We introduce a novel one-bit quantization technique tailored for uniform linear antenna arrays. Our approach leverages error-feedback quantization to dynamically shape the quantization noise in alignment with the arrival angle of the received signal. To optimize the system’s performance within a predefined range of arrival angles, we focus on maximizing the minimum SNR of the quantized received signal. We formulate the design of our quantizer as a convex optimization problem, which can be efficiently solved numerically. Our numerical results provide compelling evidence that the proposed quantizer consistently delivers robust performance across various arrival angles within the specified range.

• Overloading occurs if the amplitude of a signal exceeds a predetermined limit. • Overloading may cause a catastrophic effect. • ll norm is used to obtain state space realizations robust to overloading. • Optimal realization where an identical number of bits is assigned to each state variables. • Numerical examples confirm robustness of proposed realizations. In digital signal processing, overloading of a value occurs if the amplitude of a signal exceeds a predetermined limit. The overloading should be avoided, since it may cause a catastrophic effect on the system. To mitigate the overloading, the l 2 norm scaling has been utilized for many years. However, the l 2 norm scaling does not always work well, since it is not directly related to the amplitude of the signal. This paper presents a design method of state space realizations for digital discrete-time LTI systems that are robust to overloading. Upper bounds of the amplitudes of state variables are evaluated by using the invariant set theory. When different numbers of bits are allocated to represent the values of state variables, our realization is given by minimizing the volume of an ellipsoidal invariant set. On the other hand, when an equal number of bits is assigned to each state variable, an upper bound on the magnitude of the state variables is minimized and the optimal realization is obtained by the spherical invariant set. Numerical examples are provided to show that our realizations are robust to overloading.

1-bit Delta-Sigma-based transmitters enable constant envelop transmissions. This paper synthesizes a stable 1-bit Delta-Sigma modulator that minimizes the mean squared quantization error at the output of a Delta-Sigma-based transmitter. The 1-bit Delta-Sigma modulator is designed by solving convex optimization problems, which can be solved numerically. A numerical example is provided to demonstrate our synthesis.

Delta-Sigma modulators are often utilized to convert analog signals into digital signals. The quantization error of a Delta-Sigma modulator can be reduced by oversampling. However, oversampling increases the number of bits per time if the same number of bits are assigned to each output of the quantizer. Due to limited bandwidth, the rate-distortion relation is necessary to balance the rate and the distortion. In this paper, we analyze the relationship between the rate and the distortion of an optimal scalar Delta-Sigma modulator that minimizes the variance of the error in the output of the system connected to the Delta-Sigma modulator. Numerical examples are provided to show rate-distortion relations of the optimal Delta-Sigma modulators.

In this paper, we propose two types of noise shaping infinite impulse response (IIR) filters for ΔΣ modulators based on H2and H∞norms of the in-band quantization noise. We utilize the hybrid-design and the least-squares approximation method to obtain noise shaping IIR filters by taking an indirect approach for solving the non-convex optimization problem. In both methods, we also incorporate the non-ideal behavior of the output lowpass filter into the design criteria of our noise shaping IIR filter as a weighting function. To demonstrate the effectiveness of proposed noise shaping IIR filters, we compare it with existing design methods.

We consider MISO wiretap channels with multiple eavesdroppers. Under the deterministic channel uncertainties, the beamformer and the covariance of the artificial noise are jointly designed to minimize the transmit power subject to SINR constraints. Our design problems are resolved by using a semidefinite program, which can be numerically solved. Simulation results are provided to see the effects of channel uncertainties on the transmit power.

Optimal error feedback filters for A/D converters of remote sensors in networked control systems are studied. It is shown that if the transfer function from the quantization error to the output of interest has a minimum phase, then its inverse is the optimal error feedback filter in terms of any kind of norms of errors. For general LTI systems, the design of error feedback filters is formulated as an optimization problem, which can be numerically solved. A design example is provided to demonstrate the effectiveness of our proposed method.

We consider physical-layer security of a wireless LAN where multiple receivers collude to eavesdrop the information from the base station to the intended receiver. To enhance the physical-layer security, we design the interference signals to combat the eavesdropping. Our design problems are resolved using semidefinite relaxation problems, which can be numerically solved efficiently by the existing convex optimization solvers. Simulation results are provided to demonstrate the efficiency of the proposed designs.

