond to scaling of the round-off noise that in practice is always present at the input of the resampling filter. As will be shown through the derived bounds, the L2-norm of the corresponding filter that recovers the missing samples is generally much larger than unity. Consequently, the noise variance is generally much larger for the recovered samples than for the other samples obtained in the sampling process. Based on this observation, the paper also proposes an alternative resampling scheme for which the maximum of all L2-norms in the resampling is reduced.

The bandwidth of the sampling systems, especially for time-interleaved analog-to-digital converters, needs to be extended along with the rapid increase of the sampling rate. A digitally assisted technique becomes a feasible approach to extend the analog bandwidth, as it is impractical to implement the extension in analog circuits. This paper derives accurate order estimation formulas for the bandwidth extension filter, which is designed in the minimax sense with the ripple constraints as the design criteria. The derived filter order estimation is significant in evaluating the computational complexity from the viewpoint of the top-level system design. Moreover, with the proposed order estimates, one can conveniently obtain the minimal order that satisfies the given ripple constraints, which contributes to reducing the design time. Both the performance of the extension filter and its order estimation are illustrated and demonstrated through simulation examples.

For high-speed delta-sigma modulators the decimation filters are typically polyphase FIR filters as the recursive CIC filters can not be implemented because of the iteration period bound. In addition, the high clock frequency and short input word length make multiple constant multiplication techniques less beneficial. Instead a realistic complexity measure in this setting is the number of non-zero digits of the FIR filter tap coefficients. As there is limited control of the passband approximation error for CIC-based filters these must in most cases be compensated to meet a passband specification. In this work we investigate the complexity of decimation filters meeting CIC-like stopband behavior, but with a well defined passband approximation error. It is found that the general approach can in many cases produce filters with much smaller passband approximation error at a similar complexity.

This letter shows that, for arbitrary M-fold polyphase decompositions, the polyphase components of digital fractional-delay (FD) filters correspond to FD filters as well, but with different delays and gains. For even values of M, the components also have additional and different phase offsets. The letter also discusses the application of these results to the optimization of high-order filters with few unknowns.

This paper proposes a scheme for the recovery of a uniformly sampled sequence from the output of a time-interleaved analog-to-digital converter (TI-ADC) with static time-skew errors and missing samples. Nonuniform sampling occurs due to timing mismatches between the individual channel ADCs and also due to missing input samples as some of the sampling instants are reserved for estimating the mismatches in the TI-ADC. In addition to using a non-recursive structure, the proposed reconstruction scheme supports online reconfigurability and reduces the computational complexity of the reconstructor as compared to a previous solution.

This paper introduces a finite-length impulse response (FIR) digital filter having both a variable fractional delay (VFD) and a variable phase shift (VPS). The realization is reconfigurable online without redesign and without transients. It can be viewed as a generalization of the VFD Farrow structure that offers a VPS in addition to the regular VFD. The overall filter is composed of a number of fixed subfilters and a few variable multipliers whose values are determined by the desired FD and PS values. It is designed offline in an iterative manner, utilizing reweighted l1-norm minimization. This design procedure generates fixed subfilters with many zero-valued coefficients, typically located in the impulse response tails.

Nonuniform sampling occurs in time-interleaved analog-to-digital converters (TI-ADC) due to timing mismatches between the individual channel analog-to-digital converters (ADCs). Such nonuniformly sampled output will degrade the achievable resolution in a TI-ADC. To restore the degraded performance, digital time-varying reconstructors can be used at the output of the TI-ADC, which in principle, converts the nonuniformly sampled output sequence to a uniformly sampled output. As the bandwidth of these reconstructors increases, their complexity also increases rapidly. Also, since the timing errors change occasionally, it is important to have a reconstructor architecture that requires fewer coefficient updates when the value of the timing error changes. Multivariate polynomial impulse response reconstructor is an attractive option for an M-channel reconstructor. If the channel timing error varies within a certain limit, these reconstructors do not need any online redesign of their impulse response coefficients. This paper proposes a technique that can be applied to multivariate polynomial impulse response reconstructors in order to further reduce the number of fixed-coefficient multipliers, and thereby reduce the implementation complexity.

This paper introduces reconfigurable two-stage finite-length impulse response (FIR) Nyquist filters. In both stages, the Farrow structure realizes reconfigurable lowpass linear-phase FIR Nyquist filters. By adjusting the variable multipliers of the Farrow structure, various FIR Nyquist filters and integer interpolation/decimation structures are obtained, online. However, the filter design problem is solved only once, offline. Design examples illustrate the method.

This paper introduces a new class of linear-phase Nyquist (Mth-band) FIR interpolators and decimators based on tree structures. Through design examples, it is shown that the proposed converter structures have a substantially lower computational complexity than the conventional single-stage converter structures. The complexity is comparable to that of multi-stage Nyquist converters, although the proposed ones tend to have a somewhat higher complexity. A main advantage of the proposed structures is however that they can be used for arbitrary integer conversion factors, thus including prime numbers which cannot be handled by the regular multi-stage Nyquist converters.

This paper introduces reconfigurable nonuniform transmultiplexers (TMUXs) based on uniform modulated filter banks (FBs). Polyphase components, of any user, are processed by a number of synthesis FB and analysis FB branches of a uniform TMUX. One branch, of the TMUX, represents one granularity band and any user occupies integer multiples of a granularity band. By adjusting the number of branches, assigned to each user, a nonuniform TMUX is obtained. This only requires adjustable commutators which add no extra arithmetic complexity. The application of both cosine modulated and modified discrete Fourier transform FBs are considered and the formulations related to the appropriate choice of parameters are outlined. Examples are provided for illustration.

