WO2020210762A1 - Analog pulse sequence encoding and cycle recovery for spectrum efficient high density data - Google Patents

Abstract

Aspects of the present disclosure are related to systems and methods for an analog pulse sequence based encoding and data recovery scheme for high density data communication. One such method comprises generating a plurality of orthogonal pulses; generating a plurality of data sequences based upon different time slot combinations comprising each of the plurality of orthogonal pulses; generating a unified pulse sequence by combining the plurality of data sequences at corresponding time slots; and transmitting the unified pulse sequence.

Description

ANALOG PULSE SEQUENCE ENCODING AND CYCLE RECOVERY FOR SPECTRUM EFFICIENT HIGH DENSITY DATA

CROSS-REFERENCE TO RELATED APPLICATIONS [0001] This application claims the benefit of and priority to U.S. Provisional Application having serial number 62/832,946, having the title “ANALOG PULSE SEQUENCE ENCODING AND CYCLE RECOVERY FOR SPECTRUM EFFICIENT HIGH DENSITY DATA,” filed on April 12, 2019, the disclosure of which is incorporated herein by reference in its entirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with government support under agreement ECCS- 1813949 awarded by the National Science Foundation. The Government has certain rights to the invention.

TECHNICAL FIELD

[0003] The present disclosure is generally related to high-density data communications.

BACKGROUND

[0004] High volume data acquisition has become an important research field in wireless communications for technological advancements that can impact humanity. The proliferation of sensors and the Internet-of-Things (loT) based connected world will need immense of data flow through the wireless media. However, the limited wireless bandwidth defined by the Federal Communications Commission (FCC) limits the number of channels and data rate through a specified wireless channel.

SUMMARY

[0005] Aspects of the present disclosure are related to systems and methods for an analog pulse sequence based encoding and data recovery scheme for high density data communication. In one aspect, among others, such a method comprises generating a plurality of orthogonal pulses; generating a plurality of data sequences based upon different time slot combinations comprising each of the plurality of orthogonal pulses; generating a unified pulse sequence by combining the plurality of data sequences at corresponding time slots; and transmitting the unified pulse sequence.

[0006] In one or more aspects, the plurality of orthogonal pulses are a plurality of modified Flermitian pulses (MFIPs), a pulse width for each of the MFIPs is 20 ns, each of the plurality of data sequences are generated over 4 time slots, and/or the plurality of MFIPs are four distinct MFIP pulses.

[0007] In another aspect, synchronizing pulses are added at a beginning and at an end of the unified pulse sequence prior to transmission, the unified pulse sequence is transmitted via an ultra-wide band (UWB) antenna, each data sequence corresponds to an individual data bit, and/or the unified pulse sequence comprises 24 data sequences superimposed over 4 time slots.

[0008] In another aspect, a method for high density data communication comprises receiving a unified pulse sequence signal comprising a combination of data sequences based upon different time slot combinations of a plurality of orthogonal pulses; decoding the orthogonal pulses from each time slot of the unified pulse sequence signal using cyclic pulse elimination; and generating a recovered pulse output based upon pulse sequences of the decoded orthogonal pulses for the time slots of the unified pulse sequence signal. In one or more aspects, the pulse sequences are identified using a look-up table

[0009] Aspects of the present disclosure are also related to a system for high density data communication comprising pulse sequence generation circuitry configured to generate a plurality of modified Hermitian pulses (MHPs) that are orthogonal; generate a plurality of data sequences based upon different time slot combinations comprising each of the plurality of MHPs; and generate a unified pulse sequence by combining the plurality of data sequences at corresponding time slots. Such a method further comprises a wireless transmitter configured to transmit the unified pulse sequence.

[0010] In another aspect, the system further comprises a wireless receiver configured to receive a signal comprising the unified pulse sequence; decode MHPs from each time slot of the unified pulse sequence using cyclic pulse elimination; and generate a recovered pulse output based upon pulse sequences of the decoded MHPs for the time slots of the unified pulse sequence.

[0011] Other systems, methods, features, and advantages of the present disclosure will be or become apparent to one with skill in the art upon examination of the following drawings and detailed description. It is intended that all such additional systems, methods, features, and advantages be included within this description, be within the scope of the present disclosure, and be protected by the accompanying claims. In addition, all optional and preferred features and modifications of the described embodiments are usable in all aspects of the disclosure taught herein. Furthermore, the individual features of the dependent claims, as well as all optional and preferred features and modifications of the described embodiments are combinable and interchangeable with one another.

BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Many aspects of the present disclosure can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present disclosure. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views.

[0013] FIG. 1 is a diagram of a communication environment employing various sensor networks in different wireless data communication sectors in accordance with the present disclosure.

[0014] FIG. 2 shows a block diagram of an exemplary data communication system in accordance with various embodiments of the present disclosure.

[0015] FIG. 3 shows 4-distinct modified Hermitian pulses (MHPs) and their 25% time shifted pulses (SMHPs) in accordance with various embodiments of the present disclosure.

[0016] FIG. 4 illustrates 24-distinct pulse-sequences generated by 4-different orders of orthogonal pulses in accordance with various embodiments of the present disclosure.

[0017] FIG. 5 illustrates a composite signal having 24-distinct pulse-sequences in accordance with various embodiments of the present disclosure.

[0018] FIG. 6 shows a power spectral density of various pulses and their composite signal in accordance with various embodiments of the present disclosure.

[0019] FIG. 7 shows a composite signal with a 20 dB additive white Gaussian noise (AWGN) signal in accordance with the present disclosure. [0020] FIG. 8 is a flow chart diagram of an exemplary cyclic pulse elimination process in accordance with various embodiments of the present disclosure.

[0021] FIGS. 9A-9FI presents a table displaying correlation peaks of individual pulses for a composite signal across different time slots in accordance with various embodiments of the present disclosure.

[0022] FIGS. 10A and 10B show an ultra-wideband (UWB) communication system using existing radio frequency (RF) modules in accordance with embodiments of the present disclosure.

[0023] FIGS. 1 1 A and 1 1 B show images of an experimental set up and test results for the ultra-wideband communication system of FIGS. 10A-10B.

DETAILED DESCRIPTION

[0024] In accordance with various embodiments of systems and methods of the present disclosure, an analog pulse sequence based encoding and data recovery scheme is presented for high density data communication. In an exemplary methodology, multi-order orthogonal Flermite polynomial pulses can be arranged in distinct sequences for multiple channels and be superimposed to create a unified pulse stream for simultaneous transmission of multiple channels or bits through a limited bandwidth wireless channel without creating unwanted network congestion and latency. Such a scheme can achieve (n - 1)! times data rate improvement, where n represents that number of distinct orthogonal Flermite pulses.

[0025] In general, high volume data acquisition is a relevant research field in wireless communication for the advancement of technological impact on humans. The Ultra-wideband (UWB) system is superior for large relative bandwidths to achieve the high-density data transmission. Due to the integration of a large number of sensor recording channels in the telemetry system, the UWB technology has been widely used in sensing applications such as patient health monitoring, military surveillance, position tracking, radar applications as well as Internet of Things (loT) applications, etc. Accordingly, FIG. 1 shows different sensor networks and their broader applications in different wireless data communication sectors. UWB is one of the superior technologies for high-density data communication due to the robustness, the lower energy level of radio spectrum and low degree of interference, higher obstacles penetrations, lower power consumption, high data rate, and broader bandwidth.

[0026] The significant difficulties in high volume wireless data communication are low data transmission rate, multi-user data transmission, data interference, and successfully reception of data at the receiver end. The analog orthogonal pulse-based UWB data communication technology is superior for personal area networks, sensor networks, and short-range positioning. The main challenge in the pulse-based UWB system is the proper orthogonal pulse set generation and their higher-order derivatives.

[0027] Referring to FIG. 2, a block diagram of an exemplary communication system 200 in accordance with various embodiments of the present disclosure is shown. In accordance with the present disclosure, such a communication system 200 can leverage the state-of-the-practice wireless sensor module and integrate orthogonal pulse based impulse radio ultra-wide band (IR-UWB) telemetry. IR-UWB wireless telemetry offers energy efficient secure, reliable and relatively higher data rate communication. The integration of multi-order orthogonal pulse based encoding with the IR-UWB can offer data-compression that enables higher data density and secure communication without overburdening the communication network.