In this paper, a low complexity equalizer for single carrier transmissions over doubly selective channels is developed. The main attribute of the proposed equalizer is its low complexity compared to the existing equalizers, which is attained at the expense of a slight performance loss. Simulation results show that the performance of our proposed low complexity equalizer is as good as that of the conventional equalizers with extensive computation complexity.

Wireless communications are susceptible to eavesdropping. To interfere the eavesdropper having multiple antennas, secret information signals and interference signals that are transmitted from multiple antennas are designed. It is shown that our design can be cast into a semidefinite program, which can be numerically solved efficiently. Simulation results are provided to demonstrate the efficiency of the proposed design.

In this paper, training symbol designs for estimation of frequency selective channels and compensation of in-phase (I) and quadrature (Q) imbalances on OFDM transmitters and receivers are studied. We utilize cross entropy (CE) optimization techniques together with convex optimization to design training sequence that minimizes the channel estimate mean squared error (MSE) as well as estimating the effect of I/Q mismatch while lowering the peak power of the training signals. The proposed design provide better channel estimate MSE and bit error rate (BER) performances. The efficacies of the proposed designs are corroborated by analysis and simulation results.

We develop a closed-form approximation algorithm for de signing IIR digital filters with linear phase and guaranteed stability. In this algorithm, the stopband and passband edge frequency can be specified in the frequency domain and the filter coefficients can be easily obtained for approximating the given frequency response. Additionally, there is a property that the maximum of absolute values of all poles can be con trolled, so we can avoid the risk that the designed filters under finite word-length effects become unstable. Finally, a numerical example is given to illustrate the utility of the proposed method.

Training sequences for estimation of channel parameters have been well designed under the condition that the number of the unknown channel parameters is not greater than the number of the known symbols. Without the condition, we develop a method to obtain the optimal number of known pilot symbols for pilot-aided linear channel estimation in orthogonal frequency division multiplexing (OFDM). We derive an expression for channel estimation error covariance from which performance measures can be numerically evaluated to obtain the optimal number of pilot symbols. Using capacity lower bound as a performance measure, we demonstrate that for channels with exponential power profiles, it is better to estimate a truncated version of the channel response, which reveals the disadvantage of the existing design based on the condition.

We prove that discrete Fourier basis channel model is optimal for least squares estimation of channel coefficients used for low-complexity equalization of OFDM transmission over doubly selective channels. We show that regardless of channel statistics, the channel model order is determined by the number of coefficients used in the equalization. Our theoretical findings are numerically validated by using linear zero forcing equalizers and non-linear maximum likelihood equalizer with pilot-aided channel estimation.

Antenna selection is a simple yet efficient technique to obtain diversity advantage from Multi-Input and Multi-Output (MIMO) communication systems. Without specifying system factors such as antenna selection criterion, coding and decoding, equalization, and channel statistics, we evaluate diversity orders of antenna selections over frequency-selective MIMO channels. We show that the diversity order of any configuration approximately scales in the numbers of transmit and receive antennas. Numerical simulations are provided to validate our analysis.

Maximum Likelihood (ML) equalization for Orthogonal Frequency Division Multiplexing (OFDM) over time- and fre quency- selective channels is analyzed in this paper. An approximate expression for bit error rate (BER) performance of the ML equalizer with a limited number of taps is developed, which subsumes the matched filter bound (MFB) equalization performance as a special case, and which saves on intensive time-consuming empirical simulations. Numerical simulations validate our approximate expression.

The presence of null subcarriers in orthogonal frequency division multiplexing system complicates the design of both training preamble for channel estimation and pilot symbols for pilot-aided channel estimation that minimize the mean square error (MSE) of estimates of frequency-selective channels. In this paper, we numerically find optimal preambles, casting the MSE minimization problem into a semidefinite programming problem. Then, based on the optimal preamble, we also design pilot symbols for pilot-aided channel estimation. A design example under the same setting as IEEE 802.11a is provided to verify the efficacy of our proposal.

