This paper proposes two full-digital receive beamforming (BF) methods for low-complexity and high-accuracy uplink signal detection via Gaussian belief propagation (GaBP) at base stations (BSs) adopting massive multi-input multi-output (MIMO) for open radio access network (O-RAN). In addition, beyond fifth generation mobile communication (beyond 5G) systems will increase uplink capacity. In the scenarios such as O-RAN and beyond 5G, it is vital to reduce the cost of the BSs by limiting the bandwidth of fronthaul (FH) links, and the dimensionality reduction of the received signal based on the receive BF at a radio unit is a well-known strategy to reduce the amount of data transported via the FH links. In this paper, we clarify appropriate criteria for designing a BF weight considering the subsequent GaBP signal detection with the proposed methods: singular-value-decomposition-based BF and QR-decomposition-based BF with the aid of discrete-Fourier-transformation-based spreading. Both methods achieve the dimensionality reduction without compromising the desired signal power by taking advantage of a null space of channels. The proposed receive BF methods reduce correlations between the received signals in the BF domain, which improves the robustness of GaBP against spatial correlation among fading coefficients. Simulation results assuming realistic BS and user equipment arrangement show that the proposed methods improve detection capability while significantly reducing the computational cost.

Conventional Nyquist folding receiver (NYFR) uses zero crossing rising (ZCR) voltage times to control the RF sample clock, which is easily affected by noise. Moreover, the analog and digital parts are not synchronized so that the initial phase of the input signal is lost. Furthermore, it is assumed in most literature that the input signal is in a single Nyquist zone (NZ), which is inconsistent with the actual situation. In this paper, we propose an improved architecture denominated as a dual-channel NYFR with adjustable local oscillator (LOS) and an information recovery algorithm. The simulation results demonstrate the validity and viability of the proposed architecture and the corresponding algorithm.

The design and adjustment of the divergence in audio applications using nonnegative matrix factorization (NMF) is still open problem. In this study, to deal with this problem, we explore a representation of the divergence using neural networks (NNs). Instead of the divergence, our approach extends the multiplicative update algorithm (MUA), which estimates the NMF parameters, using NNs. The design of the extended MUA incorporates NNs, and the new algorithm is referred to as the deep MUA (DeMUA) for NMF. While the DeMUA represents the algorithm for the NMF, interestingly, the divergence is obtained from the incorporated NN. In addition, we propose theoretical guides to design the incorporated NN such that it can be interpreted as a divergence. By appropriately designing the NN, MUAs based on existing divergences with a single hyper-parameter can be represented by the DeMUA. To train the DeMUA, we applied it to audio denoising and supervised signal separation. Our experimental results show that the proposed architecture can learn the MUA and the divergences in sparse denoising and speech separation tasks and that the MUA based on generalized divergences with multiple parameters shows favorable performances on these tasks.

This paper addresses short-length sparse superposition codes (SSCs) over the additive white Gaussian noise channel. Damped approximate message-passing (AMP) is used to decode short SSCs with zero-mean independent and identically distributed Gaussian dictionaries. To design damping factors in AMP via deep learning, this paper constructs deep-unfolded damped AMP decoding networks. An annealing method for deep learning is proposed for designing nearly optimal damping factors with high probability. In annealing, damping factors are first optimized via deep learning in the low signal-to-noise ratio (SNR) regime. Then, the obtained damping factors are set to the initial values in stochastic gradient descent, which optimizes damping factors for slightly larger SNR. Repeating this annealing process designs damping factors in the high SNR regime. Numerical simulations show that annealing mitigates fluctuation in learned damping factors and outperforms exhaustive search based on an iteration-independent damping factor.

The Nyquist folding receiver (NYFR) is a novel analog-to-information architecture, which can achieve wideband receiving with a small amount of system resource. The NYFR uses a radio frequency (RF) non-uniform sampling to realize wideband receiving, and the practical RF non-uniform sample pulse train usually contains an aperture. Therefore, it is necessary to investigate the aperture impact on the NYFR output. In this letter, based on the NYFR output signal to noise ratio (SNR), the aperture impact on the NYFR is analyzed. Focusing on the aperture impact, the corresponding NYFR output signal power and noise power are given firstly. Then, the relation between the aperture and the output SNR is analyzed. In addition, the output SNR distribution containing the aperture is investigated. Finally, combing with a parameter estimation method, several simulations are conducted to prove the theoretical aperture impact.

Logical matrices are binary matrices often used to represent relations. In the map folding problem, each folded state corresponds to a unique partial order on the set of squares and thus could be described with a logical matrix. The logical matrix representation is powerful than graphs or other common representations considering its association with category theory and homology theory and its generalizability to solve other computational problems. On the application level, such representations allow us to recognize map folding intuitively. For example, we can give a precise mathematical description of a folding process using logical matrices so as to solve problems like how to represent the up-and-down relations between all the layers according to their adjacency in a flat-folded state, how to check self-penetration, and how to deduce a folding process from a given order of squares that is supposed to represent a folded state of the map in a mathematical and natural manner. In this paper, we give solutions to these problems and analyze their computational complexity.

