Time-Reversal PPM for Stress Wave Communications in Concrete Systems

 

 

Qing Ji 1, Michael Ho 2, Rong Zheng 3, Zhi Ding 4 and Gangbing Song 1,2

1. Department of Electrical Engineering, University of Houston, Houston, TX, USA.

2. Department of Mechanical Engineering, University of Houston, Houston, TX, USA. Email: gsong@uh.edu

3. Department of Computing and Software, McMaster University, Hamilton, ON, Canada.

 4. Department of Electrical Engineering, University of California, Davis, Davis, CA, USA.

 

 

ABSTRACT

 

Large concrete structures are prone to cracks and damages over time from human usage, weathers, and other environmental attacks such as flood, earthquakes, and hurricanes. The health of the concrete structures should be monitored regularly to ensure safety. A reliable method of real time communications can facilitate more frequent structural health monitoring (SHM) updates from hard to reach positions, enabling crack detections of embedded concrete structures as they occur to avoid catastrophic failures. By implementing an unconventional mode of communication that utilizes guided stress waves travelling along the concrete structure itself, we may be able to free structural health monitoring from costly (re-)installation of communication wires. In stress-wave communications, piezoelectric transducers can act as actuators and sensors to send and receive modulated signals carrying concrete status information. The new generation of lead zirconate titanate (PZT) based smart aggregates cause multipath propagation in the homogeneous concrete channel, which presents both an opportunity and a challenge for multiple sensors communication. We propose a time reversal based pulse position modulation (TR-PPM) communication for stress wave communication within the concrete structure to combat multipath channel dispersion. Experimental results demonstrate successful transmission and recovery of TR-PPM using stress waves. Compared with PPM, we can achieve higher data  rate and  longer link distance via TR-PPM. Furthermore, TR-PPM remains effective under low signal-to-noise ratio. This work also lays the foundation for implementing multiple-input multiple-output (MIMO) stress wave communication networks in concrete channels.

 

KEYWORDS

 

SHM, stress wave communication, smart aggregate, time reversal, PPM, TR-PPM.

 

Introduction

 

Concrete structures have been extensively used for over a century. However, in recent years, many such structures have aged and deteriorated to the point of structural failure, sometimes causing collapse-related accidents in many parts of the world. The problem of aging infrastructure highlights the importance of concrete structural health monitoring (SHM). With an increased focus on structural integrity to meet safety regulations, there is an acute need for real-time updates on health status of concrete structures, with continuous recording and data export throughout the life cycle. Structural health monitoring (SHM) related techniques provide an innovative potential to improve operational safety of concrete structures while cutting down installation and maintenance expenses. Recently, wireless sensor networks (WSNs) based structure health monitoring have attracted increasing attention owing to their low cost and ease of installation over conventional monitoring systems that relying on piezoelectric sensors wired to a personal computer (PC), (e.g. Li et al. 2010). Although optimized power system design and intelligent sleep management can increase the lifetime of WSN SHM systems (e.g. Li et al. 2010), the need for battery replacement remains still a key challenge for many civil applications (Hoult et al. 2009). Furthermore, for structures buried underground or submerged in water, it is difficult and often infeasible to use wireless RF communication.

 

Piezoelectric based smart aggregate (SA) has proven to be effective both as sensors and actuators, further enhacning its multi-functionality in concrete SHM, including early age strength monitoring, impact detection and structural health monitoring (Song et al. 2008). Additionally, smart aggregates can be employed for energy harvesting from ambient vibration and long distance energy charging by focusing techniques. For these reasons, it is natural and desirable to develop a fully autonomous SHM system capable of damage detection, health monitoring, self powering, and wire-free communication via the host concrete structure itself as the channel medium.

 