We present universal BER performance ordering for different antenna sizes in Multiple-Input Multiple-Output (MIMO) wireless systems with zero-forcing (ZF) equalization, which hold for all SNR. We first show that when the number of transmit antennas is fixed, BER of each symbol degrades with a decrease in the number of receive antennas even if the received SNR is kept constant. Then, we prove that when the number of receive antennas is fixed, the average BER improves with a decrease in the number of transmit antennas, which shows the tradeoff between BER and bandwidth efficiency in MIMO with ZF equalization. Furthermore, discussions on the relation of BER with the same change in the number of receive and transmit antennas show that there is no universal order in BER for any particular channel. These highlight the advantage and the limit of MIMO with ZF equalization.

In Orthogonal Frequency Division Multiplexing (OFDM) transmissions over doubly-selective channels, pilot-aided channel estimation is a practical approach to obtain channel estimates. In this paper, we apply Bessel model for channel modeling based on which pilot-aided channel estimation is performed. The utilization of Bessel model enables the estimation of intercarrier interference (ICI) effect of the neighboring subcarriers. A low complexity Viterbi-type Maximum Likelihood (ML) equalizer then uses the Bessel model-based channel estimates for equalization, displaying good bit-error rate (BER) performance. Monte-Carlo simulations show that the combination of Viterbi-type ML equalization and Bessel model-based estimates yields improved BER performance over other combinations of linear equalization and finite parameter model-based estimates.

Multicarrier multiple access with channel knowledge and prescribed power at the transmitters is shown to maximize the sum-rate for circulant intersymbol-interference (ISI) channels. A low-complexity iterative algorithm is derived for optimal subcarrier allocation to multiple users, while power is loaded per user by specializing an existing iterative algorithm to circulant ISI channels. It is analytically shown that each subcarrier should be allocated to the user having relatively better subcarrier gain and that different users may share certain subcarriers.

We study uncoded bit-error rate (BER) performance of single-carrier block transmissions, zero-padded (ZP) transmission and cyclic-prefixed (CP) transmission, when minimum mean-squared error (MMSE) equalizers are applied. We show analytically that the BER of ZP transmission with MMSE equalization degrades as the bandwidth efficiency increases, i.e. there is a trade-off between BER and bandwidth efficiency in ZP transmission. It is also proven that ZP transmission outperforms CP transmission and uncoded orthogonal frequency-division multiplexing (OFDM) on the average. Numerical examples are provided to validate our theoretical findings and to compare the block transmission systems

Multipath propagation and mobility-induced Doppler effects contribute to the time- and frequency-selectivity (doubly-selectivity) in channels. To describe the doubly-selective channel, we propose a finite parameter model composed of kernels expressed as a function of the channel correlation based on Karhunen-Loeve (KL) expansion. The proposed model is optimal in the MMSE sense, provided that the instantaneous channel correlation is matched. It can also adapt to changes in the velocity of the terminal. Even when the channel correlation is unavailable and can only be assumed from Jakes' model, the channel estimation mean square error (MSE) of our proposed model is shown to be comparable or outperforms the oversampled basis expansion model (OBEM), polynomial model (PM) and Slepian model as validated by Monte-Carlo simulations on Rayleigh fading channels. In the application in an OFDM system, the proposed model confers significant BER performance gain over OBEM and PM

Orthogonal frequency division multiplexing (OFDM) transmission is robust to frequency-selective channels but sensitive to time-selective channels. Time variations of channels destroys the orthogonality between subcarriers, resulting in a considerable performance loss due to intercarrier interference (ICI) between subcarriers. In this paper, we propose a Viterbi-type algorithm to effectively suppress the ICI, by exploiting the property of ICI terms and null subcarriers embedded in OFDM symbols for the reduction of interferences from/to adjacent bands. Simulations show that the proposed equalizer works well with affordable complexity and outperforms linear equalizers.

Coherent decoding of orthogonal space-time block codes (OSTBC) takes advantage of transmit/receive diversity to mitigate fading channel effects. Thanks to the orthogonality of OSTBC, a low-complexity linear maximum likelihood (ML) decoding becomes available if the receiver knows the channel state information (CSI). For OSTBC over time-selective channels, we develop an analytical expression of the bit error rate (BER) performance for linear decoding with minimum mean squared error (MMSE) channel estimates in place of the true channel. Based on the expression, we derive a BER performance limit in decision-directed mode where the channel is tracked with Kalman filtering. Numerical examples are provided to see the impact of time-selective fading on the BER performance.

