Nyquist Rate Signal Research Articles

WINDOW: wideband demodulator for optical waveforms.

Optical communication systems, which operate at very high rates, are often limited by the sampling rate bottleneck. The optical wideband regime may exceed analog to digital converters (ADCs) front-end bandwidth. Multi-channel sampling approaches, such as interleaved ADCs, also known as multicoset sampling in some contexts, have been proposed to sample the wideband signal using several channels. Each channel samples below the Nyquist rate such that the overall sampling rate is preserved. However, this scheme suffers from two practical limitations that make its implementation difficult. First, the inherent anti-aliasing filter of the samplers distorts the wideband signal. Second, it requires accurate time shifts on the order of the signal's Nyquist rate, which are challenging to maintain. In this work, we propose an alternative multi-channel sampling scheme, the wideband demodulator for optical waveforms (WINDOW), based on analog RF demodulation, where each channel aliases the spectrum using a periodic mixing function before integration and sampling. We show that intentionally using the inherent ADC filter to perform integration increases the signal to noise ratio (SNR). We demonstrate both theoretically and through numerical experiments that our system outperforms interleaved sampling in terms of signal recovery and symbol estimation in the presence of both thermal and quantization noise but is slightly less robust to timing jitter. The main contribution of this work is the application of RF demodulation concepts proposed in the context of sub-Nyquist sampling, e.g. random demodulator and modulated wideband converter, to optical communication signals in the Nyquist regime. We develop a sampling scheme that presents an alternative for optical links where thermal noise in the receiver is the bottleneck.

Wideband delay and Direction of Arrival Estimation using sub-Nyquist sampling

Estimating the Direction of Arrival (DOA) of the signals received by a sensor array has been at the core of the array signal processing community for decades. With the advancement of the technology, the limits on the data and data transfer are increasing day by day. Such demands of the increasing bandwidths put an immense burden on the Analog to Digital Converters (ADCs). On the other hand, in the literature most of the wideband DOA estimation algorithms depend on the narrowband signal model where the signal is first decomposed into multiple signals with narrow frequency bins, the DOA is estimated for all of them and the outputs are combined together (coherent or non-coherent) to get the final result. This process is highly computational and highly susceptible to any outliers. Compressed Sensing (CS) over the last few years has shown a great promise in overcoming these problems while preserving the structure of the signal provided it is sparse in some domain. In this paper, we propose to estimate the DOA of wideband signals using CS based reconstruction recognizing that the autocorrelation of such signals is sparse in nature. The peaks in the correlation plot represent the time delays of the corresponding signals which is directly related to their DOAs. We identify and show that the relation between the cross-correlations of the sub-Nyquist signal and the Nyquist rate signal is a block sparse CS problem. By using a block sparse CS reconstruction algorithm we are able to estimate the peak locations in the Nyquist correlation vector thereby estimating the DOAs of the wideband signals.

A New Sparse Signal-Matched Measurement Matrix for Compressive Sensing in UWB Communication

Ultra wideband (UWB) technology is suitable for high data rate short range wireless communication, localization, and imaging techniques. However, UWB systems require high sampling rate and precise synchronization. In order to reduce the sampling rate, have precise synchronization, and for low power requirement, UWB systems are implemented using compressive or sub-Nyquist rate measured samples by exploiting the sparsity of the UWB signal. Compressive sensing (CS)-based UWB systems are being designed in two ways: 1) signal demodulation or detection is performed in the CS domain without full signal recovery at the front-end. Thus, demodulation or detection works on compressive measurements. However, system performance deteriorates in the CS domain as compared with full Nyquist rate sampling and 2) after, Nyquist rate signal is recovered using efficient algorithms at the front-end, the signal demodulation or detection is performed using the conventional receiver. Thus, one requires an efficient CS/sampling of signal measurement at the front-end for better system performance for both the cases stated earlier. In this paper, we propose a deterministic (partial) UWB waveform-matched measurement matrix. The proposed measurement matrix has a circulant structure and is sparse in nature. The proposed matrix is easy to implement in hardware and is operationally time efficient as needed in a practical system. The bit error rate performance of the corresponding UWB system and the operational time complexity with the proposed measurement matrix are better as compared with the existing measurement matrices in the CS domain for both the above receiver designs. The efficacy of the proposed measurement matrix is verified through extensive simulations in both the additive white Gaussian noise and multipath communication environments. In addition, we have also compared other desirable properties of the proposed measurement matrix with the existing measurement matrices.

