Time-Reversal Wireless Paradigm for Green Internet of Things: An Overview <s> C. Low-Cost High-Speed ADC and DAC <s> It is known that a continuous time signal x(i) with Fourier transform X(/spl nu/) band-limited to |/spl nu/|</spl Theta//2 can be reconstructed from its samples x(T/sub 0/n) with T/sub 0/=2/spl pi///spl Theta/. In the case that X(/spl nu/) consists of two bands and is band-limited to /spl nu//sub 0/<|/spl nu/|</spl nu//sub 0/+/spl Theta//2, successful reconstruction of x(t) from x(T/sub 0/n) requires an additional condition on the band positions. When the two bands are not located properly, Kohlenberg showed that we can use two sets of uniform samples, x(2T/sub 0/n) and x(2T/sub 0/n+d/sub 1/), with average sampling period T/sub 0/, to recover x(t). Because two sets of uniform samples are employed, this sampling scheme is called Periodically Nonuniform Sampling of second order [PNS(2)]. In this paper, we show that PNS(2) can be generalized and applied to a wider class. Also, Periodically Nonuniform Sampling of Lth-order [PNS(L)] will be developed and used to recover a broader class of band-limited signal. Further generalizations will be made to the two-dimensional case and discrete time case. <s> BIB001 </s> Time-Reversal Wireless Paradigm for Green Internet of Things: An Overview <s> C. Low-Cost High-Speed ADC and DAC <s> This paper introduces a filterbank interpretation of various sampling strategies, which leads to efficient interpolation and reconstruction methods. An identity, which is referred to as the interpolation identity, is developed and is used to obtain particularly efficient discrete-time systems for interpolation of generalized samples as well as a class of nonuniform samples, to uniform Nyquist samples, either for further processing in that form or for conversion to continuous time. The interpolation identity also leads to new sampling strategies including an extension of Papoulis' (1977) generalized sampling expansion. <s> BIB002 </s> Time-Reversal Wireless Paradigm for Green Internet of Things: An Overview <s> C. Low-Cost High-Speed ADC and DAC <s> Time-interleaved analog-to-digital converters (TIADC) are sensitive to various mismatches that distort the sampled signal. Standard TIADC analysis assumes a sinusoidal input, which may result in pessimistic matching constraints for system-specific ADCs used with wideband input signals. Closed-form expressions bounding the acceptable phase-skew for wideband systems are derived, and are validated through simulations. In one of the examples presented it is shown that standard analysis can overconstrain the bound on acceptable phase-skew variance by a factor of three. <s> BIB003 </s> Time-Reversal Wireless Paradigm for Green Internet of Things: An Overview <s> C. Low-Cost High-Speed ADC and DAC <s> The track-and-hold stage at the front-end of high-speed, high-resolution ADCs is usually the limiting factor in their linearity performance at high input frequencies. In this paper, we propose a digital correction algorithm for the dynamic errors generated in this stage. The digital post-processing scheme uses circuit insight and judicious modeling of the relevant nonidealities to minimize complexity. We show that the number of coefficients required in our model is significantly smaller than the number of coefficients in the general form of the Volterra series. The coefficients are extracted in a foreground calibration approach using least square (LS) solutions on a set of input and output samples from training signals. Simulation results on a nonlinear track-and-hold circuit model show approximately 40 dB of improvement in linearity (SFDR) until the fourth Nyquist zone (at fs = 100 MHz). The method was also applied to a commercially available 14-bit, 155-MS/s ADC and showed to improve its SFDR to more than 83 dB up to an input frequency of 470 MHz in a lab experiment. <s> BIB004 </s> Time-Reversal Wireless Paradigm for Green Internet of Things: An Overview <s> C. Low-Cost High-Speed ADC and DAC <s> Direct digitization front end using direct radio frequency (RF) sampling is useful in multifrequency application for its flexibility and minimization of problems resulting from analog components. In such front end, the sampling frequency is the most important factor. This paper proposes the constraints and steps to design the sampling frequency using bandpass over sampling which means over sampling is based on the signal bandwidth. A new direct digitization front end for GPS L1 and L2 is then designed, implemented and tested. The digital down converter in this front end mixes the two signals to the same intermediate frequency (IF) which will facilitate the post signal processing and benefit the coherence consideration between frequencies. (4 pages) <s> BIB005 </s> Time-Reversal Wireless Paradigm for Green Internet of Things: An Overview <s> C. Low-Cost High-Speed ADC and DAC <s> Wideband analog signals push contemporary analog-to-digital conversion (ADC) systems to their performance limits. In many applications, however, sampling at the Nyquist rate is inefficient because the signals of interest contain only