Analysis and design of multirate synchronous sampling schemes for sparse multiband signals

We consider the problem of developing efficient sampling schemes for multiband sparse signals. Previous results on multicoset sampling implementations that lead to universal sampling patterns (which guarantee perfect reconstruction), are based on a set of appropriate interleaved analog to digital converters, all of them operating at the same sampling frequency. In this paper we propose an alternative multirate synchronous implementation of multicoset codes, that is, all the analog to digital converters in the sampling scheme operate at different sampling frequencies, without need of introducing any delay. The interleaving is achieved through the usage of different rates, whose sum is significantly lower than the Nyquist rate of the multiband signal. To obtain universal patterns the sampling matrix is formulated and analyzed. Appropriate choices of the parameters, that is the block length and the sampling rates, are also proposed

Alias-free Discrete-time FIR System Realisation Using Hybrid Stratified Sampling

This paper proposes a method for system realisation, where the realised system is described by a continuous-time, finite-duration impulse response. The proposed discrete-time implementation deploys Digital Alias-free Signal Processing. It means that despite the use of digital signal processing, the produced results do not suffer from aliasing. However, owing to the use of random sampling, the approach relies on constructing a suitable estimator of the system output. This paper shows that the proposed estimator is unbiased. It is also consistent, i.e. its variance goes to zero when the density of signal samples increasing. It is proven that under moderately restrictive assumptions, the estimator goes to zero proportionally to the fifth power of the average distance between the samples

Regularized sampling of multiband signals

This paper presents a regularized sampling method for multiband signals, that makes it possible to approach the Landau limit, while keeping the sensitivity to noise at a low level. The method is based on band-limited windowing, followed by trigonometric approximation in consecutive time intervals. The key point is that the trigonometric approximation "inherits" the multiband property, that is, its coefficients are formed by bursts of non-zero elements corresponding to the multiband components. It is shown that this method can be well combined with the recently proposed synchronous multi-rate sampling (SMRS) scheme, given that the resulting linear system is sparse and formed by ones and zeroes. The proposed method allows one to trade sampling efficiency for noise sensitivity, and is specially well suited for bounded signals with unbounded energy like those in communications, navigation, audio systems, etc. Besides, it is also applicable to finite energy signals and periodic band-limited signals (trigonometric polynomials). The paper includes a subspace method for blindly estimating the support of the multiband signal as well as its components, and the results are validated through several numerical examples.Comment: The title and introduction have changed. Submitted to the IEEE Transactions on Signal Processin

From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals

Conventional sub-Nyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum. Our primary design goals are efficient hardware implementation and low computational load on the supporting digital processing. We propose a system, named the modulated wideband converter, which first multiplies the analog signal by a bank of periodic waveforms. The product is then lowpass filtered and sampled uniformly at a low rate, which is orders of magnitude smaller than Nyquist. Perfect recovery from the proposed samples is achieved under certain necessary and sufficient conditions. We also develop a digital architecture, which allows either reconstruction of the analog input, or processing of any band of interest at a low rate, that is, without interpolating to the high Nyquist rate. Numerical simulations demonstrate many engineering aspects: robustness to noise and mismodeling, potential hardware simplifications, realtime performance for signals with time-varying support and stability to quantization effects. We compare our system with two previous approaches: periodic nonuniform sampling, which is bandwidth limited by existing hardware devices, and the random demodulator, which is restricted to discrete multitone signals and has a high computational load. In the broader context of Nyquist sampling, our scheme has the potential to break through the bandwidth barrier of state-of-the-art analog conversion technologies such as interleaved converters.Comment: 17 pages, 12 figures, to appear in IEEE Journal of Selected Topics in Signal Processing, the special issue on Compressed Sensin

Multirate Synchronous Sampling of Sparse Multiband Signals

Recent advances in optical systems make them ideal for undersampling multiband signals that have high bandwidths. In this paper we propose a new scheme for reconstructing multiband sparse signals using a small number of sampling channels. The scheme, which we call synchronous multirate sampling (SMRS), entails gathering samples synchronously at few different rates whose sum is significantly lower than the Nyquist sampling rate. The signals are reconstructed by solving a system of linear equations. We have demonstrated an accurate and robust reconstruction of signals using a small number of sampling channels that operate at relatively high rates. Sampling at higher rates increases the signal to noise ratio in samples. The SMRS scheme enables a significant reduction in the number of channels required when the sampling rate increases. We have demonstrated, using only three sampling channels, an accurate sampling and reconstruction of 4 real signals (8 bands). The matrices that are used to reconstruct the signals in the SMRS scheme also have low condition numbers. This indicates that the SMRS scheme is robust to noise in signals. The success of the SMRS scheme relies on the assumption that the sampled signals are sparse. As a result most of the sampled spectrum may be unaliased in at least one of the sampling channels. This is in contrast to multicoset sampling schemes in which an alias in one channel is equivalent to an alias in all channels. We have demonstrated that the SMRS scheme obtains similar performance using 3 sampling channels and a total sampling rate 8 times the Landau rate to an implementation of a multicoset sampling scheme that uses 6 sampling channels with a total sampling rate of 13 times the Landau rate.

Collaborative spectrum sensing in cognitive radio networks

The radio frequency (RF) spectrum is a scarce natural resource, currently regulated by government agencies. With the explosive emergence of wireless applications, the demands for the RF spectrum are constantly increasing. On the other hand, it has been reported that localised temporal and geographic spectrum utilisation efficiency is extremely low. Cognitive radio is an innovative technology designed to improve spectrum utilisation by exploiting those spectrum opportunities. This ability is dependent upon spectrum sensing, which is one of most critical components in a cognitive radio system. A significant challenge is to sense the whole RF spectrum at a particular physical location in a short observation time. Otherwise, performance degrades with longer observation times since the lagging response to spectrum holes implies low spectrum utilisation efficiency. Hence, developing an efficient wideband spectrum sensing technique is prime important. In this thesis, a multirate asynchronous sub-Nyquist sampling (MASS) system that employs multiple low-rate analog-to-digital converters (ADCs) is developed that implements wideband spectrum sensing. The key features of the MASS system are, 1) low implementation complexity, 2) energy-efficiency for sharing spectrum sensing data, and 3) robustness against the lack of time synchronisation. The conditions under which recovery of the full spectrum is unique are presented using compressive sensing (CS) analysis. The MASS system is applied to both centralised and distributed cognitive radio networks. When the spectra of the cognitive radio nodes have a common spectral support, using one low-rate ADC in each cognitive radio node can successfully recover the full spectrum. This is obtained by applying a hybrid matching pursuit (HMP) algorithm - a synthesis of distributed compressive sensing simultaneous orthogonal matching pursuit (DCS-SOMP) and compressive sampling matching pursuit (CoSaMP). Moreover, a multirate spectrum detection (MSD) system is introduced to detect the primary users from a small number of measurements without ever reconstructing the full spectrum. To achieve a better detection performance, a data fusion strategy is developed for combining sensing data from all cognitive radio nodes. Theoretical bounds on detection performance are derived for distributed cognitive radio nodes suffering from additive white Gaussian noise (AWGN), Rayleigh fading, and log-normal fading channels. In conclusion, MASS and MSD both have a low implementation complexity, high energy efficiency, good data compression capability, and are applicable to distributed cognitive radio networks