Low power, long range stress wave communication propagating within the concrete structure is a very attractive solution. Thus far, works on stress wave data communication in the structures are rather limited. Several research teams have investigated ultrasonic digital communication through metallic structures (e.g. Graham et al. 2009; Primerano 2010; Murphy 2006), though systematic data communication schemes remain unclear. Kokossalakis (2006) proposed using pipelines as an acoustic waveguide for modulated wave transmission. Frequency-shift keying (FSK), amplitude-shift keying (ASK) and quadrature amplitude modulation (QAM) methods are shown to have similar bit error performance. Several signal processing steps were proposed to compensate for channel dispersion. Johnson (1972) tested seismic communications with a data rate of two pulses per second at a distance of 760 ft through hard rocks by using an impedance matched piezoelectric transducer as the transmitter. Jin et al. (2011) developed a time reversal based guided elastic wave communication scheme that utilizes steel pipes as transmission channels for structural health monitoring applications. Kailaswar et al. (2012) proposed a single-input single-output (SISO) communication paradigm using cement-based SA embedded concrete channel based on the D8PSK modulation scheme. They observe that multipath is not rich in concrete medium. Although the concrete medium is mostly homogeneous, the new generation marble-based SA that consists of a piece of lead zirconate titanate (PZT) patch sandwiched between a pair of marble blocks through epoxy (Hou et al. 2012), contributing to the inhomogeneous channel environment for wave propagation. According to Snell’s law, as the stress wave passes the border between media, the wave is reflected at the interface and also refracted at an angle that depends upon the relative refractive indices of the two media. Marble-based SAs are more stable in mechanical performance compared with cement-based SAs. Hence, when applying marble-based SA for structure health monitoring, a communication scheme is required to overcome the signal delay spread caused by multipath channels. Furthermore, for future consideration of multiple-input multiple-output (MIMO) communication links that utilize stress waves propagating through concrete over the distances for structural health monitoring, diversed multipath dispersion across various transmit-receive paths can provide the useful MIMO channel gain abd MIMO capacity.  This channel diversity in MIMO system (e.g. Sharony 2006) can take advantage of the dispersive effects generated by inhomogeneous media for multiple-channel and simultaneous multi-sensor transmission over the same concrete channel. With this understanding, a communication scheme is needed to also overcome the resulting multipath distortion when taking advantage of the multipath for MIMO communications. 

 

More recently, there has been substantial interest in ultra-wide band (UWB) communications because of its potentially low complexity and low power. Among others, pulse position modulation (PPM) modulation offers notable advantage with respect to power efficiency (Ramirez-Iniguez et al. 2008). In this paper, we develop a novel method of PPM inside concrete using stress wave communications. To mitigate distortions due to multipath channel dispersion, we propose a time reversal based pulse position modulation (TR-PPM) for single channel (SISO) stress wave transmission and reception. Our work contributes to the foundation for future implementation of MIMO stress wave communications.   

 

THEORETICAL BASICS AND DISCUSSION

 

a. Channel Response and Stress Wave Propagation using different SAs

 

Two generations of SAs have been developed for structural health monitoring. For the 1st  generation, the PZT patch is embedded within a concrete block (Gu et al. 2006), whereas the 2nd generation PZT patch is sandwiched between marble blocks. Piezoelectric materials can generate electric charge in response to applied mechanic forces and can produce stress or strain when subjected to an electric field. Under an alternating potential difference, the material is set to elastic vibration, which produces stress waves.

 

In order to take full advantage of different SA properties for stress wave communication in concrete blocks, it is necessary to characterize channel response when different SAs are embedded into the concrete specimen. Thus, two concrete cylinder specimens are set up as shown in Figure 1. One cylinder is embedded with marble-based SAs embedded while the other is embedded with cement-based SAs. A 10mm thickness sponge sheet under the cylinders isolates wave propagation. For each concrete cylinder, piezoelectric actuator and the piezoelectric sensor, in the form of SAs, are positioned along the central axis of the cylinder specimen, separated by a distance of 10 inches. In the experiment, for both specimens, the actuator SA1 emits a sweep sine wave and the sensor SA2 receives the stress wave from SA1. Figure 2 shows the spectrum of the received signal by the sensors in two different specimens. The concrete channel using marble-based SAs had better response in high frequencies while the channel using cement-based SAs had better response in low frequencies.

 

IMG_2331.JPG

Figure 1.Two concrete cylinder specimens with different SAs

 

(a) Cement-based                                                       (b) Marble-based

Figure 2. Frequency response of two different specimens

 