[0028] In one embodiment, the communication system performs a novel pulse- sequence based data encoding and decoding scheme (using pulse-sequences and a cyclic pulse elimination algorithm respectively) for spectrum efficient high-density data communication, thereby increasing the data transmission rate by supporting a large number of data channels. In the figure, an analog pulse based UWB transmitter section 210, a channel, and an analog pulse based UWB receiver section 220 are depicted. The transmitter’s prime motive is to convert a data stream into symbols and map these symbols onto an analog waveform of orthogonal pulses and transmit the analog waveform via the air through the transmitting antenna (e.g., UWB antenna). In addition to an improved pulse sequence generator, the transmitter section 210 uses existing radio frequency (RF) modules including a pulse modulator, a local oscillator, a power amplifier, and the transmitting antenna. As a model-based design, in one embodiment, the pulse sequence generator is implemented in a MATLAB Simulink and is designed for sub-GHz UWB communications to produce a modified Hermitian pulse (MHP) set with a pulse width of 20ns, although different pulse widths can be utilized in different embodiments, such as 10 ns, among others.

[0029] For pulse-sequence generation, an exemplary data encoding scheme is based on properties of orthogonal Hermite pulses, in which a series of analog orthogonal pulses represent a single data bit or channel instead of a regular single Gaussian pulse for multi-user applications. Thus, a serial-parallel data transmission technique can be used to describe the data bit by a set of distinct MHP pulses. In this approach, a collection of unique pulse-sequences is assigned for different data channels or bits to encode the digital data. In one embodiment, the exemplary data encoding scheme supports a total of, as a non-limiting example, 24 data channels by applying the permutation technique of using, but not limited to only using, four (4) distinct higher-order MHP pulses. The permutation of 4-distinct orthogonal pulses (represented as MHP0, MHP1 , MHP2, MHP3) generates the sequence of pulse patterns, as shown in Table-I (below).

TABLE I: Pulse-sequence scheme for 4-different orthogonal pulses

[0030] In various embodiments, a switch matrix architecture is used to create the pulse-sequence by switching the incoming 4-MHP pulses. The MHP pulse set has the orthogonality property that coexists at a specific time slot (represented as TS1 , TS2, TS3, or TS4 in Table I) by sharing the same bandwidth of each data channel. All the 24 pulse-sequences are then superimposed with their corresponding time slots to create a unified pulse-sequence. The unified pulse-sequence occupies 4 time slots compared to a single time slot in conventional UWB. However, in an exemplary scheme, spreading of the unified pulse-sequence over 4 different time slots can generate 24 different pulse- sequences that support 24 data bits compared to 4 data bits in a conventional UWB. This data compression scheme takes place without using any sophisticated digital signal processing or computation. One benefit of an exemplary MHP based combinational pulse encoding scheme, in accordance with various embodiments of the present disclosure, is the simultaneous pulse spectrum sharing and supporting of high- density data compression within the limited bandwidth.

[0031] In such an analog orthogonal pulse-based data communication technique, a single or multiple users' data can be encoded by using 4 distinct order pulses. For example, in a single-user data encoding scheme, each pulse can represent either a single or multiple data bits using orthogonal pulses. However, in multi-user data encoding, each sequence of the pulses (containing 4-distinct pulses) can represent a single bit or a couple of bits of information. In accordance with an exemplary embodiment, FIG. 3 shows 4-distinct order MHPs and their 25% time-shifted pulses, in which the 4 distinct higher order modified Hermite Polynomial Pulses (namely zeroth, first, second, and third order pulses) are represented as MHP0, MHP1 , MHP2, and MHP3, respectively and their time-shifted pulses are represented by SMHP0, SMHP1 , SMHP2, and SMHP3, respectively.

