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 users 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.

Digital differentiators enable the computation of the derivative of a continuous-time signal at discrete time instances, and they are used in many signal processing applications. This paper derives a unified filter order estimate for digital differentiators that are realized with linear-phase finite-length impulse response filters and designed in the minimax sense. The estimate is useful at the high-level system design when assessing the implementation complexity and it enables fewer designs when finding the minimal filter order required to satisfy a prescribed tolerable approximation error. The proposed unified estimate covers both wideband and lowpass differentiators of integer degrees up to ten. Furthermore, degree-individual filter order estimates are derived which improve and extend previous results. The performance of both the unified and degree-individual order estimates is evaluated through simulation examples and compared with previous estimates.

In this paper, two different timing-mismatch compensation strategies for two-channel time-interleaved analog-to-digital converters are comprehensively analyzed and compared. In the first strategy (SA), one channel serves as a reference channel, and the other channel is compensated to match the reference channel using the timing mismatch between the channels. In the second strategy (SB), both channels are compensated to match each other, using half the value of the channel mismatch with different signs. For SB, the paper introduces a novel compensation structure that utilizes parallel differentiator-multiplier (PDM) branches. Expressions for the spurious-free dynamic range (SFDR) after compensation are derived for both strategies. These expressions reveal that the novel PDM structure achieves a remarkably greater SFDR than the existing cascaded differentiator-multiplier (CDM) compensation structure which can be used for both SA and SB. This is because, after compensation, the remaining aliasing distortion in the proposed PDM structure is shown to be of higher approximation order (in terms of the mismatch value) and thus substantially smaller than in the CDM structure. Simulations included in the paper validate the theoretical results.

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 brief 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 IFB method. For the 16-QAM signal, the error vector magnitude improvement over the IFB method is 35.48 dB.

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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.

In modern mixed-signal systems, it is important to build the conversion components with a flat frequency response over their full Nyquist frequency band. However, with increasing circuit speed, it is becoming more difficult to achieve this, due to limitations of the analog front-end circuits. This paper considers finite-length impulse-response (FIR) filters, designed in the least-squares sense, for the bandwidth extension of analog-to-digital converters, which is one of the most important applications in frequency response equalization. The main contributions of this paper are as follows: Firstly, based on extensive simulations, filter order-estimation expressions of the least-squares designed equalizers are derived. It appears to be the first time that order-estimation expressions are presented for any least-squares designed FIR filter. These expressions accurately estimate the order required for given specifications on the targeted extended bandwidth systems. Secondly, based on the derived order-estimation expressions, systematic design procedures are presented, which contribute to reducing the design time. Finally, a relation between the dynamic-range degradation and the system parameters is also derived and verified in the paper.

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.

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.

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.

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 zeroforcing receiver is employed.

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.

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In order to enhance the effective resolution of time-interleaved analog-to-digital converters (TI-ADCs), both linear and nonlinear channel mismatches should be carefully calibrated. This paper concentrates on a bandwidth-efficient background calibration method for nonlinear errors in M-channel TI-ADCs. It utilizes the least-mean square algorithm as well as a certain degree of oversampling to achieve adaptive mismatch tracking. The calibration performance and computational complexity are investigated and evaluated through behavioral-level simulations. Furthermore, a calibration strategy for narrow-band input signals is proposed and verified as an improvement of the basic calibration structure for such signals.

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.

Due to channel mismatches in time-interleaved analog-to-digital converters (TIADCs), estimation and compensation methods are required to restore the resolution of the individual converters. Whereas several methods exist for linear mismatches, nonlinearity mismatches have not been widely investigated. This brief presents an adaptive background estimation method for nonlinearity mismatches in two-channel TIADCs. It utilizes a normalized least-mean-square algorithm and assumes slight oversampling as well as a polynomial nonlinearity model that is appropriate when smooth errors dominate. Furthermore, two implementation strategies are proposed to enhance its ability for different applications. The estimation performance of the proposed method is evaluated through behavioral-level simulations.

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 brief proposes a method for designing modulated filter banks (FBs) with a large number of channels. The impulse response of the long prototype filter is parameterized in terms of a few short impulse responses, thus significantly reducing the number of unknown parameters. The proposed method starts by first obtaining an FB with a few channels. The solution of this FB is then partly reused as an initial (very close to final) solution in the design of FBs with a large number of channels. The number of unknown parameters hence drastically reduces. For example, we can first design a cosine modulated FB (CMFB) with three channels whose prototype filter has a stopband attenuation of about 40 dB. We can then reuse the solution of this CMFB in the design of a CMFB with 16 384 channels whose prototype filter has a similar stopband attenuation. With our proposed method, we need to reoptimize only 14 parameters to design the CMFB with 16 384 channels.