For cylindrical concrete structures, stress waves can be generally categorized into three families, namely the torsional (T), longitudinal (L) and flexural (F) waves. There exist several different guided wave modes in each family. Guided stress waves are known to be dispersive because the wave mode velocity varies with its frequency. The changes in phase velocity with respect to frequency are simulated for the concrete used in the experiments (Figure 3) using software GUIGUW (Bocchini et al. 2011). While the fundamental mode (L (0, 1), T (0, 1), F (0, 1)) is defined over the entire frequency range, the branches of higher modes started to propagate at their cut-off frequency. The cut-off frequencies of higher modes start from around 20 KHz. The number of wave modes increases as the frequency increases. Higher frequency signals excite more propagation modes. The fundamental torsional mode T (0, 1) is non-dispersive while the other modes are highly dispersive, especially at their respective low frequencies. In other words, a small change in frequency causes a relatively large velocity change at low frequency. It is this non-constant channel group delay that causes frequency dispersion. For each mode, as the frequency increases, the level of dispersion decreases.  In particular, a pulse may contain a wide range of frequencies and potentially excites many modes . Since the concrete channel using cement-based SAs acts as a low pass filter, only the fundamental modes are excited and the channel appears less dispersive. The concrete channel using marble-based SAs has a good high-frequency response, and the channel becomes more dispersive as more modes are stimulated. As a result, a pulse signal traveling through the concrete becomes heavily distorted when using the marble SAs. On one hand, the multipath diversity may be potentially exploited by properly designed modulation schemes in multi-antenna systems. On the other hand, the communication system must also compensate for Inter-Symbol Interference (ISI) due to channel dispersion.

C:\Users\Sunshine\Desktop\Dispersion Curves 3 inch\flexural.JPGC:\Users\Sunshine\Desktop\Dispersion Curves 3 inch\tortional.JPGC:\Users\Sunshine\Desktop\Dispersion Curves 3 inch\longitudinal.JPG

              (a) Torsional modes                           (b) Longitudinal modes                       (c) Flexural modes

Figure 3. Phase speed versus frequencies dispersion curves

 

b. Principle of Time Reversal Communication

 

In order to combat severe channel dispersion, we adopt time reversal communication utilizing the stress wave . The spatial and temporal focusing property of time reversal can take advantage of the dispersion caused by the channel by applying matched pulse-shape to focus multipath energy for increasing received SNR. Time reversal technique has been applied under dispersive channels in many applications, including defects detection in pipes (e.g. Ying et al. 2010), underwater acoustics (e.g. Edelmann et al. 2005), electromagnetic (e.g. Jin et al. 2007),  and stress wave communication, etc..

Consider an input signal x(t) generated by SA1. Let f(t) represent the corresponding impulse response function, then, y(t) received by the SA2 can be written as

                                                                                                                             

where denotes the convolution operation.

The received signal at SA2 is reversed in time, namely time reversal signal y(-t),

                                                                                                                     

When the time reversed signal is sent from SA2 to SA1, assuming the channel is reciprocal, the received signal can be given as

                                                 

wheredenotes time correlation.  

Most of input signals are time reversal symmetric, such as Gaussian pulse, sinusoidal signals, and square signals, i.e., x(-t)=x(t). Therefore, the received signal is a convolution of input signal and an autocorrelation function which is often called the time reversal operator. The operator named, is represented as

                                                                                                               

From Eq. (5), it is shown that the time reversal operator is an even function. Therefore the received signal is always time reversal symmetric in the time domain. When t=0, time reversal operator has the maximum value

                                                                                                                        

This proves that the received signal yTR(t) is a time reversal symmetric focusing signal.

 

c. Design of PPM and TR-PPM Communication

 

PPM Scheme.JPG

Figure 4. PPM and TR-PPM transmission scheme

Figure 4 illustrates the basic diagram of the (TR-)PPM transmitter in which the pulse-shaper can executive TR-PPM by adopting the time-reversed waveform it received from its partner node. This transmitter consists of the following components:

1.     The binary source provides in binary format the information = (,, ,…,) that the stress wave needs to deliver.

2.     Transmission coder applies an integer-value code = (,, ,…,) to the binary sequence a and generates a new sequence d expressed as follows: , whereis the time hopping code which plays the role of code division multiple access for multiple users, and  is the chip time.  represents the time shift specified on the given chip block and is the symbol duration introduced by the PPM which depends on the bit to be represented. In this paper, we used the basic PPM modulation scheme, that is.

