Time-Reversal Wireless Paradigm for Green Internet of Things: An Overview <s> A. Advanced Waveform Design <s> A channel with output Y = X + S + Z is examined, The state S \sim N(0, QI) and the noise Z \sim N(0, NI) are multivariate Gaussian random variables ( I is the identity matrix.). The input X \in R^{n} satisfies the power constraint (l/n) \sum_{i=1}^{n}X_{i}^{2} \leq P . If S is unknown to both transmitter and receiver then the capacity is \frac{1}{2} \ln (1 + P/( N + Q)) nats per channel use. However, if the state S is known to the encoder, the capacity is shown to be C^{\ast} =\frac{1}{2} \ln (1 + P/N) , independent of Q . This is also the capacity of a standard Gaussian channel with signal-to-noise power ratio P/N . Therefore, the state S does not affect the capacity of the channel, even though S is unknown to the receiver. It is shown that the optimal transmitter adapts its signal to the state S rather than attempting to cancel it. <s> BIB001 </s> Time-Reversal Wireless Paradigm for Green Internet of Things: An Overview <s> A. Advanced Waveform Design <s> The current state of the acoustic wave phase conjugation (PC) problem is reviewed. The generation of phase conjugate ultrasonic waves is discussed with emphasis on the parametric method using electromagnetic pumping in solids. The giant-amplification supercritical parametric PC mode is considered in detail. Ultrasonic PC with a gain in excess of 80 dB is demonstrated for a soft magnetic ceramics-based amplifier. The high quality of supercritical parametric PC sound is confirmed by acoustic-optical visualization. Acoustic PC effects, such as anomalous sound reflection at the PC mirror and the autofocusing and self-targeting of phase conjugate sound beams incident on a scatterer in a liquid, are shown. Recent experimental results demonstrating the potential of PC for applications are presented. <s> BIB002 </s> Time-Reversal Wireless Paradigm for Green Internet of Things: An Overview <s> A. Advanced Waveform Design <s> Joint power control and beamforming schemes are proposed for cellular systems where adaptive arrays are used only at base stations. In the uplink, mobile power and receiver diversity combining vectors at the base stations are calculated jointly. The mobile transmitted power is minimized, while the signal-to-interference-and-noise ratio (SINR) at each link is maintained above a threshold. A transmit diversity scheme for the downlink is also proposed where the transmit weight vectors and downlink power allocations are jointly calculated such that the SINR at each mobile is above a target value. The proposed algorithm achieves a feasible solution for the downlink if there is one and minimizes the total transmitted power in the network. In a reciprocal network it can be implemented in a decentralized system, and it does not require global channel response measurements. In a nonreciprocal network, where the uplink and downlink channel responses are different, the proposed transmit beamforming algorithm needs to be implemented in a centralized system, and it requires a knowledge of the downlink channel responses. The performances of these algorithms are compared with previously proposed algorithms through numerical studies. <s> BIB003 </s> Time-Reversal Wireless Paradigm for Green Internet of Things: An Overview <s> A. Advanced Waveform Design <s> In wireless code division multiple access (CDMA) communications systems, there has been interest in processing the transmitted down-link signal in order to shift signal processing to the transmitter where power and computational resources are plentiful, thus simplifying receiver operation and reducing the power it requires. Multiuser interference (MUI) and multipath effects observed by the receiver are anticipated and suppressed at the transmitter; channel equalization and multiuser detection are therefore not required. This paper introduces two methods that are able to combat both degradations, yet allow the receiver to remain as simple as a single user receiver for a perfect channel. For mild multipath channels, the performance of the algorithms is excellent, within a few decibels of the single user ideal channel case, at the cost of additional computation at the base station at which complete knowledge of the channels and the receiver codewords is required. One method, the decorrelating prefilter, is most flexible and applicable to existing systems yet less powerful than other previously published methods. The second, the jointly optimized sequences algorithm, has a performance on average superior to published methods. In addition to theoretical analysis and simulation of the algorithms' potential, these algorithms have also been implemented and tested on a software radio testbed and experimental data are shown. The jointly optimized sequences performed particularly well even in severe multipath and multiuser interference environments. <s> BIB004 </s> Time-Reversal Wireless Paradigm for Green Internet of Things: An Overview <s> A. Advanced Waveform Design <s> Linear transmit filters depend on current channel state information, which is available from the uplink channel estimation in time division duplex systems. For multiple antenna elements at the transmitter, we illustrate the influence of out-dated channel estimates on link level performance for symmetric and asymmetric traffic, comparing the transmit matched, zero-forcing, and Wiener filters. A Wiener predictor is proposed to improve channel knowledge of the transmitter. We observe an inherent robustness of the transmit matched filter and explain the occurrence of a minimum in the bit error ratio at a finite SNR for the transmit Wiener filter. <s> BIB005 </s> Time-Reversal Wireless Paradigm for Green Internet of Things: An Overview <s> A. Advanced Waveform Design <s> We study the possibility to transmit data over channels with large delay spreads under the constraint of a very simple receiver which has only one tap. Such a scheme is of interest when a cost-efficient way to transmit potentially high data rates are sought after. We investigate the performance of the optimal prefilter for