Channel mismatches in time-interleaved analog-to-digital converters (TIADCs) typically result in significant degradation of the ADCs dynamic performance. Offset, gain, and timing mismatches have been widely investigated whereas nonlinearity mismatches have not. In this work, we analyze the influence of nonlinearity mismatches by using a polynomial model. As a cost measure we use the signal-to-noise and distortion ratio (SNDR) and then derive a compact formula describing the dependency on nonlinearity mismatches. Based on the spectral characteristics of the TIADCs, we propose a foreground estimation method and a compensation method using a cascaded structure of adders and multipliers. Through behavioral-level simulations, we prove the validity of the derivations and demonstrate that the proposed estimation and compensation method can bring a considerable amount of improvement in the combined TIADCs dynamic performance. The proposed method is efficient assuming that a smooth approximation of the nonlinearity mismatches is sufficient.

Sub-Nyquist cyclic nonuniform sampling (CNUS) of a sparse multi-band signal generates a nonuniformly sampled signal. Assuming that the corresponding uniformly sampled signal satisfies the Nyquist sampling criterion, the sequence obtained via CNUS can be passed through a reconstructor to recover the missing uniform-grid samples. In order to recover the missing uniform-grid samples, the sequence obtained via CNUS is passed through a reconstructor. At present, these reconstructors have very high design and implementation complexity that offsets the gains obtained due to sub-Nyquist sampling. In this paper, we propose a scheme that reduces the design and implementation complexity of the  reconstructor. In contrast to the existing reconstructors which use only a multi-channel synthesis filter bank (FB), the proposed reconstructor utilizes both analysis and synthesis FBs which makes it feasible to achieve an order-of-magnitude reduction of the complexity. The analysis filters are implemented using polyphase networks whose branches are allpass filters with distinct fractional delays and phase shifts. In order to reduce both the design and the implementation complexity of the  synthesis FB, the synthesis filters are implemented using a cosine-modulated FB. In addition to the reduced complexity of the reconstructor, the proposed multi-channel recovery scheme also supports online reconfigurability which is required in flexible (multi-mode) systems where the user subband locations vary with time.

This paper introduces all-digital flexible channelizersand aggregators for multi-standard video distribution. The overall problem is to aggregate a number of narrow-band subsignals with different bandwidths (6, 7, or 8 MHz) into one composite wide-band signal. In the proposed scheme, this is carried out through a set of analysis filter banks (FBs), that channelize the subsignals into 1/2-MHz subbands, which subsequently are aggregated through one synthesis FB. In this way, full flexibility with a low computational complexity and maintained quality is enabled. The proposed solution offers orders-of-magnitude complexity reductions as compared with a straightforward alternative. Design examples are included that demonstrate the functionality, flexibility, and efficiency.

To further enhance the dynamic performance of time-interleaved analog-to-digital converters (TI-ADCs), both linear and nonlinear mismatches should be estimated and compensated for. This paper introduces a method for joint calibration of several types of linear and nonlinear mismatch errors in two-channel TI-ADCs. To demonstrate the generality of this method, we take different scenarios into account, including static and dynamic mixed mismatch models. The proposed method utilizes a normalized least-mean square (N-LMS) algorithm as well as a certain low degree of oversampling for the overall converter to estimate and compensate for the mixed mismatch errors. The calibration performance and computational complexity are investigated and evaluated through simulations.

This paper considers frequency-domain implementation of finite-length impulse response filters. In practical fixed-point arithmetic implementations, the overall system corresponds to a time-varying system which can be represented with either a multirate filter bank, and the corresponding distortion and aliasing functions, or a periodic time-varying impulse-response representation or, equivalently, a set of impulse responses and the corresponding frequency responses. The paper provides systematic derivations and analyses of these representations along with design examples. These representations are useful when analyzing the effect of coefficient quantizations as well as the use of shorter DFT lengths than theoretically required.

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, 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 brief proposes a reconstruction scheme for the compensation of frequency-response mismatch errors at the output of a time-interleaved analog-to-digital converter (TI-ADC) with missing samples. The missing samples are due to sampling instants reserved for estimating the channel mismatch errors in the TI-ADC. Compared with previous solutions, the proposed scheme offers substantially lower computational complexity.

This brief derives efficient two-stage-based polyphase structures for arbitrary-integer sampling rate conversion. For even-integer conversions, the overall structures correspond to parallelized conventional two-stage structures, but the derivations in this brief offer further insights when comparing the two cases of odd-and even-integer conversions. For the class of linear-phase finite-length impulse response Mth-band filters, it is then demonstrated through design examples that conversions by odd factors are in fact more efficient than by even factors.

