Sound as a Communication Modality for Networked Robotic Systems

Transcription

1 EINDHOVEN UNIVERSITY OF TECHNOLOGY, DEPARTMENT OF MECHANICAL ENGINEERING 1 Sound as a Communication Modality for Networked Robotic Systems Mickey Beurskens Abstract The Audio Transfer protocol is a system which uses Binary Phase Shift Keying as a way to accommodate communication in networked robotic systems through sound. It is tested using two laptops, one microphone and one speaker using Matlab. The system performance is variable due to the stability of the receiver under different circumstances. Audio Transfer is nevertheless suited to broadcast markers reliably across a distance of 7 meters. Future improvements might make the system viable for transmission of more complex data at higher speeds and with higher reliability. I. INTRODUCTION Networked robotic systems usually need a communications network such as wifi to communicate. One can think of more traditional industrial robotic manipulators, systems like self driving cars or the robot soccer teams participating in the Robocup to name a few. Communication may include sensor data, role data or other information relevant to the interaction of the system. Networked robotic systems are getting more commonplace in society. When communication fails these systems might cease to operate or in more serious cases actually become dangerous. Therefore it is relevant to look into a backup communication modality for such systems. Sound is especially useful as a modality because it is not necessary to know where to receiver is located. Therefore Audio Transfer as a way to enable robots in network to communicate using sound. It is developed for use in the Technical Challenge of the Middle Sized League of the Robocup. Each year the participants of the MSL participate in the Technical Challenge, which involves the use of the soccer robots. This year the challenge includes passing a soccer ball between two robots without the use of a wifi network. The feasibility of using sound as a viable backup communication modality is explored in this context. Audio Transfer is intended to enable two soccer robots to communicate using sound instead of the usual wifi communication in order to complete the Technical Challenge. The actual implementation of this system on the soccer robots has yet to be designed. Instead the paper consists of a theoretical treatise of Audio Transfer and a feasibility test of the system. It is tested, using a standard laptop, via Matlab to see if sound is a feasible communication modality and in what way it might be used in networked robotic systems such as the soccer robots. Advisor: Robin Soetens. Special thanks to everyone at Tech United Eindhoven. II. DIGITAL COMMUNICATION FRAMEWORK Digital communications systems can be divided into three main components: The transmitter, channel and receiver. Figure 1 shows a general representation of such a system [3]. The transmitter is responsible for converting passed information (in binary form) into a signal suitable for transmission across the channel. This implies that in the case of analog signals an analog to digital conversion is required at the input of the transmitter. In most robotic systems data is already in binary form, so this step can be skipped. The source encoder randomizes the bit stream to improve resistance against drift at the receiver. The channel encoder in the transmitter can be used to add error control bits. These bits can be used for error control or even error correction depending on the scheme used. Lastly the modulator generates an analog signal containing information encoded through the manipulation of several signal properties. The channel is the physical transportation layer of system. A channel generally introduces noise, attenuation and distortion of the transmitted signal which may give rise to communication error. The receiver is responsible for the decoding of the message signal after it has been exposed to the conditions in the channel. Error control checks usually take place in the channel decoder, as does error repair. Fig. 1. Block diagram of a general framework of digital communication systems [3]. Other functionalities include synchronisation of the transmitter and receiver, and amplification and filtering of the message signal. The goal in the end is to maximize the data rate while minimizing the Bit Error Rate (BER). The BER, which characterizes the probability that a transmitted bit is decoded wrongly at the receiver, is closely related to robustness and noise immunity. It is one of the most important performance measures in digital systems. Outside of this lower layer of communication it is also important to provide the network with some type of commu-