We study the bit-error rate (BER) performance of single-carrier (SC) zero-padded (ZP) transmissions with zero-forcing (ZF) equalization. Padded redundant zeros mitigate multipath effects but reduce the bandwidth efficiency. We show analytically that the BER improves as the bandwidth efficiency decreases, i.e., there is a clear trade-off between BER and bandwidth efficiency. We also demonstrate that ZP outperforms SC cyclic prefixed (CP) transmission.

Channels with long impulse response often arise in high-rate digital transmissions due to severe multipath. This necessitates sophisticated equalization at the receiver. On the other hand, exploiting the available multipath diversity improves bit error performance. To collect the full multipath diversity, computationally cumbersome maximum likelihood sequence estimation (MLSE) is required. Although the Viterbi algorithm (VA) for MLSE is more efficient than the exhaustive ML search, its complexity increases exponentially with the channel length, which varies with the propagation environment. Since the computational power of the receiver is limited, VA becomes infeasible for long channels. In this paper, we develop a transmission capable of handling relatively long channels. The transmitter controls the computational complexity of MLSE at the receiver by periodically inserting zeros within information-bearing symbols, depending on the channel length and the computational power of the receiver. The optimal MLSE with reduced complexity becomes available at the expense of reduced data rate.

The location, number, and power of pilot symbols embedded in multicarrier block transmissions over rapidly fading channels, are important design parameters affecting not only channel estimation performance, but also channel capacity. Considering orthogonal frequency-division multiplexing (OFDM) systems with decoupled information-bearing symbols from pilot symbols transmitted over wireless frequency-selective Rayleigh-fading channels, we show that equispaced and equipowered pilot symbols are optimal in terms of minimizing the mean-square channel estimation error. We also design the number of pilots, and the power distributed between information bearing and pilot symbols, using as criterion a lower bound on the average capacity. Numerical results corroborate our theoretical findings.

Standardized wireless transmissions include fixed-size fragments per packet. Relying on this structure, we develop two schemes for distributing redundancy across fragments, in order to improve performance of packet transmissions over frequency-selective fading channels. We prove that both schemes guarantee symbol detectability, which implies that they both enable the full multipath diversity. We test their relative merits, and compare them with competing alternatives using simulations.

High data rates give rise to frequency-selective propagation, while carrier frequency-offsets and mobility-induced Doppler shifts introduce time-selectivity in wireless links. To mitigate the resulting time- and frequency-selective (or doubly-selective) channels, an optimal training strategy is designed in this paper for block transmissions over doubly-selective channels, relying on a basis expansion channel model. The optimality in designing our PSAM parameters consists of maximizing a tight lower bound on the average channel capacity, that is also shown to be equivalent to the minimization of the minimum mean-square channel estimation error. Numerical results corroborate our theoretical designs.

We establish that practical multiple access based on finite size information blocks transmitted with prescribed power and with loaded multicarrier modulation, is optimal with respect to maximizing the sum-rate of circulant intersymbol interference (ISI) channels, that are assumed available at the transmitter. Circulant ISI channels are ensured either with cyclic prefixed block transmissions and an overlap-save reception, or, with zero-padded block transmissions and an overlap-add reception. Analysis asserts that sum-rate optimal multicarrier users could share one or more subcarriers depending on the underlying channels. Optimal loading is performed by specializing an existing iterative low-complexity algorithm to circulant ISI channels.

Enabling linear minimum-mean square error (LMMSE) based estimation of random time-selective channels, pilot symbol assisted modulation (PSAM) has well documented merits as a fading countermeasure capable of improving bit error rate performance. In this paper, we establish average-rate optimality of PSAM by showing that the insertion of equi-powered and equi-spaced pilot symbols in PSAM transmissions maximizes a tight lower bound of the average channel capacity. Relying on a simple closed form expression of this bound in terms of the LMMSE channel estimator variance, we further design PSAM transmissions with optimal spacing of pilot symbols, and optimal allocation of the transmit-power budget between pilot and information symbols.