This paper introduces a class of reconfigurable two-stage Nyquist filters where the Farrow structure realizes the polyphase components of linear-phase finite-length impulse response (FIR) filters. By adjusting the variable predetermined multipliers of the Farrow structure, various linear-phase FIR Nyquist filters and integer interpolation/decimation structures are obtained, online. However, the filter design problem is solved only once, offline. Design examples, based on the reweighted l(1)-norm minimization, illustrate the proposed method. Savings in the arithmetic complexity are obtained when compared to the reconfigurable single-stage structures.

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 add-equalize structures for the implementation of linear-phase Nyquist (th-band) finite-length impulse response (FIR) filter interpolators and decimators. The paper also introduces a systematic design technique for these structures based on iteratively reweighted -norm minimization. In the proposed structures, the polyphase components share common parts which leads to a considerably lower implementation complexity as compared to conventional single-stage converter structures. The complexity is comparable to that of multi-stage Nyquist structures. A main advantage of the proposed structures is that they work equally well for all integer conversion factors, thus including prime numbers which cannot be handled by the regular multi-stage Nyquist converters. Moreover, the paper shows how to utilize the frequency-response masking approach to further reduce the complexity for sharp-transition specifications. It also shows how the proposed structures can be used to reduce the complexity for reconfigurable sampling rate converters. Several design examples are included to demonstrate the effectiveness of the proposed structures.

This paper presents formulas for the number of optimization parameters (degrees of freedom) when designing Type I linear-phase finite-length impulse response (FIR) Lth-band filters of order 2N as cascades of identical linear-phase FIR spectral factors of order N. We deal with two types of degrees of freedom referred to as (i) the total degrees of freedom D-T, and (ii) the remaining degrees of freedom D-R. Due to the symmetries or antisymmetries in the impulse responses of the spectral factors, D-T roughly equals N/2. Some of these parameters are specifically needed to meet the Lth-band conditions because, in an Lth-band filter, every Lth coefficient is zero and the center tap equals 1/L. The remaining D-R parameters can then be used to improve the stopband characteristics of the overall Lth-band filter. We derive general formulas for D-R with given pairs of L and N. It is shown that for a fixed L, the choices of N, in a close neighborhood, may even decrease D-R despite increasing the arithmetic complexity, order, and the delay.

The paper proposes an optimization technique for the design of variable digital filters with simultaneously tunable bandedge and fractional delay using a fast filter bank (FFB) approach. In the FFB approach, full band signals are split into multibands, and each band is multiplied by a proper phase shift to realize the variable fractional delay. In the proposed technique, in the formulation of the optimization of the 0th stage prototype filter of the FFB, the ripples of the filters in the subsequent stages are all taken into consideration. In addition, a shaping filter is applied to the last retained band of the FFB to form the transition band of the variable filter, such that the transition width of each band in the FFB can be relaxed to reduce the computational complexity. In total three shaping filters, constructed from a prototype filter, can be shared by different bands, so that the extra cost incurred due to the shaping filter is low.

This paper proposes a method for designing high-order linear-phase finite-length impulse response (FIR) filters which are required as, e.g., the prototype filters in filter banks (FBs) and transmultiplexers (TMUXs) with a large number of channels. The proposed method uses the Farrow structure to express the polyphase components of the desired filter. Thereby, the only unknown parameters, in the filter design, are the coefficients of the Farrow subfilters. The number of these unknown parameters is considerably smaller than that of the direct filter design methods. Besides these unknown parameters, the proposed method needs some predefined multipliers. Although the number of these multipliers is larger than the number of unknown parameters, they are known a priori. The proposed method is generally applicable to any linear-phase FIR filter irrespective of its order being high, low, even, or odd as well as the impulse response being symmetric or antisymmetric. However, it is more efficient for filters with high orders as the conventional design of such filters is more challenging. For example, to design a linear-phase FIR lowpass filter of order 131071 with a stopband attenuation of about 55 dB, which is used as the prototype filter of a cosine modulated filter bank (CMFB) with 8192 channels, our proposed method requires only 16 unknown parameters. The paper gives design examples for individual lowpass filters as well as the prototype filters for fixed and flexible modulated FBs.

