Claims:
1. A method for transmitting a sequence of symbols, the method comprising the steps of:
converting the sequence of symbols in the form of bits (0,1);
identifying a fundamental frequency (f0) and using the fundamental frequency (f0) to form a plurality of higher harmonic frequencies (f1, f2, f3….fN-1), wherein N identified frequencies (f0, f1, f2, f3….fN-1) are orthogonal to each other over a time interval of 1/f0 seconds;
dividing the sequence of symbols in the form of bits (0,1)in ratio 1:2:3:...:N to give N partitions and transmitting each of the N partitions; and
adding all the N transmitted partitions for further processing, wherein further processing includes transmission over a transmission channel or decoding, detecting and/or estimating at a receiver.
2. The method of claim 1, wherein the transmission of each of the N partitions is performed for a same transmission duration.
3. The method of claim 1, wherein the transmission of each of the N partitions is performed in the form of an electrical signal by transmitting one of valley to peak part, peak to valley part or maintaining voltage level based on value of a bit from the sequence of symbols in the form of bits.
4. The method of claim 3, wherein when a first bit from the sequence of symbols in the form of bits is 1, peak to valley part is transmitted.
5. The method of claim 3, wherein when the first bit from the sequence of symbols in the form of bits is 0, valley to peak part is transmitted.
6. The method of claim 3, wherein when a subsequent bit from the sequence of symbols in the form of bits is same as previous bit, the voltage level is maintained.
7. The method of claim 3, wherein when the subsequent bit from the sequence of symbols in the form of bits is not same as previous bit and when the subsequent bit from the sequence of symbols in the form of bits is 1, peak to valley part is transmitted.
8. The method of claim 3, wherein when the subsequent bit from the sequence of symbols in the form of bits is not same as previous bit and when the subsequent bit from the sequence of symbols in the form of bits is 0, valley to peak part is transmitted.
9. The method of claim 1, wherein the receiver is enabled to perform distance and/or difference computation.
10. A system for transmitting a sequence of symbols, the system comprising:
a binary converter enabled to convert the sequence of symbols in the form of bits (0,1);
a frequency generator enabled to identify a fundamental frequency (f0) and form plurality of higher harmonic frequencies (f1, f2, f3….fN-1) based on the fundamental frequency (f0), wherein N identified frequencies (f0, f1, f2, f3….fN-1) are orthogonal to each other over a time interval of 1/f0 seconds;
a modulator enabled to divide the sequence of symbols in the form of bits (0,1) in ratio 1:2:3:...:N to give N partitions and further transmit each of the N partitions; and
a summer to add all the N transmitted partitions for transmission over a transmission channel.
11. The system of claim 10, wherein the modulator transmits each of the N partitions for a same transmission duration.
12. The system of claim 10, wherein the modulator performs transmission of each of the N partitions in the form of an electrical signal by transmitting one of valley to peak part, peak to valley part or maintaining voltage level based on value of a bit from the sequence of symbols in the form of bits.
13. The system of claim 12, wherein when a first bit from the sequence of symbols in the form of bits is 1, peak to valley part is transmitted.
14. The system of claim 12, wherein when the first bit from the sequence of symbols in the form of bits is 0, valley to peak part is transmitted.
15. The system of claim 12, wherein when a subsequent bit from the sequence of symbols in the form of bits is same as previous bit, the voltage level is maintained.
16. The system of claim 12, wherein when the subsequent bit from the sequence of symbols in the form of bits is not same as previous bit and when the subsequent bit from the sequence of symbols in the form of bits is 1, peak to valley part is transmitted.
17. The system of claim 12, wherein when the subsequent bit from the sequence of symbols in the form of bits is not same as previous bit and when the subsequent bit from the sequence of symbols in the form of bits is 0, valley to peak part is transmitted.
18. The system of claim 10, wherein the system further comprises a receiver to decode, detect and/or estimate the sequence of symbols.
19. The system of claim 18, wherein the receiver is enabled to perform distance and/or difference computation.
, Description:
TECHNICAL FIELD
The present disclosure relates to the field of modulation and demodulation in a communication system. More particularly, the present disclosure pertains to a system and method for transmitting a sequence of symbols using a non-linear modulation technique.
BACKGROUND
Background description includes information that may be useful in understanding the present invention. It is not an admission that any of the information provided herein is prior art or relevant to the presently claimed invention, or that any publication specifically or implicitly referenced is prior art.