The adoption of orthogonal frequency-division multiplexing by wireless local area networks and audio/video broadcasting standards testifies to the importance of recovering block precoded transmissions propagating through frequency-selective finite-impulse response (FIR) channels. Existing block transmission standards invoke bandwidth-consuming error control codes to mitigate channel fades, and training sequences to identify the FIR channels. To enable block-by-block receiver processing, we design redundant precoders with cyclic prefix and superimposed training sequences for optimal channel estimation and guaranteed symbol detectability, regardless of the underlying frequency-selective FIR channels. Numerical results are presented to access the performance of the designed training and precoding schemes.

Enabling linear minimum-mean square error (LMMSE)-based estimation of random time-selective channels, pilot-symbol-assisted modulation (PSAM) has well-documented merits as a fading counter-measure boosting bit-error rate performance. We design average-rate optimal PSAM transmissions by maximizing a tight lower bound of the average channel capacity. Relying on a simple closed-form expression of this bound in terms of the LMMSE channel estimator variance, we obtain PSAM transmissions with optimal spacing of pilot symbols and optimal allocation of the transmit-power budget between pilot and information symbols. Equi-powered transmitted symbols, channels with special Doppler spectra, and analytical and simulation based comparisons of possible alternatives shed more light on information-theoretic aspects of PSAM-based transmissions.

The adoption of orthogonal frequency-division multiplexing (OFDM) by wireless local area networks and audio/video broadcasting standards testifies to the importance of recovering block precoded transmissions propagating through frequency-selective FIR channels. Existing block transmission standards invoke bandwidth-consuming error control codes to mitigate channel fades and training sequences to identify the FIR channels. To enable low-complexity block-by-block receiver processing, we design redundant precoders with cyclic prefix (CP) and superimposed training sequences for optimal channel estimation and guaranteed symbol recovery regardless of the underlying FIR frequency-selective channels. Numerical results axe presented to access the performance of the designed training and precoding schemes.

The adoption of orthogonal frequency-division multiplexing (OFDM) by wireless local area networks and audio/video broadcasting standards testifies to the importance of recovering block precoded transmissions propagating through frequency-selective FIR channels. Existing block transmission standards invoke bandwidth-consuming error control codes to mitigate channel fades and training sequences to identify the FIR channels. For low-complexity block-by-block processing, redundant precoders with cyclic prefix (CP) along with superimposed training sequence are optimally designed to enable least squares estimation of time-varying FIR channels and symbol recovery regardless of the underlying FIR frequency-selective multipath channel. Numerical results are also presented to access the performance of the proposed affine precoders.

Delayless subband adaptive digital filters (ADFs) have been proposed to avoid the drawbacks of the conventional subband ADF, which are transmission delay associated with the filterbank and degradation of the performance due to aliasing effects. In the delayless subband ADF, the tap-weight vectors are computed in subbands and then they are transformed into the tap-weight vector in fullband by a certain transform. In this letter, a general formulation for the delayless subband ADF is proposed, and some requirements on the fullband/subband transform are investigated.

In order to attain multichannel blind deconvolution of linear time-invariant nonminimum-phase dynamic systems. Inouye and Habe (see Proc. IEEE Signal Processing Workshop on Higher-Order Statistics, p.96-100, 1995) proposed 1995 a single-stage maximization criterion. The criterion function is the sum of squared fourth-order cumulants of the equalizer outputs, and the coefficients of the equalizer are determined at once. On the other hand, one of possible approaches for multichannel blind deconvolution is to construct an equalizer based on the system identified by higher-order cumulant-matching. In this paper, it is shown that the single-stage maximization criterion is equivalent to a least-squares fourth-order cumulant-matching criterion after multichannel pre-whitening of channel outputs. This result provides us with an important interpretation of the single-stage maximization criterion.

Generally, the output of a filter bank for a stationary input signal is not stationary but cyclostationary. In this paper, by using cyclostationary spectral analysis, the spectral correlation density of this output is derived. Using this result we derive a criterion to construct an optimal 2-band perfect reconstruction filter bank which minimizes the averaged mean squared reconstruction error when the high pass band signal is dropped. By adding constrains to the filter coefficients, the biorthogonal filter bank, the conjugate quadrature filter bank and the biorthogonal linear phase filter bank are respectively obtained. Some numerical results are also presented for optimal biorthogonal and PR linear phase filter banks which are compared in terms of some performance measures.