This paper proposes optimal finite-length impulse response (FIR) digital filters, in the least-squares (LS) sense, for compensation of chromatic dispersion (CD) in digital coherent optical receivers. The proposed filters are based on the convex minimization of the energy of the complex error between the frequency responses of the actual CD compensation filter and the ideal CD compensation filter. The paper utilizes the fact that pulse shaping filters limit the effective bandwidth of the signal. Then, the filter design for CD compensation needs to be performed over a smaller frequency range, as compared to the whole frequency band in the existing CD compensation methods. By means of design examples, we show that our proposed optimal LS FIR CD compensation filters outperform the existing filters in terms of performance, implementation complexity, and delay.

This paper shows that the in-phase and quadrature (I/Q) channel mismatch problem for complex signals in zero-IF receivers (ZIFRs) is related to the real-signal channel-mismatch problem in two-channel time-interleaved analog-to-digital converters (TI-ADCs). The problems are related in that, given one of the problems, it can be converted to the other problem via relatively simple signal processing operations. This offers more options for the estimation of and compensation for I/Q and TI-ADC channel mismatches. In particular, if there is a need to perform both I/Q and TI-ADC channel mismatch correction, one can make use of the same basic estimation and/or compensation principles for both applications which may save computational resources. The use of TI-ADC mismatch estimation and/or compensation also offers real-signal processing techniques to the complex-signal mismatch estimation and compensation problem in ZIFRs.

This paper introduces two polynomial finite-length impulse response (FIR) digital filter structures with simultaneously variable fractional delay (VFD) and phase shift (VPS). The structures are reconfigurable (adaptable) online without redesign and do not exhibit transients when the VFD and VPS parameters are altered. The structures can be viewed as generalizations of VFD structures in the sense that they offer a VPS in addition to the regular VFD. The overall filters are composed of a number of fixed subfilters and a few variable multipliers whose values are determined by the desired FD and PS values. A systematic design algorithm, based on iteratively reweighted l(1)- norm minimization, is proposed. It generates fixed subfilters with many zero-valued coefficients, typically located in the impulse response tails. The paper considers two different structures, referred to as the basic structure and common-subfilters structure, and compares these proposals as well as the existing cascaded VFD and VPS structures, in terms of arithmetic complexity, delay, memory cost, and transients. In general, the common-subfilters structure is superior when all of these aspects are taken into account. Further, the paper shows and exemplifies that the VFDPS filters under consideration can be used for simultaneous resampling and frequency shift of signals.

In this paper, we explore two nonrecursive reconstructors which recover the uniform-grid samples from the output of a time-interleaved analog-to-digital converter (TI-ADC) that uses some of the sampling instants for estimating the mismatches in the TI-ADC. Nonuniform sampling occurs due to timing mismatches between the individual channel ADCs and also due to missing input samples. Compared to a previous solution, the reconstructors presented here offer substantially lower computational complexity.

This paper proposes a method to design variable fractional-delay (FD) filters using the Farrow structure. In the transfer function of the Farrow structure, different subfilters are weighted by different powers of the FD value. As both the FD value and its powers are smaller than 0.5, our proposed method uses them as diminishing weighting functions. The approximation error, for each subfilter, is then increased in proportion to the power of the FD value. This gives a new distribution for the orders of the Farrow subfilters which has not been utilized before. This paper also includes these diminishing weighting functions in the filter design so as to obtain their optimal values, iteratively. We consider subfilters of both even and odd orders. Examples illustrate our proposed method and comparisons, to various earlier designs, show a reduction of the arithmetic complexity.

Sub-Nyquist sampling makes use of sparsities in analog signals to sample them at a rate lower than the Nyquist rate. The reduction in sampling rate, however, comes at the cost of additional digital signal processing (DSP) which is required to reconstruct the uniformly sampled sequence at the output of the sub-Nyquist sampling analog-to-digital converter. At present, this additional processing is computationally intensive and time consuming and offsets the gains obtained from the reduced sampling rate. This paper focuses on sparse multi-band signals where the user band locations can change from time to time and the reconstructor requires real-time redesign. We propose a technique that can reduce the computational complexity of the reconstructor. At the same time, the proposed scheme simplifies the online reconfigurability of the reconstructor.

In time-interleaved analog-to-digital converters (TI-ADCs), the timing mismatches between the channels result in a periodically nonuniformly sampled sequence at the output. Such nonuniformly sampled output limits the achievable resolution of the TI-ADC. In order to correct the errors due to timing mismatches, the output of the TI-ADC is passed through a digital time-varying finite-length impulse response reconstructor. Such reconstructors convert the nonuniformly sampled output sequence to a uniformly spaced output. Since the reconstructor runs at the output rate of the TI-ADC, it is beneficial to reduce the number of coefficient multipliers in the reconstructor. Also, it is advantageous to have as few coefficient updates as possible when the timing errors change. Reconstructors that reduce the number of multipliers to be updated online do so at a cost of increased number of multiplications per corrected output sample. This paper proposes a technique which can be used to reduce the number of reconstructor coefficients that need to be updated online without increasing the number of multiplications per corrected output sample.

