Accurate estimation of fractional delay and Doppler shifts in multipath channels is essential for integrated sensing and communication (ISAC) systems operating in high-mobility environments. Such channels exhibit doubly selective fading in both time and frequency. Orthogonal Time Frequency Space (OTFS) modulation provides a simple and robust means for channel compensation under these conditions. However, the presence of fractional delay and Doppler components introduces inter-path interference, which degrades estimation accuracy. In this paper, we propose a two-stage estimation method based on Prony’s technique using OTFS pilot signals with M subchannels and N pilot repetitions. In the first stage, Doppler frequencies are estimated by jointly solving M coupled Prony equations, exploiting the periodicity of the pilot signal. In the second stage, delays are estimated by applying the discrete Fourier transform (DFT) and Prony’s method to each Doppler component obtained in the first stage. The proposed method can accurately estimate up to N −1 delay-Doppler parameters under noiseless conditions. In noisy environments, conventional information criteria such as AIC and BIC yield suboptimal performance; thus, a heuristic model order selection is adopted. Numerical simulations confirm that the proposed method achieves high estimation accuracy, highlighting its potential for future ISAC frameworks.

Marton’s optimal error exponent for the lossy source coding problem is defined as a non-convex optimization problem. This fact had prevented us to develop an efficient algorithm to compute it. This problem is caused by the fact that the rate-distortion function$R(\Delta |P)$is potentially non-concave in the probability distribution P for a fixed distortion level$\Delta $. The main contribution of this paper is the development of a parametric expression that is in perfect agreement with the inverse function of the Marton exponent. This representation has two layers. The inner layer is convex optimization and can be computed efficiently. The outer layer, on the other hand, is a non-convex optimization with respect to two parameters. We give a method for computing the Marton exponent based on this representation.

The error exponent of fixed-length lossy source coding was established by Marton. Ahlswede showed that this exponent can be discontinuous at a rate R, depending on the probability distribution P of the given information source and the distortion measure d(x, y). The reason for the discontinuity in the error exponent is that there exists (d, ∆) such that the rate-distortion function R(∆|P) is neither concave nor quasi-concave with respect to P. Arimoto’s algorithm for computing the error exponent in lossy source coding is based on Blahut’s parametric representation of the error exponent. However, Blahut’s parametric representation is a lower convex envelope of Marton’s exponent, and the two do not generally agree. The contribution of this paper is to provide a parametric representation that perfectly matches the inverse function of Marton’s exponent, thus avoiding the problem of the rate-distortion function being nonconvex with respect to P. The optimal distribution for fixed parameters can be obtained using Arimoto’s algorithm. Performing a nonconvex optimization over the parameters successfully yields the inverse function of Marton’s exponent.

Dueck and Körner's reliability function for discrete memoryless channels for rates above the capacity coincides with Arimoto's exponent of correct decoding probability. The two exponent functions are described by seemingly different optimization problems over the space of probability distributions. Arimoto gave an iterative algorithm for solving the optimization problem that appears in his exponent function. However, no algorithm to solve the optimization problem that appears in Dueck and Körner's exponent has been proposed. This paper proposes a new iterative algorithm for solving the minimization problem in Dueck and Körner's exponent. In the proposed algorithm, a double minimization form with respect to two joint distributions on input and output symbols is introduced. This double minimization is connected to another double minimization that appears in Arimoto's algorithm. Such a connection leads to a quadruple minimization problem, by which the match of Arimoto and Dueck-Körner exponents is easily proved.

Hayashi and Matsumoto gave two lower bounds for the secrecy exponent for wiretap channels in 2011 and 2016. They proved that the latter exponent function is greater than or equal to the former one for any positive rate, input distribution and conditional probability of wiretapper's channel. In this paper, we give a new and simple proof of the inequality between the two exponent functions. To prove the inequality we use non-negativity of Kullback-Leibler distance together with a lemma that was introduced by Arimoto to derive a computation algorithm for error and correct decoding probability exponent for discrete memoryless channels.

One of the important tasks in wireless communications is propagation delay estimation. It has been found that the channel estimation accuracy of compressed sensing is superior to the existing method based on signal parameter estimation through MUltiple SIgnal Classification (MUSIC) and Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT). However, there is a problem in the method that multipath delays may not be resolved if they span between the grids. This problem leads to inaccurate channel estimation. In this paper, we describe the Atomic Norm Minimization (ANM) that enables super resolution channel estimation. In additions, we propose ANM by using Spread Spectrum (SS) signal. In this study, we show new experiments using Gold code for Global Positioning System (GPS). We have also added a new experiment to check the performance of the ANM with SS signal.

