Many physical phenomena can be modeled by compressible signals, i.e., the signals with rapidly declining sample amplitudes. Although all the samples are usually nonzero, due to practical reasons such signals are attempted to be approximated as sparse ones. Because sparsity of compressible signals cannot be unambiguously determined, a decision about a particular sparse representation is often a result of comparison between a residual error energy of a reconstruction algorithm and some quality measure. The paper explores a relation between mean square error (MSE) of the recovered signal and the residual error. A novel, practical solution that controls the sparse approximation quality using a target MSE value is the result of these considerations. The solution was tested in numerical experiments using orthogonal matching pursuit (OMP) algorithm as the signal reconstruction procedure. The obtained results show that the proposed quality metric provides fine control over the approximation process of the compressible signals in the mean sense even though it has not been directly designed for use in compressed sensing methods such as OMP.

Channel estimation scheme for OFDM modulated transmissions usually combines an initial block-pilot-assisted stage with a tracking one based on comb or scattered pilots distributed among user data in the signal frame. The channel reconstruction accuracy in the former stage has a significant impact on tracking efficiency of the channel variations and the overall transmission quality. The paper presents a new block-pilot-assisted channel reconstruction procedure based on the DFT-based approach and the Least Square impulse response estimation. The proposed method takes into account a compressibility feature of the channel impulse response and restores its coefficients in groups of automatically controlled size. The proposition is analytically explained and tested in a OFDM simulation environment. The popular DFT-based methods including compressed sensing oriented one were used as references for comparison purposes. The obtained results show a quality improvement in terms of Bit Error Rate and Mean Square Error measures in low and mid ranges of signal-to-noise ratio without significant computational complexity growth in comparison to the classical DFT-based solutions. Moreover, additional multiplication operations can be eliminated, compared to the competitive, in terms of estimation quality, compressed sensing reconstruction method based on greedy approach.

A physical model of a wireless transmission channel in the time domain usually consists of the main propagation path and only a few reflections. The reasonable assumptions made about the channel model can improve its parameters’ estimation by a greedy OFDM (Orthogonal Frequency Division Multiplexing) equalizer. The equalizer works flawlessly if delays between propagation paths are in the sampling grid. Otherwise, the channel impulse response loses its compressible characteristic and the number of coefficients to find increases. It is possible to get back to the simple channel model by data oversampling. The paper describes how the above idea helps the OMP (Orthogonal Matching Pursuit) algorithm estimate channel coefficients. The authors analyze the oversampling algorithm on the one hand to assess the influence of filtering function and signal resolution on the quality of the channel impulse response reconstruction. On the other hand, the abilities of the OMP algorithm are analyzed to distinguish components of the oversampled signal. Based on these analyses, we proposed modifications to the compressible channel’s impulse response reconstruction algorithm to minimize the number of transmission errors. A distinction was made between the filters used in the OMP search and channel reconstruction stages before calculating equalizer coefficients. Additionally, the results of the search stage were considered as elements within the groups.

We present a quantum-assisted data authentication protocol that integrates classical information-theoretic security with quantum communication techniques. We assume only that the participants have access to open classical and quantum channels, and share a random static key material. Building on the Wegman–Carter paradigm, our scheme employs universal hashing for message authentication and leverages quantum channels to securely transmit random nonces, eliminating the need for key recycling. The protocol utilizes polar codes within Wyner’s wiretap channel model to ensure confidentiality and reliability, even in the presence of an all-powerful adversary. Security analysis demonstrates that the protocol inherits strong guarantees from both classical and quantum frameworks, provided the quantum channel maintains low loss and noise.

Effective delay resolution of propagation paths recovery can be controlled by oversampling used at the delay estimation stage of Orthogonal Matching Pursuit (OMP) method. Unfortunately, a finer resolution increases the number of inner products to be computed there. In order to reduce their quantity, a modification called Successive Delay Approximation (SDA) is proposed. The SDA selects an approximated path delay calculating only two extra inner products for each subsequent doubling of the oversampling ratio. The proposed solution is numerically efficient without significant transmission quality loss that has been proven in the simulations.