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 l(1)-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 considers finite-length impulse response (FIR) filter approximation of differentiators and integrators, collectively called differintegrators. The paper introduces and compares three different FIR filter structures for this purpose, all of which are optimized in the minimax sense using iterative reweighted l(1)-norm minimization. One of the structures is the direct-form structure, but featuring equal-valued taps and zero-valued taps, the latter corresponding to sparse filters. The other two structures comprise two subfilters in parallel and cascade, respectively. In their basic forms, nothing is gained by realizing the filters in parallel or in cascade, instead of directly. However, as the paper will show, these forms enable substantial further complexity reductions, because they comprise symmetric and antisymmetric subfilters of different orders, and also features additional equal-valued and zero-valued taps. The cascade structure employs a structurally sparse filter. The additional sparsity, as well as tap equalities, are for all three structures found automatically in the design via the l(1)-norm minimization. Design examples included reveal feasible multiplication complexity savings of more than 50% in comparison with regular (unconstrained) direct-form structures. In addition, an example shows that the proposed designs can even have lower complexity than existing infinite-length impulse response filter designs.

In this paper, the fixed-point implementation of adjustable fractional-delay filters using the Farrow structure is considered. Based on the observation that the sub-filters approximate differentiators, closed-form expressions for the L-2-norm scaling values at the outputs of each sub-filter as well as at the inputs of each delay multiplier are derived. The scaling values can then be used to derive suitable word lengths by also considering the round-off noise analysis and optimization. Different approaches are proposed to derive suitable word lengths including one based on integer linear programming, which always gives an optimal allocation. Finally, a new approach for multiplierless implementation of the sub-filters in the Farrow structure is suggested. This is shown to reduce register complexity and, for most word lengths, require less number of adders and subtracters when compared to existing approaches.

This paper considers two-rate based structures for variable fractional-delay (VFD) finite-length impulse response (FIR) filters. They are single-rate structures but derived through a two-rate approach. The basic structure considered hitherto utilizes a regular half-band (HB) linear-phase filter and the Farrow structure with linear-phase subfilters. Especially for wide-band specifications, this structure is computationally efficient because most of the overall arithmetic complexity is due to the HB filter which is common to all Farrow-structure subfilters. This paper extends and generalizes existing results. Firstly, frequency-response masking (FRM) HB filters are utilized which offer further complexity reductions. Secondly, both linear-phase and low-delay subfilters are treated and combined which offers trade-offs between the complexity, delay, and magnitude response overshoot which is typical for low-delay filters. Thirdly, the HB filter is replaced by a general filter which enables additional frequency-response constraints in the upper frequency band which normally is treated as a dont-care band. Wide-band design examples (90, 95, and 98% of the Nyquist band) reveal arithmetic complexity savings between some 20 and 85% compared with other structures, including infinite-length impulse response structures. Hence, the VFD filter structures proposed in this paper exhibit the lowest arithmetic complexity among all hitherto published VFD filter structures.

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This paper introduces multimode transmultiplexers (TMUXs) in which the Farrow structure realizes the polyphase components of general lowpass interpolation/decimation filters. As various lowpass filters are obtained by one set of common Farrow subfilters, only one offline filter design enables us to cover different integer sampling rate conversion (SRC) ratios. A model of general rational SRC is also constructed where the same fixed subfilters perform rational SRC. These two SRC schemes are then used to construct multimode TMUXs. Efficient implementation structures are introduced and different filter design techniques such as minimax and least-squares (LS) are discussed. By means of simulation results, it is shown that the performance of the transmultiplexer (TMUX) depends on the ripples of the filters. With the error vector magnitude (EVM) as the performance metric, the LS method has a superiority over the minimax approach.

This paper introduces a realization of finite-length impulse response (FIR) filters with simultaneously variable bandwidth and fractional delay (FD). The realization makes use of impulse responses which are two-dimensional polynomials in the bandwidth and FD parameters. Unlike previous polynomial-based realizations, it utilizes the fact that a variable FD filter is typically much less complex than a variable-bandwidth filter. By separating the corresponding subfilters in the overall realization, significant savings are thereby achieved. A design example, included in the paper, shows about 65 percent multiplication and addition savings compared to the previous polynomial-based realizations. Moreover, compared to a recently introduced alternative fast filter bank approach, the proposed method offers significantly smaller group delays and group delay errors.