a small number of significant frequencies relative to the band limit, although the locations of the frequencies may not be known a priori. For this type of sparse signal, other sampling strategies are possible. This paper describes a new type of data acquisition system, called a random demodulator, that is constructed from robust, readily available components. Let K denote the total number of frequencies in the signal, and let W denote its band limit in hertz. Simulations suggest that the random demodulator requires just O(K log(W/K)) samples per second to stably reconstruct the signal. This sampling rate is exponentially lower than the Nyquist rate of W hertz. In contrast to Nyquist sampling, one must use nonlinear methods, such as convex programming, to recover the signal from the samples taken by the random demodulator. This paper provides a detailed theoretical analysis of the system's performance that supports the empirical observations. <s> BIB006 </s> Time-Reversal Wireless Paradigm for Green Internet of Things: An Overview <s> C. Low-Cost High-Speed ADC and DAC <s> 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 low-pass 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, real-time 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. <s> BIB007
The inherent nature of TR communications is to fully harvest energy from the surrounding environment by exploiting the multi-path propagation to re-collect all the signal energy that could be collected. To have superior advantage, the TR communications need to operate in a rich multi-path environment, which generally require wide bandwidth. As a consequence, the sampling rate is typically high. Moreover, to avoid missing the peak during the sampling and simplify the synchronization process, a two to four times oversampling is generally required, which make the sampling even more challenging. Therefore, one key implementation issue in TR communications is the high sampling rate of the ADC. Fortunately, due to the advance of semiconductor technologies and the continuous driven from the emerging wideband communication applications, the performance of ADC has been improved a lot during the past decade in terms of both sampling rate and resolution. For example, there are 17 different commercial off-the-shelf ADCs from Texas Instrument with sampling rate at least 1 GHz and resolution at least 8 bits  . However, the price of such ADCs is typically high, e.g., an ADC with two-channel 2-GHz sampling rate and 8 bits resolution costs US$329, which may barrier the application of TR technique on IoT. In such a case, there is a need to find cheaper solutions to high sampling rate ADCs. There are two possible ways to reduce the cost of high sampling rate ADCs. The first way is to implement the ADC on chip. In such a case, the cost of ADC comes from the silicon cost, which depends on silicon wafer cost and the size of the ADC on silicon. In general, with silicon implementation, the cost of ADC can be reduced from several hundred dollars to several cents without considering the capital cost. Nevertheless, since the capital cost is typically very high, such kind of implementation is only suitable for large volume productions. The other way to reduce the cost is using a set of low sampling rate cheap ADCs to achieve the high sampling rate. As the price of commercial ADCs grows exponentially with the increase in sampling rate, by replacing the high sampling rate ADCs with a set of low sampling rate ADCs, the cost can be reduced dramatically. One straightforward way is to use time interleaving  , BIB001 . In such an approach, the input signal is passed through a series of parallel interleaved low sampling rate ADCs where the interleaving is achieved through the time shifts. After the sampling, the samples are passed through the de-interleaver to generate the high sampling rate signal. However, the front end of a commercial ADC has an inherent analog bandwidth limitation BIB003 , BIB004 , due to which the time interleaving approach is not practical. The second approach is to use parallel bandpass sampling approach BIB002 , BIB005 where the input signal is passed through a series of filter bank before the ADCs and the reconstruction method depends on the corresponding filters in the filter bank. This kind of approach can resolve the analog bandwidth limitation but necessitates sophisticated digital algorithms for accurate frequency synchronization. Another approach is to use random demodulation BIB006 , BIB007 where the input signal is passed through parallel channels. In each channel, the input signal is first multiplied by a periodic random waveform in the analog domain, then lowpass filtered, and finally sampled using low sampling rate ADC. The random demodulation approaches overcomes the disadvantages of the time interleaving approach and the parallel bandpass sampling approach, but is limited by the technology for generating the periodic random waveforms. Note that in all these approaches, the costly high sampling rate ADC is traded with the computation complexity for reconstruction in digital domain which is relatively cheap.