[0032] In this pulse encoding scheme, each distinct pulse sequence represents a distinct wireless channel. Since the UWB pulses have the orthogonality at a certain time slot, the entire pulse sequence from the individual mobile agent (channel) can use same bandwidth. For example, in an exemplary method, 4 distinct MHP pulses create a total of 24 data sequence channels which can be transmitted together within a certain time instant. Adding all of the 24 data sequences at the corresponding time slots creates a unified pulse sequence (UPS) that can be transmitted via the transmitting antenna. In various embodiments, two synchronizing pulses are added at the beginning of the data sequence and at the end of the sequence for proper synchronizing before transmission. [0033] In an exemplary embodiment, MATLAB tools can be used to generate an exemplary encoding scheme of pulse sequences using the MHP pulse set. Accordingly, FIG. 4 illustrates 24-distinct pulse-sequences generated by 4-different orders of MHPs. All the MHP pulses are normalized within the amplitude ranges from -1 to 1 . These pulses are orthogonal to each other such that each can coexist with other pulses. Due to the orthogonality of the MHPs at a specific time slot, the entire pulse-sequence can use the same bandwidth and all the pulse-sequences can be superimposed to make a composite signal. Thus, due to the orthogonality properties of Hermite pulses, a composite signal can be generated by superimposing the MHP pulse sequences to increase the data transmission rate by supporting multi-user communication within the same frequency band, in accordance with various embodiments of the present disclosure. As such, FIG. 5 illustrates a composite signal of all the 24-distinct sequence of pulses (shown in FIG. 4) made over 4-distinct time slots.

[0034] To verify the power requirements of the transmitted signal in the UWB communication defined by the Federal Communication Commission (FCC), the power spectral density (PSD) is plotted in MATLAB, in which the PSDs of individual MHPs, shifted MHPs, and the composite signal are shown in FIG. 6. The power spectral density of all MHP pulses meets the FCC Equivalent Isotropically Radiated Power (EIRP) mask for indoor communications. The simulation results show that all the individual pulses and their composite signal meet the FCC requirement. Therefore, sets of orthogonal MHPs and SMHPs can be used to transmit digital data in a UWB communication system.

[0035] For the analog pulse based UWB receiver section 220, the receiver collects the transmitted pulses, reconstructs them, and maps symbols into a binary stream. In FIG. 2, the receiver section 220 is composed of existing RF modules including a receiving antenna, a low noise amplifier, a pulse demodulator, and a local oscillator in addition to a correlator based cyclic pulse elimination block or circuitry. In the receiving section, the correlator block can decode the composition of the received composite pulses and, in our non-limiting example, determine the 4 bits data (represented by the distinct MHP pulses) from the transmitted pulse sequence by analyzing the composition of the received pulses.

[0036] In the correlator block, the composite pulses are received and applied to the cyclic pulse elimination (CPE) process to recover the transmitted data. For example, the receiver can determine if a channel is transmitting a binary 1 or 0 by matching the assigned pulse-sequence corresponding to the transmitter pulse pattern. If the recovered pulse-sequence is matched with the corresponding transmitter pulse- sequence pattern, then the message comes from that particular channel. The cyclic pulse elimination (CPE) process is performed as part of the pulse decoding scheme. In one embodiment, a 20 dB additive white Gaussian noise (AWGN) may be introduced with a composite signal during transmission, as shown in FIG. 7. Nonetheless, the cyclic pulse elimination (CPE) process can easily detect the pulse with a higher correlation peak. Accordingly, FIG. 8 shows a flow chart of an exemplary CPE technique or process in accordance with embodiments of the present disclosure.

[0037] As shown in FIG. 8, a correlation coefficient or peak value is found of a composite signal with each pulse and the coefficient peak value is compared with a predefined threshold level. If the correlation peak value is greater than the threshold value, then the corresponding highest correlation peak signal is subtracted from the composite signal and the eliminated pulses are stored. This pulse elimination process will continue until all the distinct pulses from the composite signal are decoded. Similarly, the CPE algorithm is applied in each time slot and all the individual pulses are decoded for each time slot, respectively. Finally, the eliminated single pulses are matched with the prior known pulse template to find the data that comes from the data channel. In one embodiment, a look-up table at the receiver end will identify the pulse sequence based on the decoded orthogonal pulses and the respective time slots. The decoded pulse sequence will indicate the presence or absence of a data channel.

[0038] For an illustrative simulation example, the correlation peak of individual pulses for a composite signal (in each iteration corresponding to each time slot) is shown in Table II (that is illustrated across FIGS. 9A-9FI). The correlation peak value in the first-time slot depicts that, in the first iteration, MFIP3 has the highest correlation peak among others. According to CPE technique, the pulse corresponding to the highest correlation peak is subtracted from the composite signal. Therefore, in this case, the MFIP3 pulse is subtracted from the composite signal. After the first iteration, the MFIP3 pulse is eliminated, and the rest of the pulse remains in the composite signal as shown in in Table II (FIGS. 9A-9FI) in TS1 . Similarly, the rest of the distinct pulses are removed sequentially according to the correlation peak table. This pulse decoding algorithm continues until all the 24 pulses from the composite signal are decoded. After eliminating all the pulses, the AWGN signal remains in the composite signal, and the correlation peaks corresponding to each pulse are much lower than the predefined threshold level set at 0.2.