Recently, Parizi, Telatar, and Merhav [1] determined the exact random coding secrecy exponents for a wiretap channel. In this study, we focus on the computation of such secrecy exponents. To obtain the exact random coding secrecy exponent for a constant composition random coding ensemble, optimization with respect to two stochastic matrices must be performed. Parizi et al. suggested that inner optimization is a convex optimization problem and therefore can be solved efficiently and that the outer optimization is not guaranteed to have convex structure and is solved by an exhaustive search. In this paper, we develop an efficient computation of the exact random coding secrecy exponent.

The form of Dueck and Körner's exponent function for correct decoding probability for discrete memoryless channels at rates above the capacity is similar to the form of Csiszár and Körner's exponent function for correct decoding probability in lossy source coding for discrete memoryless sources at rates below the rate distortion function. We recently gave a new algorithm for computing Dueck and Körner's exponent. In this paper, we give an algorithm for computing Csiszár and Körner's exponent. The proposed algorithm can also be used to compute cutoff rate and the rate distortion function.

For a discrete memoryless channel, a lower bound for the correct decoding probability exponent was derived by Arimoto. He also gave an iterative algorithm for computing the exponent. Subsequently, Dueck and Körner determined the optimal exponent function of the correct decoding probability. In this paper, a new iterative algorithm that computes Dueck and Körner's exponent is presented.

Estimation of the channel distortion characteristics is of crucial importance for realizing a reliable communication. In order to estimate the channel, a received signal is sampled at some rate. The Nyquist rate is widely used notion to determine the sampling rate of the received signal. On the other hand, Vetterli introduced the concept of rate of innovation that is the degree of freedom of the signal space and proposed annihilating filter method, which solves a nonlinear simultaneous equation by means of finding roots of the characteristic polynomial of the equation. By using this technique, the number of samples can be reduced from the Nyquist rate. In this paper, we employ the annihilating filter method to perform the estimation of a multi-path channel. A spread spectrum signal with a wide bandwidth is transmitted, while the received signal is sampled at a very low sampling rate that is determined according to the rate of innovation.

The Separable Property (SP) condition for time and frequency synchronization compels us to determine phase correction terms in the Gabor Division/Spread Spectrum System (GD/S3). The phase correction technique has led us to design a GD/S3receiver equipped with phase-tuned layers for Mary phase shift keying (MPSK). The resulting signal points of the time domain (TD) and frequency domain (FD) correlator outputs of each layer for M = 16 consist of only three lines, called a main-lobe with a layer-dependent phase angle and sidelobes with phase angle ±2π/16. The two sidelobes suggesting bit errors are removed by using code division multiple target (CDMT), inspired by code division multiple-access (CDMA) philosophy. The simulation result for 16PSK is confirmed.

A non-binary analog-to-digital converter (ADC) based on β-expansion, called a β-encoder, can reportedly achieve robustness against large process variation and widespread environment change. The quantization error of the β-encoder is not uniformly distributed, which makes mean squared error (MSE) evaluation difficult. In this work, an analysis method for giving the upper bound of the MSE of the quantization error is proposed. We also gave an evaluation of signal-to-noise-ratio (SNR), which is effective for designing β-encoders.

Delay and Doppler determination of a time-delayed and frequency-shifted signal is one of fundamental problems in communication. The two-parameter estimation is reduced to two one-parameter estimation problems in time- and frequency-domain signals. Motivated by Gabor's communication theory, we proceed further parallelism between time- and frequency-domain signals and solve the two problems individually and cooperatively. Simulation results without prescribed information are reported.

Recently proposed new Time-Domain (TD) synchronization using frequency integration and TD Spread Spectrum (SS) codes has been shown to be robust to frequency offset, that has its dual Frequency-Domain (FD) synchronization using time integration and FD SS codes which is robust to timing offset. Separable Property (SP) is defined for time-frequency synchronization under the condition containing time and frequency deviations to be performed separately and cooperatively. The SP compels us to design phase correction on SS codes and transmitted data.

Non-coherent signal with unknown delay and Doppler is recovered by Gabor division/spread spectrum system. Separable property (SP) condition for time and frequency synchronization leads us to determine delay and Doppler precisely. This paper gives an enlargement of acceptable delay and Doppler region by using multiple codes and their associated receivers simultaneously without increasing computation time. As its application, two-target simultaneous determination is discussed.