this scheme and compare it to a simplified, so-called time-reversal (TR) prefilter which has very low complexity. At low SNRs, the TR prefilter and the optimal prefilter are equivalent. At high SNRs, the TR prefilter achieves a performance that is independent from the delay spread of the channel and hence its performance is the same for any bandwidth. In applications where bandwidth is abundant, such as ultra-wide band (UWB) communications, any required performance can be obtained by TR prefilters with a rate back-off transmission (i.e. transmission rate lower than the allowable bandwidth). Similar performance can also be obtained with full-rate transmission using several transmit antennas. This performance is guaranteed, since the high diversity of the large delay spread channel effectively eliminates any fading. <s> BIB006 </s> Time-Reversal Wireless Paradigm for Green Internet of Things: An Overview <s> A. Advanced Waveform Design <s> In this paper, Tomlinson-Harashima Precoding for multiple-input/multiple-output systems including multiple-antenna and multiuser systems is studied. It is shown that nonlinear preequalization offers significant advantages over linear preequalization which increases average transmit power. Moreover, it outperforms decision-feedback equalization at the receiver side which is applicable if joint processing at the receiver side is possible, and which suffers from error propagation. A number of aspects of practical importance are studied. Loading, i.e., the optimum distribution of transmit power and rate is discussed in detail. It is shown that the capacity of the underlying MIMO channel can be utilized asymptotically by means of nonlinear precoding. <s> BIB007 </s> Time-Reversal Wireless Paradigm for Green Internet of Things: An Overview <s> A. Advanced Waveform Design <s> A high impedance voltage probe with excellent high frequency response and extremely light loading of the circuit under test. The probe uses an IGFET input device having its source connected to a constant current source and to an amplifying device, and its drain connected to a variable voltage source. The output of the amplifying device is connected to a constant current source, to a non-linear voltage translating device and to an output terminal. The voltage translating device is also connected to the variable current source. <s> BIB008 </s> Time-Reversal Wireless Paradigm for Green Internet of Things: An Overview <s> A. Advanced Waveform Design <s> We consider the design of ultra-wideband (UWB) systems that enable high data rate communications for short-range wireless applications. In particular, we consider the downlink of a direct sequence UWB (DS-UWB) system in which the base station is equipped with multiple antennas and employs pre-rake combining, while each user employs a simple single antenna receiver. We propose the use of multiuser filters for the purpose of pre-equalization at the transmitter in order to mitigate the combined effects of intersymbol interference (ISI) and multiuser interference (MUI) that are generated at the receivers as a result of the wideband nature of the users' channels. For this system, we study the joint design of the transmitter's pre-equalization filters and each receiver's scalar gain under two design criteria. The first design minimizes the total transmitted power from the base station subject to achieving physical layer quality of service requirements of different users. For this design, we show that the calculation of the pre-equalization filters and the receiver gains can be formulated as an efficiently solvable convex optimization problem. In the second design, we consider the minimization of a weighted sum of each user's mean-square error. In order to obtain a computationally tractable solution for this design criterion, we exploit the dual DS-UWB uplink that employs rake combining and post-equalization filters at a central receiver. The numerical studies for each design criterion under realistic models of UWB channel propagation demonstrate the effectiveness of the proposed multiuser pre-equalization filter designs in mitigating ISI and MUI, and thus their ability to enable reliable pre-rake DS-UWB downlink transmission. <s> BIB009 </s> Time-Reversal Wireless Paradigm for Green Internet of Things: An Overview <s> A. Advanced Waveform Design <s> Utilizing channel reciprocity, the traditional time- reversal technique boosts the signal-to-noise ratio at the receiver with very low transmitter complexity. However, the large delay spread gives rise to severe inter-symbol interference (ISI) when the data rate is high, and the performance is further degraded in the multiuser downlink due to the inter-user interference (IUI). In this work, we study the weighted sum rate optimization problem in the time-reversal multiuser downlink using waveform design. By exploiting the relation between the allocated power and the SINR targets, an iterative algorithm is proposed to optimize the waveform design through a new power allocation algorithm. Simulation results are shown to demonstrate the superior performance of the proposed algorithm in comparison with other traditional methods. <s> BIB010
In our discussion of TRDMA in the previous section, the TR CIR serves as the transmit signature waveform to modulate symbols. The received signal is the transmitted waveform convolving with the multi-path channel with additive noise. Such a time-reversed waveform is essentially the matched filter  , which guarantees the optimal BER performance by virtue of its maximum signal-to-noise ratio (SNR). However, in high data rate scenario such as video streaming, when the symbol duration is smaller than the channel delay spread, the transmit waveforms are overlapped and thus interfere with each other. When the symbol rate is very high, such ISI can be notably severe and causes crucial performance degradation, i.e., the BER performance can be very poor with a basic time-reversed waveform. Further, in multi-user downlink scenario, the TR BS uses each user's particular CIR as its specific waveform to modulate the symbols intended for that user. Despite