2 EINDHOVEN UNIVERSITY OF TECHNOLOGY, DEPARTMENT OF MECHANICAL ENGINEERING nication protocol. At the individual layer the data that needs to be transmitted or received needs to be queried at the proper time. At the network layer, protocols need to make sure that the correct robot is sending or receiving. In both layers errors in communication need to handled appropriately because digital communication systems are stochastic by nature and error are unavoidable. III. DIGITAL MODULATION TECHNIQUES Modulation techniques of a sinusoidal carrier signal depend on the variation of the properties of the message signal. The three main methods of modulation are Amplitude-, Phase- and Frequency Shift Keying (ASK, PSK and FSK respectively). Using these methods in different combinations and in different ways gives rise to different modulation schemes. A. Modulation schemes Of the many modulation schemes Binary Shift Keying is the simplest to implement. BSK relies on two possible states of the signal. Take for example FSK, where two different frequencies are chosen []. One frequency corresponds to 0, the space frequency, and on to 1, the mark frequency. However, more complicated systems are also possible. These systems can use for example multiple frequency, phase or amplitude channels to transmit data in a parallel fashion. Quadrature Shift Keying (QSK) relies on four possible states, and ties each state to a bit combination: 0-0, 0-1, 1-0 and 1-1 [1]. These techniques have either a higher baud rate (symbols per second), bit rate or both. However the analysis and implementation of these techniques is more complicated than BSK. Only BSK techniques are compared. However please note that bit rate performance could be increased drastically, at the cost of a higher complexity and higher power and bandwidth requirements. A scheme can be either coherent or non-coherent. Coherent schemes require a reference signal at the receiver that is matched in phase to the transmitted signal. Non-Coherent schemes do not have knowledge of the phase of the carrier but do require bit-timing information. Non-coherent schemes are generally less complex, but also perform worse when compared to its coherent counterpart. B. Comparison Of Binary Modulation Techniques The BER of each binary modulation technique can be compared only in similar conditions. Figure shows a comparison of coherent and non-coherent binary schemes for comparable noise levels, the same energy per bit E b and the same bit time T s. The figure plots the average bit energy to noise power E b N 0. BAFK and BFSK have the same BER for both coherent and non-coherent detection. In general resistance against noise is worst when using amplitude modulation. Both phase and frequency modulation are less sensitive. Especially in a noisy environment like a soccer match noise is abundant. Therefore phase or frequency modulation seems preferable. Fig.. BER performance of several binary modulation schemes [4]. Considering both noise and BER performance BPSK is preferable. BPSK requires more complicated ways of demodulation. However, using sound to communicate requires a highly robust modulation scheme because noise is abundant in many possible applications of the system. Therefore BPSK is the modulation scheme of choice in Audio Transfer. IV. BINARY PHASE SHIFT KEYING The BPSK procedure produces a message wave with sinusoidal characteristics. Such signals, and any other set of M finite energy signals s i (t), can be represented by a linear combination of N orthogonal basis functions where N M. This procedure is called the Gram-Schmidt Orthogonalization Procedure [4]. This means that Equation 1 holds, where φ is one of these basis functions. { Ts 1, i = k φ i (t)φ k (t)dt (1) 0, i k 0 A BPSK signal can be constructed using Equation where E b is the energy per bit in the signal. { A sin(πf c t + 0) = A sin(πf c t), bit = 1 s BP SK (t) = A sin(πf c t + π) = A sin(πf c t), bit = 0 () Only the orthogonal basis function in Equation 3 is needed to construct this type of signal. φ 1 (t) = A sin(πf c t) (3)

3 EINDHOVEN UNIVERSITY OF TECHNOLOGY, DEPARTMENT OF MECHANICAL ENGINEERING 3 Here, f c is the carrier frequency of the signal and A the amplitude of the signal. The signal can be demodulated using either a non-coherent or coherent scheme. Both methods will be compared. A. Non-Coherent Versus Coherent BPSK Non-coherent demodulation of a BPSK signal can be done using a differential coding scheme. The differential coding technique uses a starting bit which is know beforehand. It looks at the phase shift of the signal at each bit time step to determine if the bit has to be switched or not. A simple way of implementing this procedure is by taking the current signal with a length of one bit time and multiplying this with the previous bit signal. This signal is then integrated. A decision rule is implemented to determine whether the state of the bit has changed, where a negative integral results in flipping of the bit [5]. Figure 3 shows a block diagram indicative of differential coding. Fig. 4. Block diagram of a Costas loop [6]. A. Mathematical Description Of The Costas Loop Referring to Figure 4, the input signal in Equation 4 is constructed using a modulating signal m(t) and the orthogonal BPSK basis function in Equation 3. Here A i is the amplitude of the received signal, ω i t is the frequency of