Frequency division spread spectrum system (FD/S3) has been recently proposed, which uses frequency domain spreading codes and can allow frequency offsets between users. Motivated by the conventional time-domain code acquisition, we propose a frequency (F)-domain code acquisition method using time (T)-domain integrator, which permits frequency offset, which leads to a new T-domain code acquisition using F-domain integrator. Recently proposed Gabor division (GD)/S3system permits us to use both F- and T-domain code acquisitions separately and cooperatively*.

We propose a Gabor division (GD)-CDMA system which permits time and frequency offsets. Negatively correlated time- and frequency-domain spreading codes have shown to reduce the variances of mutual- and self-interferences. In this paper, we show that such negatively correlated spreading codes have another important property that they flatten the time-frequency energy distributions of signals in GD-CDMA system.

This paper proposes a low power architecture for second order digital phase-locked loop (DPLL). High power consumption of DPLL results from using a look-up table (LUT) in implementing the numerically controlled oscillator (NCO). A new design for NCO is presented in which no LUT is used. Proposed architecture implemented using field programmable gate array (FPGA) consumed 15.44 mw at 100 MHz clock frequency which means a more than 25% saving in power consumption compared to traditional NCO. Furthermore, proposed method also saves FPGA resources and works at faster clock frequency.

It is believed that the dimension of the signal space with interval T and bandwidth W is 2WT, while we cannot make the out-of-band and out-of-time energies of any waveform zero. We propose a Gaussian pulse shaping for multi-carrier CDMA systems to utilize the time and frequency resources effectively. Gaussian pulses have ICI and ISI; they are not orthogonal. Markovity of spreading codes save the drawback of ICI and ISI. Overlapped Gaussian pulses increase the spectral efficiency.

Slepianpsilas prolate spheroidal wave function (PSWF) is optimum in energy concentration within given frequency bandwidth and time-width. However it is not employed in communications mainly because its inter-symbol interference is unfavorable. We show that introducing Markovian spreading codes makes PSWF be a strong candidate for the chip waveform in CDMA systems. For design tractability, Gaussian waveform is recommended.

Pulse shaping filters are commonly implemented by FIR filters. Motivated by Slepian's philosophy of discrete prolate spheroidal sequences (DPSS), we investigate Welch's lower bound on aperiodic auto- and cross-correlations for oversampled sequences. An oversampled sequence set having minimum cross-correlations in chip-asynchronous CDMA system is provided under a given bandwidth condition.

Performance of chip-asynchronous DS/CDMA system depends on chip waveform as well as spread spectrum (SS) codes. In case of rectangular chip waveform, SS codes generated by a Markov chain were shown to improve bit error rate (BER) performance. However, in commercial CDMA systems, a band-limited root raised cosine (RRC) pulse is used, where the superiority of Markov codes is reduced. RRC pulse fulfills inter-chip interference (ICI)-free condition. In CDMA systems, multiple-access interference (MAI) is of crucial importance. Gaussian pulse used in conjunction with Markovian codes reduces MAI although it does not has the ICI-free property. Computer simulations show that Gaussian pulse with same excess bandwidth energy as the RRC pulse significantly reduces BER.

It is known that spreading codes generated by a Markov chain improve bit error rate performance of direct sequence/code division multiple access (DS/CDMA) systems if the chip pulse is rectangular. Real analysis tells us that a pair of the rectangular and sine functions is one of Fourier transform and its inverse Fourier transform and vice versa. On the other hand, Gaussian pulses have the self-duality property: they have the same expression in both time and frequency domains. Gaussian chip pulses sacrifice inter-symbol interference. However, the use of Markovian codes together with a Gaussian pulse increases the system performance approximately 30% in terms of the number of users

Multiple-access interference (MAI) depends on chip pulse shapes in chip-asynchronous direct sequence/code division multiple access (DS/CDMA) systems. The mean squared MAI averaged over relative time delays is expressed in a quadratic form, where a coefficient matrix is derived from the pulse shapes, while a variable vector consists of aperiodic autocorrelation functions of the signature sequences. This quadratic form gives a lower bound of the mean squared MAI, which is equivalent to the Welch bound if the pulse shape is a delta function. For any continuous pulse shapes, however, the mean squared MAI is shown to be reduced beyond the Welch bound. In case of rectangular pulse, the mean squared MAI is reduced by 13.4%, whereas the reduction ratio is 5.2% for band-limited pulses with excess bandwidth 0.5