3.     PPM Modulator generates a sequence of united pulses which are located at times.

4.     Pulse shaper functions as a filter with impulse response. 

a.     For the conventional PPM method, it can be the Gaussian modulated sine waveform

Where  is the amplitude,  is the normalized bandwidth,  is the attenuation, is the center frequency (Hz),  is the delay, and  is the samples.

b.     For the TR-PPM method,  where is the channel impulse response, is the time reversed channel response waveform. The transmitting TR-PPM modulated signal takes the form of

 

EXPERIMENTAL SETUP

 

Text Box: Concrete BlockText Box: NI DAQ BoardText Box: SA1Text Box: SA5Text Box: SA4Text Box: SA3Text Box: SA2Text Box: PZT AmplifierText Box: Laptop with Experimental Software

Figure 5. Experimental setup

 

The experimental setup (Figure 5) includes a concrete block of dimension 72”x5”x3”with multiple marble-based SAs embedded inside. An network interface (NI) USB X Series 6361 Data Acquisition System interfaced with a laptop through LabVIEW software collects data, while a PZT amplifier boosts signal transmission. The maximum input sampling rate of data acquisition system is 2 MHz per channel and the input/output dynamic range is [-10V, 10V]. The data acquisition system sent a signal through the analog output port to a PZT amplifier. The amplified signal excites one of the SAs (as the  actuator) in concrete. The vibrating signal propagated through the concrete, and is received by the other SA (as the sensor). The analog input port of the data acquisition sensed the SA vibration and acquired the received waveform for information extraction and  decoding.

 

EXPERIMENTAL PROCEDURES

 

We use the stress wave communication between SA2 and SA3 as an example to describe the following steps in the experiments.

1. Selection of a concrete channel resonance frequency as the center frequency for modulated Gaussian pulse: We use a sweep sine wave as the source signal to find the suitable channel resonance frequency. Figure 6 shows a Gaussian modulated sinewave with 36 kHz center frequency.

Figure 6. Gaussian modulated sine waveform

2. Transmission of a modulated Gaussian pilot signal is sent, and measuring channel response between two SA:. Figure 7 shows received signal from SA3 when SA2 transmits a modulated Gaussian pulse at center frequency of 36 KHz. The modulated Gaussian pulse waveform experiences substantial dispersion after traveling through the concrete. This severe time spreading response results from channel multipath and dispersion of stress waves.

    Figure 7. Channel response (SA2, SA3)

3. Reversal of normalized sounding signal and feedback:  The channel sounding signal is time reversed (Figure 8) and amplitude normalized (maximum amplitude value was scaled to 500V), and then is retransmitted back to the same channel. The received signal is a focused signal (Figure 9) with a distinct peak, indicating that most energy from different wave modes arrive at the receiver simultaneously. This peak allowed for accurate synchronization and signal decoding when transmitting data streams. The reversed channel response waveform is used to replace each pulse when modulating the data information in step 4. 

                                    

     Figure 8. Time reversed signal (SA2, SA3)   Figure 9. Received time reversal focused waveform (SA2, SA3) 

4. Transmission and reception of modulated time reversal signals to the SA2 after encoding a stream of binary bits. The binary streams were encoded through relative pulse shift within each data frame based on the time reversed channel response signal. The experiments are tested out at the data rates of 200 bps, 500 bps and 1 Kbps, respectively. The maximum amplitude value of output waveforms from the analog output port, which was the input of the amplifier, is scaled to the same value at all times for fair comparison between PPM and TR-PPM communication methods.

                     

EXPERIMENTAL RESULTS

                          

Conventional PPM and TR-PPM communication experiments are each carried out between different SA pairs under multiple transmission data rates of 200 bps, 500 bps, and 1 Kbps. The following sub-sections compare the results between the two different communication schemes under three transmission data rates in three different scenarios: short range communication, low signal-to-noise ratio (SNR) communication and relatively long distance communication.  

 

a. Short Range Stress Wave Communication Experiments via PPM and TR-PPM

 

Figure 10 shows the experimental results at three different data rates between the nearest SA pairs (SA2 and SA3) transmitting the bit stream [1101010011]. The amplifier connected to the SA2 (as actuator) outputs the excitation signal of peak amplitude value 500V. The received information-bearing waveforms encoded by two different modulation communication methods are compared. SA3 received the decodable waveforms for  both PPM and TR-PPM at data rate of 200 bps. For PPM communications, the received waveform becames harder to discern (or demodulate) at 500 bps and actually fails to show signal peaks at 1 Kbps because of the severe signal dispersion. However, TR-PPM communication results clearly show focusing peaks at both 500 bps and 1 Kbps data rates. We notice that there are several weak peaks at data rates of 500 bps and 1 Kbps due to ISI. As the data transmission rate grows, the ISI becames more significant. We conclud that transmitted stress wave signals can be decoded better according to the clearly visible signals peaks in TR-PPM at higher data transmission rate.