the signal and θ i signifies the phase. u i (t) = A i m(t)sin(ω i t + θ i ) (4) The modulating signal will consist of either 1 or -1, indicating a 1 bit or 0 bit respectively. This signal is multiplied by the signals generated by the VCO, where u o is offset 90 degrees from u o1. Fig. 3. Block diagram of a differential binary phase shift keying demodulation set-up [5]. u o1 (t) = A o sin(ω i t + θ o ) (5) Coherent demodulation uses the absolute phase of the received signal to determine the state of a bit. To determine what part of the signal forms a bit the receiver needs to be synchronised with the transmitter. Using a Costas loop in the receiver takes care of both demodulation and synchronisation simultaneously. Demodulation using non-coherent differential coding is easier to implement then its coherent counterpart using the Costas loop. However coherent demodulation generally has a lower BER and thus more robust performance under noisy conditions, illustrated in Figure. Because of the importance of robust performance in the current system the Costas loop will be used for demodulation. V. THE COSTAS LOOP Shown in Figure 4, the Costas loop not only demodulates the signal but also enables synchronisation of receiver and transmitter [6]. The Costas loop consists of an internal oscillator which is normally controlled by a voltage (hence Voltage Controlled Oscillator or VCO). Low pass filters (LPF) and loop filters (LF) are used in the loop to filter unwanted signal components. This particular loop is used to demodulate a BPSK signal. Other Costas loop implementations can be used to demodulate quaternary schemes as well. u i (t) = A o cos(ω i t + θ o ) (6) These signals should have the same base frequency as the BPSK signal, yet can have a different phase indicated by θ o. Multiplication and rewriting using trigonometric rules provides the next set of equations. u d1 (t) = A oa i u d1 (t) = A oa i m(t)cos(θ i θ o ) A oa i m(t)sin(ω i t+θ i +θ o ) (7) m(t)sin(θ i θ o )+ A oa i m(t)sin(ω i t+θ i +θ o ) (8) These are then passed through the LPF to filter out the high frequency components produced by the second part of the equations. This filtering action provides u I (t) and u Q (t) which are dependent on the phase difference θ i θ o of the received signal and the internal oscillator. These signals are multiplied to obtain u d (t). u I (t) = A oa i m(t)cos(θ i θ o ) (9) u Q (t) = A oa i m(t)sin(θ i θ o ) (10) u d (t) = (A oa i m(t)) sin((θ i θ o )) (11) 8

4 EINDHOVEN UNIVERSITY OF TECHNOLOGY, DEPARTMENT OF MECHANICAL ENGINEERING 4 The multiplied signal is passed through a loop filter and is low pass filtered. Because m(t) is either -1 or 1, m(t) = 1. Thus u f (t) is produced which is used to compensate the phase θ o of the VCO signal. u f (t) = (A oa i ) sin((θ i θ o )) (1) 8 When the phase is sufficiently compensated so that θ i θ o once can approximate Equation 9 and 10 with 13 and 14. u I (t) = A oa i m(t)cos(0) = A oa i m(t) (13) u Q (t) = A oa i m(t)sin(0) = 0 (14) The modulated signal m(t) can then directly be read through u I (t) by setting A i = 1 and A 0 =. The resulting phase compensation can be used to calculate the internal lag of the receiver compared to the transmitter. This enables the starting point of each bit to be determined. This way a separate signal with a reference clock is not needed. B. Filter Design Two filters are used in the Costas loop: A low pass filter and a loop filter [6]. The low pass filter is designed using the transfer function of Equation 15. All frequencies above the relevant carrier frequency f c are filtered with K lpf the filter gain and τ = 1 f c. LP F = K lpf τs + 1 (15) The loop filter is a third order phase locked loop with a transfer function equal to the one in Equation 16. The parameters T = 1 ω and T 3 = 1 ω 3 are determined using corner frequencies ω and ω 3 which are defined in Equation 17 and 18. VI. ERROR CONTROL CODING Basic forms of error control coding are used to check the correctness of transmitted messages. More advanced schemes can even be used to correct certain errors on the receiver side. Currently, a checksum is used to detect validity of the received data. The implemented checksum cannot be used to correct errors, only to detect them. The checksum is a combination of bits which is obtained by doing certain binary operation on the bits to be transmitted. The checksum is (very) unique and sent is sent along with the message to the receiver. At the receiver side the checksum is evaluated against a local checksum over the same bits. When the checksums match it is very probable that the message had been delivered correctly. The method introduces overhead into a packet, meaning that the information bits need to be accompanied by several bits of checksum data. This reduces the effective data rate across the channel. VII. AUDIO TRANSFER MATLAB IMPLEMENTATION Audio Transfer is implemented using Matlab. The Matlab script is build up out of scripts corresponding to Figure 1 with exception of the source encoding block, which has not been