The basic theory underlying channel capacity was developed by Claude Shannon and Ralph Hartley, wherein Shannon-Hartley Theorem is an application of noisy channel coding theorem to an archetypal case of a continuous-time analog communications channel subject to Gaussian noise. The theorem is based on an assumption that signal power is bounded and Gaussian noise process is characterized by a known power or power spectral density. The theorem establishes maximum amount of error-free digital data that can be transmitted over a communications channel with a specified bandwidth in the presence of noise.
Considering all possible multi-level and multi-phase encoding techniques, according to the Shannon-Hartley theorem, channel capacity C, meaning theoretical upper bound on the rate of error free data that can be sent with a given average signal power S through an analog communication channel subject to additive white Gaussian noise of power N is given by;
C=B ¬?log?_2 (1+S/N)
Where:
C is channel capacity in bits per second,
B is bandwidth of the channel in hertz,
S is total signal power over the bandwidth, measured in watts,
N is total noise power over the bandwidth, measured in watts, and
S/N is signal-to-noise ratio (SNR) of the communication signal to the Gaussian noise interference, expressed as a straight power ratio.
Various attempts have been made and various techniques have been developed to beat this formula. One such method used wavelength-based modulation by identifying a fundamental frequency, other higher harmonic frequencies and identifying wavelength of each of the harmonic frequencies. Further, modulating each of the identified wavelengths with a symbol and then summing all the modulated harmonics for transmission over a transmission channel. However, a high spectral leak was evidently seen in these techniques. If there is a high spectral leak, it can cause unwanted interference and can have serious regulatory issues. For example, if a system having high spectral leak is provided a bandwidth of 10 MHz, then there is a high possibility of leakage to adjacent band.
Therefore, there is a need in the art to develop a modulation and demodulation technique that prevents high spectral leak and at the same time gives higher throughput than Hartley-Shannon formula.
As used in the description herein and throughout the claims that follow, the meaning of “a,” “an,” and “the” includes plural reference unless the context clearly dictates otherwise. Also, as used in the description herein, the meaning of “in” includes “in” and “on” unless the context clearly dictates otherwise.
The recitation of ranges of values herein is merely intended to serve as a shorthand method of referring individually to each separate value falling within the range. Unless otherwise indicated herein, each individual value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g. “such as”) provided with respect to certain embodiments herein is intended merely to better illuminate the invention and does not pose a limitation on the scope of the invention otherwise claimed. No language in the specification should be construed as indicating any non-claimed element essential to the practice of the invention.
Groupings of alternative elements or embodiments of the invention disclosed herein are not to be construed as limitations. Each group member can be referred to and claimed individually or in any combination with other members of the group or other elements found herein. One or more members of a group can be included in, or deleted from, a group for reasons of convenience and/or patentability. When any such inclusion or deletion occurs, the specification is herein deemed to contain the group as modified thus fulfilling the written description of all groups used in the appended claims.

OBJECTS OF THE INVENTION
An object of the present disclosure is to provide a system and method for transmitting a sequence of symbols.
An object of the present disclosure is to provide a system and method for transmitting a sequence of symbols having low spectral leakage.
An object of the present disclosure is to provide a system and method for transmitting a sequence of symbols that provides higher throughput than Shannon-Hartley formula.
An object of the present disclosure is to provide a system and method for transmitting a sequence of symbols that uses less number of components, consumes low power and therefore is cost effective.

SUMMARY
Embodiments of the present disclosure relate to systems and methods for transmitting a sequence of symbols.
An embodiment of the present disclosure provides a method for transmitting a sequence of symbols, the method comprising the steps of: converting the sequence of symbols in the form of bits (0,1); identifying a fundamental frequency (f0) and using the fundamental frequency (f0) to form a plurality of higher harmonic frequencies (f1, f2, f3….fN-1), wherein N identified frequencies (f0, f1, f2, f3….fN-1) are orthogonal to each other over a time interval of 1/f0 seconds; dividing the sequence of symbols in the form of bits (0,1) in ratio 1:2:3:...:N to give N partitions and transmitting each of the N partitions; and adding all the N transmitted partitions for further processing, wherein further processing includes transmission over a transmission channel or decoding, detecting and/or estimating at a receiver.
In an aspect, the transmission of each of the N partitions is performed for a same transmission duration.