[0039] Similarly, the individual pulses are decoded from time slots TS2, TS3, and TS4, respectively, by applying the CPE algorithm. After eliminating all the pulses, corresponding to the 4-distinct time slots, the pulse-sequences are matched with the prior known template to identify a missing pulse-sequence. The missing pulse- sequence can be determined by finding the absent pulses in each time slot using a correlation peak analysis. Usually, the correlation peak of a missing pulse is much lower than the threshold level. In the decoding scheme, if any pulse (among 4-distinct order) is missing corresponding to the first time slot, then the missing pulse will be in that group. For example, if one MFIP1 is missing in the first time slot, then the missing pulse- sequence will be one from channel number 7 to 12. In the second and fourth time slot, each of the MFIP0, MFIP2, and MFIP3 has a 50% chance to absent. Flowever, the second time slot can quickly identify the missing pulse-sequence based on the pulse absent in the second time slot. Similarly, any pulse-sequence among the above 24 sequences of pulses can be identified by the correlation peak analysis.

[0040] A communication system in accordance with the present disclosure can be characterized as a spectrum efficient high volume data communication system and can work with existing networks and use the same communication architecture. In various embodiments, the communication channel can be configured using commercially available RF modules according to the design requirements shown in Table III (below).

TABLE III

[0041] Accordingly, FIGS. 10A and 10B shown an impulse radio ultra-wideband (UWB) communication system using existing RF modules in accordance with embodiments of the present disclosure. To configure the communication channel, initially, an RF signal is generated using a function generator and mixed with a local oscillator (LO) using an amplitude modulation technique. Then, the IF signal of the mixer block or circuitry (Pulse Modulator) is amplified by the power amplifier (PA) before transmitting via the TX antenna, as shown in FIG. 10A. In the receiver section shown in FIG. 10B, the received signal from the RF antenna is amplified first by LNA and fed to a mixer block (Pulse Demodulator). In the mixer circuit, the received RF signal is multiplied with the same LO signal and the low-frequency functional generator signal is demodulated. Next, the demodulated signal is passed through a low pass filter (LPF) to suppress the unwanted higher frequency noise signal. The output of the LPF can be observed using an oscilloscope.

[0042] For testing purposes, a communication channel configuration test set up is implemented in accordance with the system arrangement of FIGS. 10A and 10B. FIG. 1 1 A shows an image of the test setup and an image of the resulting transmitting and receiving signals are shown in FIG. 1 1 B. During testing, a low frequency 50 MHz, 1 .0 Vpp sinusoidal signal was generated using the function generator and modulated with a 500 MHz high-frequency carrier signal using an RF mixer circuit. Then, the IF signal output from the RF mixer circuit was amplified and supplied to the TX antenna. The receiving antenna received the signal transmitted from the TX antenna through air media, in which the signal was amplified by LNA. Then, the received signal was demodulated and passed through a low pass filter. The output of the received signal was observed from the oscilloscope, as shown in FIG. 1 1 B. In the figure, the top and bottom traces represent the 50 MHz transmitting and receiving signals. This result shows that the communication channel is operational and can send and receive a signal from the transmitter to the receiver.

[0043] Embodiments of the present disclosure can deploy an innovative next generation wireless data solution for network reliability and faster transmission speed as part of an innovative wireless sensor platform for simultaneous multi-channel wireless communication for real-time sensing, monitoring, assessment, and control operation. With an exemplary pulse encoding scheme of the present disclosure, a (/?— 1 )!-fold data rate improvement can be achieved, and a traditional 16-channel system can function with n!*16-channel without overburdening the communication bandwidth and creating unwanted network congestion. In accordance with embodiments of the present disclosure, pulse sequence generator circuitry of an exemplary communication system can have a modular circuit architecture with coupled dynamics enabling higher order orthogonal pulse generation and utilizing a combinatorial pulse-sequence based encoding, thereby allowing simultaneous multi-channel wireless telemetry with superb spectrum-efficient data density. In accordance with various embodiments, an innovative cyclic-elimination receiver facilitates the successful recovery of multi-channel orthogonal UWB impulses. Efficacy of such a communication system in terms of data volume, speed, and power consumption can provide an enabling technology for large scale wireless sensing applications. Potential benefits of wireless sensor networking will include enabling new applications by eliminating need for wires, improving the safety by automating processes previously managed manually, reducing costs associated with maintenance with greater reliability and extended battery life, and minimizing deployment time and costs with easy installation and no cabling.

