Sparse Multiband Signal Research Articles

Wideband spectrum compressive sensing utilizing photonic multi-coset sampling with dual low-rate optical pulses

A wideband spectrum compressive sensing approach for sparse multiband signals utilizing photonic multi-coset sampling (MCS) is presented. The method employs dual low-rate optical pulses, initially modulated by separate pseudo-random binary sequences (PRBSs), which are then multiplexed to achieve the desired multi-coset pattern. It results in a substantial reduction of the rate requirements for both the sampling optical pulses and PRBSs, leading to a significant enhancement of system bandwidth. In simulations, an instantaneous system bandwidth of 21 GHz is achieved at a low mean sampling rate of 4.8 GS/s, employing two optical pulses with rates of 8.4 GHz and 6 GHz, respectively. The spectra of a mixed signal with six passbands are accurately identified, illustrating the capability of the scheme to recognize the spectra of various types of multiband signals. Furthermore, a comparative analysis of the performance between our proposed scheme and traditional MCS techniques is conducted.

Multicoset-based deterministic measurement matrices for compressed sensing of sparse multiband signals

Signal acquisition is a basic function in signal processing systems. In the context of digital communications, the analog-to-digital (ADC) converters have to be carefully designed as part of the radio frequency front end, to reduce power consumption while avoiding aliasing. When operating with sparse multiband signals, compressive sampling becomes an attractive alternative to enable low sampling rates at the front end. Starting from previous results on multicoset sampling and compressed sensing, we analyze sampling strategies for sparse multiband signals based on the operation of a set of ADC converters working in parallel. Different architectures are considered, with equal and different sampling rates in the ADCs, and their associated deterministic measurement matrices and sampling patterns are studied. The matrices involved in the corresponding reconstruction equations for the different architectures are also analyzed in terms of their mutual coherence. As a result, we are able to design different universal multicoset sampling patterns. We obtain the parameters for the different sampling architectures that guarantee reconstruction of the multiband sparse signal, even at high compression rates. Simulation results show the effectiveness of the theoretical designs for sparse reconstruction of this type of signals.

Rapid reconstruction of sparse multiband signals based on MMV-SWACGP algorithm

In this paper, an MMV-SWACGP algorithm is proposed, in order to solve the problem of pseudo-inverse computation in the iterative process of OMPMMV algorithm for multi-band signal reconstruction by compressed sensing. This algorithm reduces the complexity and computation of OMPMMV reconstruction algorithm. It is of great significance to the fast reconstruction of sparse multiband signals. Theoretical analysis and simulation results show that the proposed algorithm has faster computation speed and better noise stability.

Time-Frequency Sparse Reconstruction of Non-Uniform Sampling for Non-Stationary Signal

We address the problem of the reconstruction of time-frequency characteristics of sparse multi-band signals by using the discrete multi-coset sampling (DMCS) model. In this article, the signal is characterized by complicated time-variable components. According to the feature of the short-time Fourier transform (STFT) analysis method, we obtain the rewritten matrix form of the discrete STFT. Then, an analysis method of the multi-coset sliding window (MCSW) is proposed, and the discrete multi-coset sampling sequence is locally windowed. The sparse signal reconstruction algorithm is used to obtain the optimal time-frequency reconstruction value of the original signal. Numerical simulations show the feasibility of this method. We simulate the effects of measurement noise, sampling rate, and time-frequency analysis parameters on the reconstruction accuracy. Our method can carry out time-frequency reconstruction for undersampled signals obtained from multi-coset sampling to ensure the time-varying feature of the original signals, which can well highlight the characteristics of signals. The method is of great significance to the research and development of the sub-Nyquist sampling technique.

Design of Sparse Multiband Signal for Precise Positioning With Joint Low-Complexity Time Delay and Carrier Phase Estimation

This paper presents a methodology to design a sparse multiband ranging signal with a large virtual bandwidth, from which time delay and carrier phase are estimated by a low complexity multivariate maximum likelihood (ML) method. In the estimation model for a multipath channel, not all reflected paths are considered, and time delay and carrier phase are estimated in a step-wise manner to further reduce the computational load. By introducing a measure of dependence and a measure of bias for a multipath reflection, we analyse the bias, precision and accuracy of time delay and carrier phase estimation. Since these two indicators are determined by the signal spectrum pattern, they are used to formulate an optimization for signal design. By solving the optimization problem, only a few bands from the available signal spectrum are selected for ranging. Consequently, the designed signal only occupies a small amount of signal spectrum but has a large virtual bandwidth and can thereby still offer a high ranging precision with only a small bias, based on the low-complexity simplified ML method. Numerical and laboratory experiments are carried out to evaluate the ranging performance of the proposed estimation method based on sparsely selected signal bands. Relative positioning, in which we only measure a change in position, based on either the time delay estimates or the carrier phase estimates, is presented as a proof-of-concept for precise positioning. The results show that positioning based on only 7 out of 16 signal bands, sparsely placed in the available spectrum, achieves a decimeter level accuracy when using time delay estimates, and a millimeter level accuracy when using carrier phase estimates. Compared with the case of using all available bands, and without largely decreasing the positioning performance, the computational complexity when using the sparse multiband signal can be reduced by about 80%.