the inherent randomness of the CIRs, as long as they are not orthogonal to each other, which is almost always the case, these waveforms will inevitably interfere with each other when transmitted concurrently. Hence, the performance of TRDMA can be impaired and even limited by the IUI. Based on given design criteria such as system performance, QoS constraints, or fairness among users, the waveform design can be formulated as an optimization problem with the transmitted waveforms as the optimization valuables. The basic idea of waveform design is to carefully adjust the amplitude and phase of each tap of the waveform based on the channel information, such that after convolving with the channel, the received signal at the receiver retains most of the intended signal strengths and rejects or suppresses the interference as much as possible. To rewrite (15) in a vector from, we define the following notations. The multipath channel between the base-station and the th user is denoted by a vector , a column vector of elements where and . Let denote an information symbol for user , and be the transmit waveform for user , where in  . The length of is also . The received signal vector at user , where in  , is given by where is the Toeplitz matrix of size with the first column being , and denotes the AWGN with . User estimates the symbol by the sample . Note that BIB002 represents the received signal when the rate backoff factor > . When < , the received waveforms of different symbols overlap with each other and give rise to the ISI. To characterize the effect of ISI, the decimated channel matrix of size , where , is defined as where is the th column of a identity matrix. In other words, is obtained by decimating the rows of by , i.e., centering at the th row, every th row of is kept in while the other rows are discarded. The center row index of is . Then the sample for symbol estimation can be written as where denotes the th row of , and denotes user 's th symbol. It can be seen from (31) that the symbol , the th symbol of user , is interfered by the previous symbols and the later symbols as well as other users' symbols, and also corrupted by the noise. The design of waveforms has critical influence to the symbol estimation and thus the system performance. It can be observed that the mathematical structure of waveform design is similar to the beamforming problem, which is also known as the multi-antenna precoder design BIB003 - BIB005 . Therefore, beamforming approaches, such as singular value decomposition (SVD), zero forcing (ZF), and minimal mean square error (MMSE), can be analogously employed in waveform design. In the literature, there have been many studies investigating the problems of designing advanced waveforms to suppress the interference BIB010 , BIB006 , BIB009 - BIB004 . If the basic TR waveforms are adopted, i.e., , then the intended signal power for each user is maximized but without considering the interference caused by other symbols. As such, the performance is limited by the interference when the transmit power is high. Another possible waveform design is ZF BIB008 , which minimizes all the interference signal power but without taking into account the intended signal power. Thus, the resulting SNR can be very low and causes severe performance degradation especially when the transmit power is relatively low. In BIB010 , it has been shown that well-designed waveforms can strike a balance between enhancing the intended signal power and suppressing the interference power. Besides the channel information, another important side information the transmitter can exploit in waveform design, is the transmitted symbol information. The waveform of one symbol, when arriving at the receiver, induces ISI to the previous symbols as well as the following symbols. Given what has been transmitted, the causal part of ISI can be canceled in advance in designing the waveform of the current symbol. Such a design pholosophy is analogous to the transmitter-based interference pre-subtraction BIB007 - BIB001 in the nonlinear precoding literature. A notable distinction for TR systems is that only the causal part of ISI can be canceled while the anti-causal part of ISI cannot be canceled and needs to be suppressed by the waveform design based on channel information  . Fig. 16 shows the BER performance for a single user TR system when using different waveforms, including basic TR waveform, the waveform design in BIB010 , and the joint waveform design and interference pre-cancelation in  . It can be seen that when , the ISI is so severe that the BER curve of the basic TR waveform starts to saturate at even middle SNR, which is unacceptable. The waveform design in BIB010 is able to suppress the interference and make the BER keep decreasing when SNR increases. The joint waveform design and interference precancelation in  can further improve the performance significantly since it makes use of more information, i.e., the transmitted symbols, to cancel the ISI in advance. It is evident that the dramatic performance improvement brought from the waveform design demonstrates its inevitable necessity in TR systems. Fig. 17 shows the performance comparison in terms of achievable rate of the TRDMA system with 500-MHz bandwidth with two OFDM systems: one is LTE system with 20-MHz bandwidth and the other is LTE-A system with 100-MHz bandwidth. We can see that for one user case, even with basic TR waveform, the TRDMA scheme can achieve much better performance than LTE in all SNR region and better performance than LTE-A in most SNR region. With optimal waveform, the performance of TRDMA can be further improved. When there are 10 users, due to the selectivity among different users, the achievable rate of LTE and LTE-A can be enhanced, due to which LTE-A can achieve comparable and even slightly better performance than TRDMA with basic TR waveform. Nevertheless, with optimal waveform, TRDMA can still outperform LTE and LTE-A in most SNR region, which demonstrates that TRDMA can achieve higher throughput than OFDM systems when the bandwidth is wide enough, e.g., five times as in the simulations.