implemented. This might be an opportunity to increase system performance in future works. The current set-up is not a realtime implementation of Audio Transfer. A. Transmitter A string of text is entered and converted to 8-bit integer values. These values are then converted into binary strings, which are fed into the channel encoder function. The channel encoder uses the string of binary values to construct packets. These packets, shown in Figure 5, will later be send across the audio channel one at a time. LF = k o k d 1 + st s T 1 (1 + st 3 ) (16) ω = ω T 10 (17) ω 3 = ω T 10 (18) Here ω T is defined as ω T = ω 3dB 1.33 with the 3dB closed loop bandwidth ω 3dB = 0.05ω 0 and VCO center frequency ω 0. The parameter T 1 has been chosen to make sure that the loop gain is 1 at ω = ω T as shown in Equation 19. LF = k o k d 1 + st s T 1 (1 + st 3 ) (19) Both filters are transformed to discrete transfer functions in the digital version of the Costas loop. Fig. 5. Representation of a packet sent over a sound channel using Matlab. A packet contains a flag, data bits and a checksum. The flag is used in the channel decoder on the receiver side to mark the beginning of each packet. The checksum is used to determine the correctness of the received packet and is calculated using the flag and data bits. The current size of the packet is bits. Once the packets have been constructed, the modulator modulates a BPSK signal to be transmitted. The message signal s mes consists of a binary signal s bin, a carrier signal s car and an envelope signal s end according to Equation 0. Examples of these signals are shown in Figures 6 and 7. s mes = s bin s car s env (0)

5 EINDHOVEN UNIVERSITY OF TECHNOLOGY, DEPARTMENT OF MECHANICAL ENGINEERING 5 Fig. 6. An example of the binary signal and the carrier signal used to construct a message signal. Fig. 8. A measured signal at 10 bit/s and carrier frequency 3000 Hz without an envelope signal. Fig. 7. An example of an envelope signal and message signal. Fig. 9. A measured signal at 10 bit/s and carrier frequency 3000 Hz using an envelope signal to reduce amplitude spikes. The envelope signal is designed to reduce the amplitude of the signal to zero at each phase switch in the system [5]. Figures 9 and 8 show signals at the receiver side (bandpass filtered at the carrier frequency), one with envelope function and one without. A switch in phase forces a speaker to drastically adjust its membrane to accommodate for the received signal. This produces a clicking sound which has a high amplitude compared to the rest of the signal, due to the speed necessary to produce the signal. This clicking noise interferes with the locking of the Costas loop. The envelope signal reduces this problem. B. Receiver Both demodulation and synchronisation at the receiver side are handled by a digital Costas loop. In addition to the filters described earlier used in the loop a bandpass filter is used. It has been designed using Matlabs fdesign.bandpass function. It lets signals at the carrier frequency of the BPSK signal pass and suppresses the rest. In this way, unwanted noise is filtered out of the incoming signal. This filtered signal is then normalized using the highest remaining amplitude in the signal and fed into the Costas loop. The Costas loop implementation works by first initializing the necessary filters. This initialization is used to determine the transfer function coefficients used at the wanted carrier frequency of the message signal. The transfer functions have been converted into discrete time domain functions, and the coefficients are used to complete the filter functions [7]. This makes implementation of the filters easier in other programming languages. An internal signal is generated based on the difference of the received signal phase and internal signal phase as shown in Equation 1. This signal is multiplied by a loop gain K l to be able to tune the Costas loop and influence performance. This changes Equation 1 slightly into equation 1. u f (t) = K l (A oa i ) sin((θ i θ o )) (1) 8 When the loop locks, the decoded signal should match the transmission. A script is used to implement a decision rule over the average of the amount of samples per bit. The samples are offset by the phase which is gained from the Costas loop, resulting in a string of bits which are sent to the channel