[0044] It should be emphasized that the above-described embodiments of the present disclosure are merely possible examples of implementations set forth for a clear understanding of the principles of the disclosure. Many variations and modifications may be made to the above-described embodiment(s) without departing substantially from the spirit and principles of the disclosure. In various embodiments, systems and methods, in accordance with the present disclosure, can be used with wireless sensor platforms for simultaneous multi-channel wireless communication for real-time sensing, monitoring, assessment and control operation. A modular circuit architecture with coupled dynamics can enable higher order orthogonal pulse generation. All such modifications and variations are intended to be included herein within the scope of this disclosure and protected by the following claims.

Claims

CLAIMS Therefore, at least the following is claimed:

1. A method for high density data communication comprising: generating a plurality of orthogonal pulses;

generating a plurality of data sequences based upon different time slot combinations comprising each of the plurality of orthogonal pulses;

generating a unified pulse sequence by combining the plurality of data sequences at corresponding time slots; and

transmitting the unified pulse sequence.

2. The method of claim 1 , wherein the plurality of orthogonal pulses are a plurality of modified Hermitian pulses (MHPs).

3. The method of claim 2, wherein a pulse width for each of the MHPs is

20 ns.

4. The method of claim 2, wherein each of the plurality of data sequences are generated over 4 time slots.

5. The method of claim 2, wherein the plurality of MHPs are four distinct MHP pulses.

6. The method of claim 1 , wherein synchronizing pulses are added at a beginning and at an end of the unified pulse sequence prior to transmission.

7. The method of claim 1 , wherein the unified pulse sequence is transmitted via an ultra-wide band (UWB) antenna.

8. The method of claim 1 , wherein each data sequence corresponds to an individual data bit.

9. The method of claim 1 , wherein the unified pulse sequence comprises 24 data sequences superimposed over 4 time slots.

10. A system for high density data communication comprising:

pulse sequence generation circuitry configured to:

generate a plurality of modified Hermitian pulses (MHPs) that are orthogonal;

generate a plurality of data sequences based upon different time slot combinations comprising each of the plurality of MHPs; and

generate a unified pulse sequence by combining the plurality of data sequences at corresponding time slots; and

a wireless transmitter configured to transmit the unified pulse sequence.

1 1 . The system of claim 10, wherein each of the plurality of data sequences are generated over 4 time slots.

12. The system of claim 10, further comprising:

a wireless receiver configured to:

receive a signal comprising the unified pulse sequence;

decode MHPs from each time slot of the unified pulse sequence using cyclic pulse elimination; and

generate a recovered pulse output based upon pulse sequences of the decoded MHPs for the time slots of the unified pulse sequence.

13. The system of claim 12, wherein the unified pulse sequence comprises 24 data sequences superimposed over 4 time slots.

14. A method for high density data communication comprising:

receiving a unified pulse sequence signal comprising a combination of data sequences based upon different time slot combinations of a plurality of orthogonal pulses;

decoding the orthogonal pulses from each time slot of the unified pulse sequence signal using cyclic pulse elimination; and

generating a recovered pulse output based upon pulse sequences of the decoded orthogonal pulses for the time slots of the unified pulse sequence signal.

15. The method of claim 14, wherein the pulse sequences are identified using a look-up table.

16. The method of claim 14, wherein the plurality of orthogonal pulses are a plurality of modified Hermitian pulses (MHPs).

17. The method of claim 16, wherein a pulse width for each of the MHPS is

20 ns.

18. The method of claim 16, wherein each data sequence is a series of MHP pulses over 4 time slots.

19. The method of claim 16, wherein the unified pulse sequence signal comprises 24 data sequences superimposed over 4 time slots.

20. The method of claim 16, wherein the MHPs are decoded based upon a correlation with an individual MHP of the plurality of modified Hermitian pulses (MHPs).