This paper discusses some issues related to the filter design in a class of multimode transmultiplexers (TMUXs). These TMUXs cover a large set of frequency division multiplexed (FDM) scenarios with simple reconfigurations. The reconfiguration is performed by changing the values of some multipliers. The paper outlines a direct filter design to decrease the level of inter-symbol and inter-carrier interference by the use of time-varying periodic filters. These time-varying periodic filters are derived from the known FDM scenarios and they are included as additional constraints in the filter design. Both minimax and constrained least-squares approaches are treated and it is shown that by including the additional constraints, the level of the TMUX noise can be reduced. This results in a better approximation of perfect reconstruction and makes the filter design direct.

In this work we consider scaling of fractional delay filters using the Farrow structure. Based on the observation that the subfilters approximate the Taylor expansion of a differentiator, we derive estimates of the L2-norm scaling values at the outputs of each subfilter as well as at the inputs of each delay multiplier. The scaling values can then be used to derive suitable wordlengths in a fixed-point implementation.

This paper introduces a structure for the realization of wide-band linear-phase finite-length impulse response (FIR) differentiators. It is based on multirate and frequency-response masking techniques. Examples show that this structure achieves computational savings between some 10% and 65% for bandwidths in the range between 0.9 pi and 0.98 pi in comparison with conventional linear-phase differentiators.

This paper introduces a multi-mode transmultiplexer (TMUX) consisting of Farrow-based variable integer sampling rate conversion (SRC) blocks. The polyphase components of general interpolation/decimation filters are realized by the Farrow structure making it possible to achieve different linear-phase finite-length impulse response (FIR) lowpass filters at the cost of a fixed set of subfilters and adjustable fractional delay values. Simultaneous design of the subfilters, to achieve overall approximately Nyquist (Mth-band) filters, are treated in this paper. By means of an example, it is shown that the subfilters can be designed so that for any desired range of integer SRC ratios, the TMUX can approximate perfect recovery as close as desired.

Linear-phaseMth-band finite-length impulse response (FIR) filters are characterized by everyMth impulse response coefficient being equal to zero, except for the middle tap. This leads to a realization with few multiplications. However, other properties include that the passband ripple is bounded by the stopband ripple and that the transition band is symmetric around π/Mrad. Depending on the filter specifications this may sometimes lead to an overly constrained filter design. In this work we investigate the trade-off betweenMth-band and general linear-phase FIR filters. The results are bounds on the filter specification for when the linear-phaseMth-band or general FIR filter is advantageous to use.

This paper introduces polynomial impulse response time-varying FIR filters for reconstruction of two-periodic nonuniformly sampled signals. The main advantages of using these reconstruction filters are that on-line filter design is avoided, and filters with fixed dedicated multipliers can be used in an implementation (except for a few general multipliers). This is in contrast to existing filters that require on-line design as well as general multipliers in the implementation. By using the proposed filters, the overall implementation cost can therefore be reduced dramatically in applications where the s ampling pattern changes now and then

We discuss time-interleaved analog-to-digital converters (ADCs) as a prime example of merging analog and digital signal processing. A time-interleaved ADC (TI-ADC) consists of M parallel channel ADCs that alternately take samples from the input signal, where the sampling rate can be increased by the number of channels compared to a single channel. We recall the advantages of time interleaving and investigate the problems involved. In particular, we explain the error behavior of mismatches among the channels, which distort the output signal and reduce the system performance significantly, and provide a concise framework for dealing with them. Based on this analysis, we review the principle possibilities of calibrating TI-ADCs, where we point out the necessities and advantages of digital enhancement. To this end, we discuss open issues of channel mismatch identification as well as channel mismatch correction

An important issue in the next-generation satellite-based communication systems is the satellite on-board reallocation of information which calls for digital flexible frequency-band reallocation (FFBR) networks. This paper introduces a new class of FFBR networks based on variable oversampled complex-modulated filter banks (FBs). The new class can outperform previously existing ones when flexibility, low complexity and inherent parallelism, perfect frequency-band reallocation, and simplicity are considered simultaneously.

In this paper a novel structure for frequency masking based on a single filter is introduced. By using the proposed frequency masking approach the maximal sample frequency for narrow-band recursive digital filters is increased. This increase in sample frequency can be utilized either for faster filters or for lower power consumption by trading excess speed for low power. As the subfilters are identical (except for the number of delays), the filter can be mapped onto a single hardware structure which leads to area-efficient implementation.

This paper introduces new classes of frequency-response masking (FRM) FIR filters. In the FRM approach, the overall filter makes use of periodic model filters and nonperiodic masking filters which makes it possible to obtain FIR filters requiring few arithmetic operations even when the transition band is narrow. A reason for considering the new classes of FRM filters in this paper is that they are useful for multirate filter banks. The overall filters can be designed by separately optimizing the model and masking filters. Design examples are included.

This paper introduces a class of two-channel hybrid analog and digital filter banks which find application in high-speed A/D conversion. The distortion caused by mismatch errors in time-interleaved A/D converters is attenuated using hybrid filter banks. The proposed class of filter banks satisfy perfect reconstruction within certain tolerances that can be controlled in the filter design. The filter design uses both linear and nonlinear programming.