6 EINDHOVEN UNIVERSITY OF TECHNOLOGY, DEPARTMENT OF MECHANICAL ENGINEERING 6 decoder. This string of bits is looped through to check for flag bits or the inverse. This inverse is checked because the output of the Costas loop is inverted when the transmitted signal has a phase difference larger then π. Figures 10 and 11 show the output of the Costas loop for both situations. Both the normal and inverse packets are checked using the checksum sent at the end of each packet. The correct packets are then decoded and the result is stored in a character string. VIII. MEASUREMENTS AND RESULTS The development of Audio Transfer has been accompanied with a number of measurements. Of these measurements the final ones will be treated here as an indication of the performance of the system. The first test will not use an audio channel. Instead, the data will be send directly to the receiver to eliminate any noise and interference. The second test uses the hardware of a HP Elitebook 8570w. The last four test are measured using SPEAKER EN MIC MODEL which are modular units and can be hooked up to the laptop using an USB connection. All tests took place in the Robocup soccer field at the TU/e with different placements and noise. The following experiments have been performed: 1) The audio data is directly passed to the receiver without producing any sound. ) The hardware of a HP Elitebook 8570w is used on the same laptop to send and receive messages in close proximity. There is no noise in the environment. 3) Two laptops are placed on an indoor soccer field approximately 7 meters apart. There is a direct line of sight and little environmental noise. Fig. 10. Signal from Costas loop without phase shift. The transmission signal has been transmitted directly to the receiver. 4) Two laptops are placed on an indoor soccer field approximately 7 meters apart. There is no direct line of sight and little environmental noise. 5) Again two laptops at the same distance. There is a direct line of sight and the environmental noise is considerable (loud music). 6) Again two laptops at the same distance. There is no direct line of sight and the environmental noise is considerable (loud music). Fig. 11. Signal from Costas loop with a phase shift of 180 degrees. The transmission signal has been transmitted directly to the receiver. Both the normal and inverse correct packet counters are checked against each other. The largest value determines which method is correct. An interesting addition to Audio Transfer in the future might therefore be to reduce calculation overhead caused by this method of decoding. All this eventually leads to a received message. In addition to the demodulation the scripts also shows data and plots used to analyse performance. The main measure of performance in this case it the packet loss across the channel. Additional tools include time and frequency domain plot of the send and received signals and filter transfer functions. In addition all experiments have been performed at a carrier frequency of 3000 Hz and a bit frequency of 10 bit per second. A total of 10 packets has been sent every time. The sound has been sampled at Hz. Therefore the sampled signal stays well within the bounds of the NyquistShannon sampling theorem. The resulting packet loss is shown in Table I. Packet loss is defined as ratio of correctly received packets divided by total amount of packets transmitted. It is related to the Bit Error Rate and indicates the quality of each transmission. TABLE I EXPERIMENTAL RESULTS Experiment number Packet loss [-] During experiment 1 no losses should occur during transmission. Yet the packet loss is not zero. The cause seems to be the time needed for the Costas loop to lock to the receiver signal. The first few bits are not decoded correctly, and as a consequence the first packet does not arrive correctly. The quality of processing the signals is subject to the chosen loop gain used by the VCO of the Costas loop. For the

7 EINDHOVEN UNIVERSITY OF TECHNOLOGY, DEPARTMENT OF MECHANICAL ENGINEERING 7 Fig. 1. Phase compensation for experiment 1. K l : Fig. 14. Phase compensation for experiment. K l : same experiment a different loop gain can be the difference between a stable phase compensation with a nearly flawless data transfer and an unstable system where no packet is detected correctly at all. Plotting the phase compensation θ o introduced in 5 in Figures 1 and 13 shows the impact of a higher loop gain leading to instability of the system. However, the phase compensation of experiment shown in Figure 14 shows that compensation can seem unstable while still having good system performance at 10 percent packet loss. Fig. 15. Value of u f for experiment 1. K l : Fig. 13. Phase compensation for experiment 1 where loop gain is to high. K l : Stability of the receiver is not necessarily indicated by a steady slope in phase compensation. When phase drift occurs between the receiver and the transmitter the phase compensation does not have to be constant, but the value of u f of 1 should be always go to zero when the Costas loop is stable. Figures 15, 16 and 17 show u f as a function of time for the first and second experiments. This shows that both the first and second experiment are indeed stable for the correct loop gain K l, but can become unstable if the loop gain is chosen incorrectly. Fig. 16. Value of u f for experiment 1. K l : It can be concluded that in order for the receiver to work the loop gain must be chosen in such a way that stability of the Costas loop is guaranteed. It seems however that it is not always possible to choose a gain which ensures this. The results presented here are the result of tuning the loop gain