Compressed Measurements Based Spectrum Sensing for Wideband Cognitive Radio Systems

Spectrum sensing is the most important component in the cognitive radio (CR) technology. Spectrum sensing has considerable technical challenges, especially in wideband systems where higher sampling rates are required which increases the complexity and the power consumption of the hardware circuits. Compressive sensing (CS) is successfully deployed to solve this problem. Although CS solves the higher sampling rate problem, it does not reduce complexity to a large extent. Spectrum sensing via CS technique is performed in three steps: sensing compressed measurements, reconstructing the Nyquist rate signal, and performing spectrum sensing on the reconstructed signal. Compressed detectors perform spectrum sensing from the compressed measurements skipping the reconstruction step which is the most complex step in CS. In this paper, we propose a novel compressed detector using energy detection technique on compressed measurements sensed by the discrete cosine transform (DCT) matrix. The proposed algorithm not only reduces the computational complexity but also provides a better performance than the traditional energy detector and the traditional compressed detector in terms of the receiver operating characteristics. We also derive closed form expressions for the false alarm and detection probabilities. Numerical results show that the analytical expressions coincide with the exact probabilities obtained from simulations.

COMPRESSED MEASUREMENTS BASED CYCLOSTATIONARY DETECTOR FOR WIDEBAND COGNITIVE RADIOS

Cyclostationary feature detection is one of the most powerful spectrum sensing techniquesused for cognitive radio (CR) systems. This is because of its robustness against noiseuncertainties. However, this technique needs high sampling rates, which is limited by thestate-of the-art analog to digital converters (ADCs), especially in wideband regime.Comressive sensing (CS) was used by many researchers for solving this problem viasub-Nyquist sampling rates. However CS solves the high sampling rate problem, but it doesnot reduce complexity considerably. This is because spectrum sensing is performed in threesteps: sensing compressed measurements, then reconstructing the Nyquist rate signal, andfinally performing cyclostationary detection (CD) on the reconstructed signal. In this paperwe suggest performing CD directly on the compressed measurements skipping thereconstruction step which is the most complex step in CS. This can be realized by designingthe sensing matrix with constraints different from those used in the conventional CS. Resultsshow that performance is improved relative to applying CD on the Nyquist rate signal. Thisis in addition to reduction in receiver complexity resulting from reducing sampling rates. Adetection probability of 78.7% can be achieved with only 7% of samples used by theconventional cyclostationary detection technique that achieves a detection probability of32.7%.

A channelized digital ultrawideband receiver

A channelized digital ultrawideband (UWB) receiver that efficiently samples the UWB signal at a fraction of the chip frequency is proposed. The received signal is channelized in the frequency domain by employing a bank of mixers and low-pass filters. After sampling at a much reduced frequency, digital synthesis filters optimally estimate the transmitted signals. The signal-to-noise ratio (SNR) of the proposed receiver has been solved and compared against an ideal conventional receiver, which is defined as a receiver that samples at the signal Nyquist rate. When finite resolution analog-to-digital converters (ADC) are employed in the presence of a large narrowband interferer, the proposed receiver significantly outperforms the ideal conventional receiver. For example, the SNR of the proposed receiver is as much as 20 dB higher than the ideal conventional receiver when a 4-bit ADC is used in the presence of a 50 dB (relative to the noise floor) brickwall narrowband interferer with a bandwidth of 15% of the chip frequency.

Minimizing power consumption in direct sequence spread spectrum correlators by resampling IF samples-Part I: performance analysis

Most modern digital receivers sample the received RF signal at an intermediate frequency (IF), then downconvert to the baseband in the digital domain. The baseband samples are subsequently correlated with a time-limited square pulse, which is readily implemented as an integrator. Since correlation is performed at the sampling frequency, the receiver correlates at an unnecessarily high frequency. This high frequency results in significant power dissipation especially if parallel correlators are employed. By downsampling after appropriate filtering to slightly above the signal Nyquist rate, correlation is achieved at a fraction of the sampling frequency, resulting in corresponding reduction in power consumption. Furthermore, by resampling to an integer number of samples per chip, architectural changes in the correlators are possible, allowing even more reduction in power consumption. In this paper, a resampling correlator with minimal hardware overhead that outperforms the conventional correlator is presented.