In an aspect, the proposed method transmits each of the N partitions in the form of an electrical signal by transmitting one of valley to peak part, peak to valley part or maintaining voltage level based on value of a bit from the sequence of symbols in the form of bits. When a first bit from the sequence of symbols in the form of bits is 1, peak to valley part is transmitted. Alternatively, when the first bit from the sequence of symbols in the form of bits is 0, valley to peak part is transmitted. Further, when a subsequent bit from the sequence of symbols in the form of bits is same as previous bit, the voltage level is maintained. Alternatively, when the subsequent bit from the sequence of symbols in the form of bits is not same as previous bit and when the subsequent bit from the sequence of symbols in the form of bits is 1, peak to valley part is transmitted, otherwise, when the subsequent bit from the sequence of symbols in the form of bits is not same as previous bit and when the subsequent bit from the sequence of symbols in the form of bits is 0, valley to peak part is transmitted.
In an aspect, the receiver is enabled to perform distance and/or difference computation.
Another embodiment of the present disclosure provides a system for transmitting a sequence of symbols, the system comprising: a binary converter enabled to convert the sequence of symbols in the form of bits (0,1); a frequency generator enabled to identify a fundamental frequency (f0) and form plurality of higher harmonic frequencies (f1, f2, f3….fN-1) based on the fundamental frequency (f0), wherein N identified frequencies(f0, f1, f2, f3….fN-1) are orthogonal to each other over a time interval of 1/f0 seconds; a non-linear modulator enabled to divide the sequence of symbols in the form of bits (0,1) in ratio 1:2:3:...:N to give N partitions and further transmit each of the N partitions ; and a summer to add all the N transmitted partitions for transmission over a transmission channel.
In an aspect, the modulator transmits each of the N partitions for a same transmission duration.
In an aspect, the modulator performs transmission of each of the N partitions in the form of an electrical signal by transmitting one of valley to peak part, peak to valley part or maintaining voltage level based on value of a bit from the sequence of symbols in the form of bits. When a first bit from the sequence of symbols in the form of bits is 1, peak to valley part is transmitted. Alternatively, when the first bit from the sequence of symbols in the form of bits is 0, valley to peak part is transmitted. Further, when a subsequent bit from the sequence of symbols in the form of bits is same as previous bit, the voltage level is maintained. Alternatively, when the subsequent bit from the sequence of symbols in the form of bits is not same as previous bit and when the subsequent bit from the sequence of symbols in the form of bits is 1, peak to valley part is transmitted, otherwise, when the subsequent bit from the sequence of symbols in the form of bits is not same as previous bit and when the subsequent bit from the sequence of symbols in the form of bits is 0, valley to peak part is transmitted.
In an aspect, the system further comprises a receiver to decode, detect and/or estimate the sequence of symbols.
In an exemplary aspect, the receiver is enabled to perform distance and/or difference computation.

BRIEF DESCRIPTION OF THE DRAWINGS
In the Figures, similar components and/or features may have the same reference label. Further, various components of the same type may be distinguished by following the reference label with a second label that distinguishes among the similar components. If only the first reference label is used in the specification, the description is applicable to any one of the similar components having the same first reference label irrespective of the second reference label.
FIG. 1 illustrates an exemplary block diagram representing basic elements of a communication system.
FIG. 2 illustrates an exemplary representation of a spectrum plot obtained from a typical communication system.
FIG. 3A illustrates an exemplary representation of a method for transmitting a sequence of symbols using a modulation technique in accordance with an exemplary embodiment of the present disclosure.
FIG. 3B illustrates an exemplary architecture of a system for transmitting a sequence of symbols, in accordance with an exemplary embodiment of the present disclosure.
FIG. 4 illustrates an exemplary representation of a spectral plot obtained from a system and method using a modulation technique in accordance with the embodiments of the present disclosure.

DETAILED DESCRIPTION
The following is a detailed description of embodiments of the disclosure depicted in the accompanying drawings. The embodiments are in such detail as to clearly communicate the disclosure. However, the amount of detail offered is not intended to limit the anticipated variations of embodiments; on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the present disclosure as defined by the appended claims.
Each of the appended claims defines a separate invention, which for infringement purposes is recognized as including equivalents to the various elements or limitations specified in the claims. Depending on the context, all references below to the "invention" may in some cases refer to certain specific embodiments only. In other cases it will be recognized that references to the "invention" will refer to subject matter recited in one or more, but not necessarily all, of the claims.
Various terms as used herein are shown below. To the extent a term used in a claim is not defined below, it should be given the broadest definition persons in the pertinent art have given that term as reflected in printed publications and issued patents at the time of filing.
Embodiments of the present disclosure relates to systems and methods for transmitting a sequence of symbols.