8 EINDHOVEN UNIVERSITY OF TECHNOLOGY, DEPARTMENT OF MECHANICAL ENGINEERING 8 in such a way that the phase compensation is stable when possible and the resulting package loss is minimal. Fig. 18. Phase compensation of experiment 3. K l : Fig. 17. Value of u f of experiment. K l : From experiment 4 through 6 it is possible to conclude that a direct line of sight between the microphone and speaker is needed for the system to perform well. Both experiment 4 and 6 result in a packet loss of 1. The broken line of sight influences the quality of the received signal significantly. As only reflections of the signal can reach the microphone, phase tracking becomes unstable. This behaviour is observed in the phase compensation of experiment 4 and 6 shown in Figures 19 and 1.The receiver is not able to lock in either experiment. However, surrounding noise does not seem to be a problem. On the contrary, the experiment with noise shows no packet loss whatsoever. The cause possibly lies in the initial phase difference between the transmitting signal and internal receiver signal. Figures 18 and 0 show the phase compensation of experiment 3 and 5 respectively. The phase at experiment 5 is stable throughout the whole experiment. The phase at experiment 3 on the other hand shows plateaus of stable tracking interleaved with unstable behaviour. This behaviour could be explained due to the initial phase difference between transmitter and receiver. Equation 1 shows that if u f is smaller initially, the resulting phase correction is smaller as well. In short the system also shows stochastic behaviour in the form of the initial phase difference between transmitter and receiver, but is not heavily influenced by loud noise in its surroundings. IX. CONCLUSION AND FUTURE IMPROVEMENTS Sound is especially useful because it is not necessary to know where the receiver is located. In this way a large network of robots can be reached simultaneously. Data has been successfully transmitted at a bit-rate of 10 bits per second. At close ranges closer than 1 meter the transmission is near perfect with a packet loss of about 10 percent. Performance at 7 meter distance show more variance with packet loss between Fig. 19. Phase compensation of experiment 4. K l : Fig. 0. Phase compensation of experiment 5. K l : and 60 percent. When no direct line of sight is present the system has difficulty locking and packet loss is 100 percent. The biggest problem as of now is the need for tuning the loop gain K l of the receiver. Each situation seems to require a different gain to function optimally. Eliminating this need

9 EINDHOVEN UNIVERSITY OF TECHNOLOGY, DEPARTMENT OF MECHANICAL ENGINEERING 9 [6] B. Shamla and K. G. Gayathri Devi. Design and implementation of Costas loop for BPSK demodulator. 01 Annual IEEE India Conference, INDICON 01, pages , 01. [7] B Silvano. Digital Implementation of discrete-time controllers. (June), 001. Fig. 1. Phase compensation of experiment 6. K l : would make the system much more practical for actual use. Other limiting factors include the quality of the used hardware such as sound cards, microphones and speakers and the current need for a direct line of sight between transmitter and receiver. The system in its current form is suited for repeated transmission of data at a low data rate. Transmission of markers is a feasible way to implement Audio Transfer. The marker can consist of an 8-bit integer which is used to communicate state information between individual robots in a network. It is possible to for multiple robots to broadcast at once at different carrier frequencies. However experiments on the interference of parallel broadcasting need to be performed to test performance under such conditions. Future improvements on the system might enable reliable communication of more complex forms of data such as sensor-, state- or world model data. Future implementations of Audio Transfer could explore other error control coding schemes to increase robustness, add data reconstruction capability or decrease overhead in the data packets. Furthermore, the current packet arrangement can be optimized. The amount of information bits is small relative to the checksum resulting in a large overhead in the packet. Future implementations might use a smaller checksum and data compression for increased performance. Broadcasting of data across across an open area is the most logical possibility when taking current system limitations into account. If robustness is increased, sound proves to be a viable communication modality for the networked robotic systems of the future. REFERENCES [1] R H S Budé. Comparison of Phase Demodulation techniques for the DCF77. pages 1 7, 015. [] Schnyder Franz and Haller Christoph. Implementation of FM Demodulator Algorithms on a High Performance Digital Signal Processor. Spectrum, 00. [3] Ali Grami. Introduction. Introduction to Digital Communications, pages 1 10, 016. [4] Ali Grami. Passband Digital Transmission. Introduction to Digital Communications, pages , 016. [5] Francis Iannacci and Yanping Huang. ChirpCast: Data Transmission via Audio. ArXiv, pages 1 10, 015.