A Joint Optimization Algorithm Using Adaptive Minimum Coset Number Based Discrete Multi-Coset Sampling

We address the problem of sparse multi-band signal reconstruction in the case of unknown band position through the discrete multi-coset sampling (DMCS). In this article, the signal has complex frequency components, and the minimum coset number is determined on the assumption that there is only one frequency component with same characteristics. According to the frequency characteristics, we analyze the influence of the parameterized compressed matrix on the two reconstruction algorithms, and get that a single algorithm does not have universal adaptability to different frequency components. In order to solve this problem, under the discrete multi-coset sampling model, a joint optimization algorithm with discriminant factor (DF-JOA) is proposed to identify the different characteristics and automatically select an appropriate algorithm for signal reconstruction, numerical simulation experiments show the effectiveness of the algorithm. We also simulate the reconstruction success ratio of amplitude and the total coset number under different compressed matrices, determine the influence law, and confirm the improvement of signal reconstruction probability by joint optimization algorithm. Our method ensures the spectrum reconstruction of the multi-band signal. This article can guide how to better select the coset parameters under the condition that the channels of the discrete multi-coset sampling system are limited but the minimum coset number can be guaranteed. It will have a great significance to the sub-Nyquist sampling technique.

Successive‐phase correction calibration method for modulated wideband converter system

The modulated wideband converter (MWC) is a sub-Nyquist sampling system recently proposed for sampling sparse multi-band signals. However, due to non-ideal analogue components, transfer-matrix calibration is required for the successful reconstruction. In practice, it is difficult to control the phases of the consecutive sinusoidal inputs precisely which are used to calibrate the transfer-matrix. Here, the authors propose a method of transfer-matrix calibration for the MWC with digital expanded channels when the phases of the sinusoidal inputs are unknown. As the oblique elements of the MWC transfer-matrix are equal, the authors can estimate the unknown phases first. The authors then obtain the actual transfer-matrix by phase correction. Finally, the validity of this method is verified by simulation and hardware experiment. The system performance is measured by computing the signal-to-noise ratio and the mean-square error between the original and reconstructed signals.

Multiband signal acquisition using improved modulated wideband converter

In this study, the authors stress the problem of sampling and recovering sparse wideband signals. A new methodology for sparse multiband signal acquisition using sinusoidal frequency modulation (SMF) multiplier-based modulated wideband converter (MWC) is presented. The harmonic property of the SMF signals enables sparse multiband signal to be precisely recovered from the sub-Nyquist measurements without any high-speed devices. The proposed architecture offers very close recovery accuracy to the existing pseudorandom binary sequences (PRBS)-based MWC in the absence of the prior knowledge of sparse wideband signals, while it provides more accurate recovery performance than the PRBS-MWC in the presence of prior information concerning sparsity. Besides, the proposed architecture is easier for hardware implementation than the PRBS-MWC. The experimental results demonstrate the effectiveness of the proposed scheme.

Sparse multiband signal spectrum sensing with asynchronous coprime sampling

Cognitive radio requires spectrum sensing over a broad frequency band and leads to a high sampling rate. In this paper, we propose an asynchronous coprime sampling technique for capturing and reconstructing of sparse multiband signals that occupy a small part of a given broad frequency band. The band locations of signal are not known a priori. In this proposed approach, we use a sub-Nyquist sampling rate by exploiting a low-dimensional representation of the original high-dimensional signal. A common input sparse multiband signal is digitized using a pair of uniform samplers, which are (not necessarily synchronously) clocked at coprime sampling rates. The captured samples are then re-sequenced and the multi-coset signal processing algorithm is employed. We derive the system model in the frequency domain, where the phase mismatch is compensated. Compared to the conventional multi-coset sampling, the proposed approach needs fewer samplers and does not require synchronous clock phase. Simulation results are provided to demonstrate the feasibility and effectiveness of the proposed asynchronous coprime sampling for sparse multiband signal.