 

  (a) PPM at 200 bps data rate              (b) PPM at 500 bps data rate                  (c) PPM at 1 Kbps data rate

   

      (d) TR-PPM at 200 bps data rate         (e) TR-PPM at 500 bps data rate         (f) TR-PPM at 1 Kbps data rate

Figure 10. PPM and TR- PPM communication between SA3 and SA4 with bit stream [1101010011].

 

b. Low SNR Stress Wave Communication Experiments via PPM and TR-PPM

 

To further evaluate the link performance at low SNR, we reduces the maximum amplitude value of the modulated signal to 25V without changing the main experimental settings (using SA2 and SA3). Similar to the previous experiment, PPM and TR-PPM communication are tested and compared in three different data rates (Figure 11). Comparing their received signals in Figure 10, it is clear that the SNR is lower given the reduced excitation signal. For PPM, the received signal is fully submerged in noise and undetectable due to the low SNR for all three data rates cases.  But TR-PPM demonstrates robustness in low SNR conditions and the advantage of energy focusing through time-reversal pulse shaping. Although the peak values in Figure 11 are lower by roughly 10 times below those of Figure 10, the focused TR-PPM peaks still clearly convey the transmitted binary data. Hence, TR-PPM method allows signal transmission at substantially reduced SNR conditions.

 

  

       (a) PPM at 200 bps data rate                  (b) PPM at 500 bps data rate               (c) PPM at 1 Kbps data rate

 

     (d) TR-PPM at 200 bps data rate         (e) TR-PPM at 500 bps data rate        (f) TR-PPM at 1 Kbps data rate

Figure 11. PPM and TR- PPM communication between SA3 and SA4 in low SNR with bit stream [1101010011].

 

c. Long Distance Stress Wave Communication Experiments via PPM and TR-PPM

 

Figure 12 shows the received pulse focusing waveform and the received waveform at data rates of 200 bps, 500 bps and 1 Kbps between the farthest SA pairs (i.e., SA1 and SA5). The maximum amplitude of excitation signal is 500 V. Compared with Figure 9, the focused peaks between SA1 and SA5 become wider than those between SA2 and SA3. This is because of the substantial signal attenuation at longer distance that weakened  multipath signal strength, since time reversal techniques achieve signal focusing by using energy from all paths, Also, background noise becomes relatively stronger to degrade the received signal energy quality due to the weaker signal strength through longer distance.

 

We find the received PPM signal peaks become difficult to detection under all three different transmission rates. For TR-PPM, the peaks clearly convey the stream of binary data at 200 bps. When the transmission data rate increases to 500 bps or 1 kbps, the peaks starts to widen and overlap and became less distinguishable because of the relatively longer channel delay spread versus the modulated pulse interval. Although it is expected for  achievable transmission rate to drop as transmission distance groups, TR-PPM maintains its performance edge over the traditional PPM.  

(a) Received time reversal focused waveform (SA1, SA5)

 

          (b) PPM at 200 bps data rate              (c) PPM at 500 bps data rate                (d) PPM at 1 Kbps data rate

       (e) TR-PPM at 200 bps data rate        (f) TR-PPM at 500 bps data rate        (g) TR-PPM at 1 Kbps data rate

        Figure 12. PPM and TR- PPM communication between SA1 and SA5 with bit stream [1101010011].

 

Conclusions

 

In this paper, we studied Marble-based SA pairs as actuator and sensor for transmitting and receiving encoded binary data information over concrete channels. We show that the received stress wave signal encounters severe channel dispersion when using conventional PPM and often becomes difficulty to detect. We introduce a time reversal technique for PPM (TR-PPM) that can focus pulsed waves through inhomogeneous multipath channels by utilizing the scattering of waves. Compared with PPM communication, TR-PPM substantially improves data rate, transmission distance, and is robust at lower SNR environment.   This work further provides a foundation for future implementation of MIMO stress wave communication links in concrete channels.

 

ACKNOWLEDGMENTS

 

The authors are grateful to Dr. Peng Li for assisting with SA integrated system testing, analysis of the concrete communication channel, and also for providing suggestions and expertise on conducting the communication experiments in concrete. This material is based upon work supported by NSF awards (CNS-0832089 and CCSS-CPS1102195).