Deep unfolding is a promising deep-learning technique, whose network architecture is based on expanding the recursive structure of existing iterative algorithms. Although deep unfolding realizes convergence acceleration, its theoretical aspects have not been revealed yet. This study details the theoretical analysis of the convergence acceleration in deep-unfolded gradient descent (DUGD) whose trainable parameters are step sizes. We propose a plausible interpretation of the learned step-size parameters in DUGD by introducing the principle of Chebyshev steps derived from Chebyshev polynomials. The use of Chebyshev steps in gradient descent (GD) enables us to bound the spectral radius of a matrix governing the convergence speed of GD, leading to a tight upper bound on the convergence rate. Numerical results show that Chebyshev steps numerically explain the learned step-size parameters in DUGD well.

In this paper, we introduce a path embedding problem inspired by the well-known hydrophobic-polar (HP) model of protein folding. A graph is said bicolored if each vertex is assigned a label in the set {red, blue}. For a given bicolored path P and a given bicolored graph G, our problem asks whether we can embed P into G in such a way as to match the colors of the vertices. In our model, G represents a protein's “blueprint,” and P is an amino acid sequence that has to be folded to form (part of) G. We first show that the bicolored path embedding problem is NP-complete even if G is a rectangular grid (a typical scenario in protein folding models) and P and G have the same number of vertices. By contrast, we prove that the problem becomes tractable if the height of the rectangular grid G is constant, even if the length of P is independent of G. Our proof is constructive: we give a polynomial-time algorithm that computes an embedding (or reports that no embedding exists), which implies that the problem is in XP when parameterized according to the height of G. Additionally, we show that the problem of embedding P into a rectangular grid G in such a way as to maximize the number of red-red contacts is NP-hard. (This problem is directly inspired by the HP model of protein folding; it was previously known to be NP-hard if G is not given, and P can be embedded in any way on a grid.) Finally, we show that, given a bicolored graph G, the problem of constructing a path P that embeds in G maximizing red-red contacts is Poly-APX-hard.

Folding an m×n square grid pattern along the edges of a grid is called map folding. We consider a decision problem in terms of whether a partial overlapping order of the squares aligning on the boundary of an m×n map is valid in a particular fold model called simple fold. This is a variation of the decision problem of valid total orders of the map in a simple fold model. We provide a linear-time algorithm to solve this problem, by defining an equivalence relation and computing the folding sequence sequentially, either uniquely or representatively.

The modern radar signals are in a wide frequency space. The receiving bandwidth of the radar reconnaissance receiver should be wide enough to intercept the modern radar signals. The Nyquist folding receiver (NYFR) is a novel wideband receiving architecture and it has a high intercept probability. Chirp signals are widely used in modern radar system. Because of the wideband receiving ability, the NYFR will receive the concurrent multiple chirp signals. In this letter, we propose a novel parameter estimation algorithm for the multiple chirp signals intercepted by single channel NYFR. Compared with the composite NYFR, the proposed method can save receiving resources. In addition, the proposed approach can estimate the parameters of the chirp signals even the NYFR outputs are under frequency aliasing circumstance. Simulation results show the efficacy of the proposed method.

A novel Nyquist Folding Receiver (NYFR) based passive localization algorithm with Sparse Bayesian Learning (SBL) is proposed to estimate the position of a spaceborne Synthetic Aperture Radar (SAR).Taking the geometry and kinematics of a satellite into consideration, this paper presents a surveillance geometry model, which formulates the localization problem into a sparse vector recovery problem. A NYFR technology is utilized to intercept the SAR signal. Then, a convergence algorithm with SBL is introduced to recover the sparse vector. Furthermore, simulation results demonstrate the availability and performance of our algorithm.

Blind nonlinear compensation for RF receivers is an important research topic in 5G mobile communication, in which higher level modulation schemes are employed more often to achieve high capacity and ultra-broadband services. Since nonlinear compensation circuits must handle intermodulation bandwidths that are more than three times the signal bandwidth, reducing the sampling frequency is essential for saving power consumption. This paper proposes a novel blind nonlinear compensation technique that employs sub-Nyquist sampling analog-to-digital conversion. Although outband distortion spectrum is folded in the proposed sub-Nyquist sampling technique, determination of compensator coefficients is still possible by using the distortion power. Proposed technique achieves almost same compensation performance in EVM as the conventional compensation scheme, while reducing sampling speed of analog to digital convertor (ADC) to less than half the normal sampling frequency. The proposed technique can be applied in concurrent dual-band communication systems and adapt to flat Rayleigh fading environments.