Sparse Multiband Signal Acquisition Receiver With Co-Prime Sampling

Cognitive radio (CR) requires spectrum sensing over a broad frequency band. One of the crucial tasks in CR is to sample wideband signal at high sampling rate. In this paper, we propose an acquisition receiver with a co-prime sampling technique for wideband sparse signals, which occupy a small part of band range. In this proposed acquisition receiver, we use two low speed analog-to-digital converters (ADCs) to capture a common sparse multiband signal, whose band locations are unknown. The two ADCs are synchronously clocked at co-prime sampling rates. The obtained samples are re-sequenced into a group of uniform sequences with low rate. We derive the mathematical model for the receiver in the frequency domain and present its signal reconstruction algorithm. Compared with the existing sub-Nyquist sampling techniques, such as multi-coset sampling and modulated wideband converter, the proposed approach has a simple system architecture and can be implemented with only two samplers. Experimental results are reported to demonstrate the feasibility and advantage of the proposed model. For sparse multiband signal with unknown spectral support, the proposed system requires a sampling rate much lower than Nyquist rate while producing satisfactory reconstruction.

Orthogonal circulant structure and chaotic phase modulation based analog to information conversion

Modulated wideband converter (MWC) is used to implement analog to information conversion (AIC) to realize sub-Nyquist sampling of sparse multiband analog signal. In this paper, we combine orthogonal circulant matrix with chaos to develop an orthogonal circulant structure and chaotic phase modulation based modulated wideband converter (OCSCPM-MWC). Firstly, random waveforms of different channels in the system correspond to the row vectors of measurement matrix. We use the frequency-domain approach to construct orthogonal circulant matrix. The waveforms of different channels can be generated by various cyclic shifts of the same original waveform and orthogonal to each other. This can greatly reduce the degrees of freedom of the random waveforms, and a superior recovery performance can be obtained. Secondly, we construct chaotic phases of generating elements of orthogonal circulant matrix. The input signal is modulated according to the power spectrum of chaos. We derive the theoretical condition for the orthogonal circulant measurement matrix to satisfy expected restricted isometry property (ExRIP). In addition, we analyze the impact of measurement noise and signal noise on the OCSCPM-MWC system, respectively. Computer simulations are carried out under different situations and they confirm the effectiveness of the proposed approach.

Random Triggering-Based Sub-Nyquist Sampling System for Sparse Multiband Signal

We propose a novel random triggering-based modulated wideband compressive sampling (RT-MWCS) method to facilitate efficient realization of sub-Nyquist rate compressive sampling systems for sparse wideband signals. Under the assumption that the signal is repetitively (not necessarily periodically) triggered, RT-MWCS uses random modulation to obtain measurements of the signal at randomly chosen positions. It uses multiple measurement vector method to estimate the nonzero supports of the signal in the frequency domain. Then, the signal spectrum is solved using least square estimation. The distinct ability of estimating sparse multiband signal is facilitated with the use of level triggering and time-to-digital converter devices previously used in random equivalent sampling scheme. Compared to the existing compressive sampling (CS) techniques, such as modulated wideband converter (MWC), RT-MWCS is with simple system architecture and can be implemented with one channel at the cost of more sampling time. Experimental results indicate that, for sparse multiband signal with unknown spectral support, RT-MWCS requires a sampling rate much lower than Nyquist rate, while giving great quality of signal reconstruction.

Sub-sampling Techniques for Sampling a Sparse Wideband Signal in Wireless Communications

Background/Objectives: The popularity of Wireless technologies, for applications that urges high bandwidth, increases the demand of Radio frequency (RF) spectrum which leads to scarsity in the spectrum resources. Hence it is required to sense the spectrum of a wideband signal at low sampling rates compared to the Nyquist rate. Methods/Statistical analysis: If the wide band signal is Sparse in frequency domain, then it is used to get over the problem of high sampling rates under the compressive sensing framework. Two different efficient schemes called Modulated Wideband Converter (MWC) and Asynchronous Multi-rate (AMR) are proposed here for wideband spectrum sensing at sub-Nyquist rates. The key features of these methods are also compared with the traditional sub-Nyquist sampling approach called Multi-Coset (MC). Findings: The MC sampling is capable of sampling at different time offsets, but unable to poses channel synchronisation. In MWC sampling, the sparse multiband signal is multiplied by a periodic waveform to shift the spectral components of the band of interest to the origin, then filtered and sampled at low rate. This also makes the computational time to reduce greatly. In AMR sampling, the sparse signal is under sampled at different sampling frequencies to produce sample sets with different aliasing spectra. Later these spectra are compared on a common frequency grid to detect the active bands. This mechanism takes fewer samples there by reduces thee computational cost. The simulation results exhibit these advantages over the traditional sampling techniques for wide band spectrum sensing. Application/Improvements: The trade-off between the selection of MWC for less computational time and MR for low complexity in design makes these sub Nyquist schemes suitable for wide band spectrum sensing in cognitive radio like applications.