 

References

 

Li, P., Gu, H., Song, G., Zheng, R. and Mo, Y.L. (2010). “Concrete structural health monitoring using piezoceramic-based wireless sensor networks. Smart Structures and Systems, 6(5-6), 731-748.

Li, P., Olmi, C. and Song, G. (2010). “Energy efficient wireless sensor network for structural health monitoring using distributed embedded piezoelectric transducers”, In [SPIE Smart Structures and Materials+ Nondestructive Evaluation and Health Monitoring], International Society for Optics and Photonics, 764715-764715.

Hoult, N.A., Fidler, P.R.A. and Middleton, C.R. (2009). “Wireless Structural Health Monitoring of Bridges: Current Challenges and Future Innovations”, Proceedings of the 7th AustRoads Bridge Conference, 1-12.

Song, G., Gu, H. and Mo, Y.L. (2008). “Smart aggregates: multi-functional sensors for concrete structures—a tutorial and a review”, Smart Materials and Structures, 17 (3), 1-17.

Graham, D., Neasham, J., and Sharif, B. (2009). “High bit rate communication through metallic structures using electromagnetic acoustic transducers", OCEANS 2009-EUROPE, 1-6.

Primerano, R. A. (2010). “High Bit-rate Digital Communication through Metal Channels", Doctoral thesis, Drexel University.

Murphy, T. (2006). “Ultrasonic Digital Communication System for a Steel Wall Multipath Channel: Methods and Results", Master's thesis, Rensselaer Polytechnic Institute.

Kokossalakis, G. (2006). “Acoustic Data Communication System for In-pipe wireless sensor network”, PhD thesis, Massachusetts Institute of Technology, Cambridge, MA.

Johnson, C. C. (1972). “A seismic communications investigation employing a piezoelectric transducer”.

Jin, Y., Zhao, D., and Ying, Y. (2011). “Time reversal data communications on pipes using guided elastic waves - Part I: Basic principles”, in [SPIE Smart Structures/NDE Conference], 1-12.

Jin, Y., Ying, Y., and Zhao, D. (2011). “Time reversal data communications on pipes using guided elastic waves - Part II: Experimental studies”, in [SPIE Smart Structures/NDE Conference], 1-11.

Kailaswar, S.,  Zheng, R., Kovitz, J., Phung Q.Wang H., Ding Z. and Song, G. (2012). “ConcreteCom: A New Communication Paradigm for Building Structural Health Monitoring”, in Proceedings of the Fourth ACM Workshop on Embedded Sensing Systems for Energy-Efficiency in Buildings, 131-137.

Hou S., Zhang H.B., and Ou J.P. (2012) “A PZT-based smart aggregate for compressive seismic stress monitoring”, Smart Materials and Structures, 21(10), 105035, 1-9.

Sharony, J. (2006). “Introduction to Wireless MIMO–Theory and Applications”, CEWIT–Center of Excellence in Wireless and Informational Technology, Stony Brook University, IEEE LI, 1-63.

Ramirez-Iniguez, R., Idrus, S. M., and Sun, Z. (2008). “Optical wireless communications: IR for wireless connectivity”, Boca Raton: CRC Press. 

Gu, H., Song G., Dhonde H., Mo Y.L., and Yan S. (2006). “Concrete early-age strength monitoring using embedded piezoelectric transducers”, Smart Materials and Structures, 15(6), 1837-1845.

Bocchini P., Marzani A., and Viola E. (2011). “Graphical user interface for guided acoustic waves”, Journal of Computing in Civil Engineering, 25(3), 202-210.

Ying, Y., Soibelman, L., Garrett, J., Jin, Y., Moura, J., Oppenheim, I., O’Donoughue, N., and Harley, J. (2010). “Time reversal detection in pipes”, in [SPIE Conference on Smart Structures/NDT], 7647, 76473S-1-12.

Edelmann, G., Song, H., Kim S., Hodgkiss, W., Kuperman, W., and Akal, T. (2005). “Underwater acoustic communication using time reversal”, IEEE J. Ocean. Eng., 30(4), 852-864.

Jin, Y., Jiang, Y., and Moura, J. M. F. (2007). “Multiple antenna time reversal transmission in ultra-wideband communications”, in [IEEE Globe Communication Conference], 3029-3033.