Nyquist folding receiver (NYFR) is a novel reconnaissance receiving architecture and it can realize wideband receiving with small amount of equipment. As a tradeoff of non-cooperative wideband receiving, the NYFR output will add an unknown key parameter that is called Nyquist zone (NZ) index. In this letter, we concentrate on the NZ index estimation of the NYFR output. Focusing on the basic pulse radar signals, the constant frequency signal, the binary phase coded signal and the linear frequency modulation signal are considered. The matching component function is proposed to estimate the NZ indexes of the NYFR outputs without the prior information of the signal modulation type. In addition, the relations between the matching component function and the parameters of the NYFR are discussed. Simulation results demonstrate the efficacy of the proposed method.

Syndrome key equation solution is one of the important processes in the decoding of Reed-Solomon codes. This paper proposes a low power key equation solver (KES) architecture where the power consumption is reduced by decreasing the required number of multiplications without degrading the decoding throughput and latency. The proposed method employs smaller number of multipliers than a conventional low power KES architecture. The critical path in the proposed KES circuit is minimized so that the operation at a high clock frequency is possible. A low power folded KES architecture is also proposed to further reduce the hardware complexity by executing folded operations in a pipelined manner with a slight increase in decoding latency.

We prove NP-completeness of deciding whether a given loop of colored right isosceles triangles, hinged together at edges, can be folded into a specified rectangular three-color pattern. By contrast, the same problem becomes polynomially solvable with one color or when the target shape is a tree-shaped polyomino.

The large Doppler offset that exists in high dynamic environments poses a serious impediment to the acquisition of direct sequence spread spectrum (DSSS) signals. To ensure acceptable detection probabilities, the frequency space has to be finely divided, which leads to complicated acquisition structures and excessively long acquisition time at low SNR. A local frequency folding (LFF) method designed for combined application with established techniques dedicated to PN-code synchronization is proposed in this paper. Through modulating local PN-code block with a fixed waveform obtained by folding all frequency cells together, we eliminate the need for frequency search and ease the workload of acquisition. We also analyze the performance of LFF and find that the detection performance degradation from folding can be compensated by FFT-based coherent integration. The study is complemented with numerical simulations showing that the proposed method has advantages over unfolding methods with respect to detection probability and mean acquisition time, and the advantage becomes obvious but limited if the folded number gets larger.

This paper presents a folded surface detection and tracking method for augmented maps. First, we model a folded surface as two connected planes. Therefore, in order to detect a folded surface, the plane detection method is iteratively applied to the 2D correspondences between an input image and a reference plane. In order to compute the exact folding line from the detected planes for visualization purpose, the intersection line of the planes is computed from their positional relationship. After the detection is done, each plane is individually tracked by the frame-by-frame descriptor update method. We overlay virtual geographic data on each detected plane. As scenario of use, some interactions on the folded surface are introduced. Experimental results show the accuracy and performance of folded surface detection for evaluating the effectiveness of our approach.

This paper presents a high-speed SHA-1 implementation. Unlike the conventional unfolding transformation, the proposed unfolding transformation technique makes the combined hash operation blocks to have almost the same delay overhead regardless of the unfolding factor. It can achieve high throughput of SHA-1 implementation by avoiding the performance degradation caused by the first hash computation. We demonstrate the proposed SHA-1 architecture on a FPGA chip. From the experimental results, the SHA-1 architecture with unfolding factor 5 shows 1.17 Gbps. The proposed SHA-1 architecture can achieve about 31% performance improvements compared to its counterparts. Thus, the proposed SHA-1 can be applicable for the security of the high-speed but compact mobile appliances.

In this paper, a 65 nm 1.2 V 7-bit 1GSPS folding-interpolation A/D converter with a digitally self-calibrated vector generator is proposed. The folding rate is 2 and the interpolation rate is 8. A self-calibrated vector generation circuit with a feedback loop and a recursive digital code inspection is described. The circuit reduces the variation of the offset voltage caused by process mismatches, parasitic resistors, and parasitic capacitances. The chip has been fabricated with a 65 nm 1-poly 6-metal CMOS technology. The effective chip area is 0.87 mm2 and the power consumption is about 110 mW with a 1.2 V power supply. The measured SNDR is about 39.1 dB when the input frequency is 250 MHz at a 1 GHz sampling frequency. The measured SNDR is drastically improved in comparison with the same ADC without any calibration.

A 7 bit 1.0 Gsps Cascaded Folding ADC is presented. This ADC employs cascaded folding architecture with 3-degree folders. A new reset technique and layout shuffling enable the ADC to operate at high-speed with low power consumption. Implemented in a 90 nm CMOS process technology the ADC consumes 230 mW with 1.2 V and 2.5 V supplies and has a SNR of 38 dB.