Minimum Rate Sampling and Spectrum-Blind Reconstruction in Random Equivalent Sampling

The random equivalent sampling (RES) is a well-known sampling technique that can be used to capture a high-speed repetitive waveform with low sampling rate. In this paper, the feasibility of spectrum-blind multiband signal reconstruction for data sampled from RES is investigated. We propose a RES sampling pattern and its corresponding mathematical model that guarantees well-conditioned reconstruction of multiband signal with unknown spectral support. We give the minimum number of RES acquisitions that hold overwhelming probability to successfully reconstruct original signal. We demonstrate that for signal with specific spectral occupation, the minimum number of RES acquisitions and the minimum sampling rate could be approached. The signal reconstruction is studied in the framework of compressive sampling theory. The eigen-decomposition and minimum description length criteria are adopted to adaptively estimate the dimension of signal, and the number of unknowns of reconstruction problem is reduced. Experimental results are reported to indicate that, for a spectrum-blind sparse multiband signal, the proposed reconstruction algorithm for RES is feasible and robust.

Efficient Recovery of Sub-Nyquist Sampled Sparse Multi-Band Signals Using Reconfigurable Multi-Channel Analysis and Modulated Synthesis Filter Banks

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. 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 feasitble 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.

Multiband signal reconstruction for random equivalent sampling.

The random equivalent sampling (RES) is a sampling approach that can be applied to capture high speed repetitive signals with a sampling rate that is much lower than the Nyquist rate. However, the uneven random distribution of the time interval between the excitation pulse and the signal degrades the signal reconstruction performance. For sparse multiband signal sampling, the compressed sensing (CS) based signal reconstruction algorithm can tease out the band supports with overwhelming probability and reduce the impact of uneven random distribution in RES. In this paper, the mathematical model of RES behavior is constructed in the frequency domain. Based on the constructed mathematical model, the band supports of signal can be determined. Experimental results demonstrate that, for a signal with unknown sparse multiband, the proposed CS-based signal reconstruction algorithm is feasible, and the CS reconstruction algorithm outperforms the traditional RES signal reconstruction method.

Channel gain mismatch and time delay calibration for modulated wideband converter‐based compressive sampling

The modulated wideband converter (MWC) is a recently proposed compressive sampling system for acquiring sparse multiband signals. For the MWC with digital sub-channel separation block, channel gain mismatch and time delay will lead to a potential performance loss in reconstruction. These gains and delays are represented as an unknown multiplicative diagonal matrix here. The authors formulate the estimation problem as a convex optimisation problem, which can be efficiently solved by utilising least squares estimation. Then the calibrated system model is obtained and the estimates of the gains and time delays of physical channels from the estimate of this matrix are calculated. Numerical simulations verify the effectiveness of the proposed approach.

UWB signal receiver with sub-Nyquist rate sampling based on compressed sensing

Purpose – The purpose of this paper is to present a compressed sensing (CS)-based sampling system for ultra-wide-band (UWB) signal. By exploiting the sparsity of signal, this new sampling system can sub-Nyquist sample a multiband UWB signal, whose unknown frequency support occupies only a small portion of a wide spectrum. Design/methodology/approach – A random Rademacher sequence is used to sense the signal in the frequency domain, and a matrix constructed by Hadamard basis is used to compress the signal. The probability of reconstruction is proved mathematically, and the reconstruction matrix is developed in the frequency domain. Findings – Simulation results indicate that, with an ultra-low sampling rate, the proposed system can capture and reconstruct sparse multiband UWB signals with high probability. For sparse multiband UWB signals, the proposed system has potential to break through the Shannon theorem. Originality/value – Different from the traditional sub-Nyquist techniques, the proposed sampling system not only breaks through the limitation of Shannon theorem but also avoids the barrier of input bandwidth of analog-to-digital converters (ADCs).

Complexity-reduced digital predistortion for subcarrier multiplexed radio over fiber systems transmitting sparse multi-band RF signals

A novel multi-band digital predistortion (DPD) technique is proposed to linearize the subcarrier multiplexed radio-over-fiber (SCM-RoF) system transmitting sparse multi-band RF signal with large blank spectra between the constituent RF bands. DPD performs on the baseband signal of each individual RF band before up-conversion and RF combination. By disregarding the blank spectra, the processing bandwidth of the proposed DPD technique is greatly reduced, which is only determined by the baseband signal bandwidth of each individual RF band, rather than the entire bandwidth of the combined multi-band RF signal. Experimental demonstration is performed in a directly modulated SCM-RoF system transmitting two 64QAM modulated OFDM signals on 2.4GHz band and 3.6GHz band. Results show that the adjacent channel power (ACP) is suppressed by 15dB leading to significant improvement of the EVM performances of the signals on both of the two bands.