An embodiment of the present disclosure provides, a method for transmitting a sequence of symbols, the method comprising the steps of: converting the sequence of symbols in the form of bits (0,1); identifying a fundamental frequency (f0) and using the fundamental frequency (f0) to form a plurality of higher harmonic frequencies (f1, f2, f3….fN-1), wherein N identified frequencies (f0, f1, f2, f3….fN-1) are orthogonal to each other over a time interval of 1/f0 seconds; dividing the sequence of symbols in the form of bits (0,1) in ratio 1:2:3:...:N to give N partitions and transmitting each of the N partitions; and adding all the N transmitted partitions for further processing, wherein further processing includes transmission over a transmission channel or decoding, detecting and/or estimating at a receiver.
In an aspect, the transmission of each of the N partitions is performed for a same transmission duration.
In an aspect, the method transmits each of the N partitions in the form of an electrical signal by transmitting one of valley to peak part, peak to valley part or maintaining the voltage level based on value of a bit from the sequence of symbols in the form of bits. When a first bit from the sequence of symbols in the form of bits is 1, peak to valley part is transmitted. Alternatively, when the first bit from the sequence of symbols in the form of bits is 0, valley to peak part is transmitted. Further, when a subsequent bit from the sequence of symbols in the form of bits is same as previous bit, the voltage level is maintained. Alternatively, when the subsequent bit from the sequence of symbols in the form of bits is not same as previous bit and when the subsequent bit from the sequence of symbols in the form of bits is 1, peak to valley part is transmitted, otherwise, when the subsequent bit from the sequence of symbols in the form of bits is not same as previous bit and when the subsequent bit from the sequence of symbols in the form of bits is 0, valley to peak part is transmitted.
In an aspect, the receiver is enabled to perform distance and/or difference computation.
Another embodiment of the present disclosure provides a system for transmitting a sequence of symbols, the system comprising: a binary converter enabled to convert the sequence of symbols in the form of bits (0,1); a frequency generator enabled to identify a fundamental frequency (f0) and form plurality of higher harmonic frequencies (f1, f2, f3….fN-1) based on the fundamental frequency (f0), wherein N identified frequencies (f0, f1, f2, f3….fN-1) are orthogonal to each other over a time interval of 1/f0 seconds; a modulator enabled to divide the sequence of symbols in the form of bits (0,1) in ratio 1:2:3:...:N to give N partitions and further transmit each of the N partitions; and a summer to add all the N transmitted partitions for transmission over a transmission channel.
In an aspect, the modulator transmits each of the N partitions for a same transmission duration.
In an aspect, the modulator performs transmission of each of the N partitions in the form of an electrical signal by transmitting one of valley to peak part, peak to valley part or maintaining voltage level based on value of a bit from the sequence of symbols in the form of bits. When a first bit from the sequence of symbols in the form of bits is 1, peak to valley part is transmitted. Alternatively, when the first bit from the sequence of symbols in the form of bits is 0, valley to peak part is transmitted. Further, when a subsequent bit from the sequence of symbols in the form of bits is same as previous bit, the voltage level is maintained. Alternatively, when the subsequent bit from the sequence of symbols in the form of bits is not same as previous bit and when the subsequent bit from the sequence of symbols in the form of bits is 1, peak to valley part is transmitted, otherwise, when the subsequent bit from the sequence of symbols in the form of bits is not same as previous bit and when the subsequent bit from the sequence of symbols in the form of bits is 0, valley to peak part is transmitted.
In an aspect, the system further comprises a receiver to decode, detect and/or estimate the sequence of symbols.
In an exemplary aspect, the receiver is enabled to perform distance and/or difference computation.
FIG. 1 illustrates an exemplary block diagram representing basic elements of a communication system.
As illustrated a general communication system includes three basic elements; a transmitter (102), a transmission channel (106) and a receiver (104). The transmitter (102) is enabled to convert the input signal carrying information data into a form suitable for transmission over a transmission channel. The transmitter (102) performs modulation and can also perform encoding. The transmission channel (106) can be an electrical medium that provides a bridge between the transmitter (102) and the receiver (104). The transmission channel (106) can be a wired medium such as pair of wires or coaxial cable, or a wireless medium such as radio wave or laser beam. The transmission channel (106) can introduce transmission loss which may progressively decrease the signal power on increasing distance. The receiver (104) includes operations such as amplification to compensate for transmission loss. The receiver (104) can also perform demodulation and decoding to reproduce the sequence of symbols or a signal carrying information data.
FIG. 2illustrates an exemplary representation of a spectrum plot obtained from a typical communication system. For clarity, it is considered that a decimal of value “2” is transmitted over 6 symbols or 3 orthogonal frequencies, i.e. when N=3. The obtained spectral plot (200) is as illustrated in FIG. 2. It is to be appreciated that the obtained shape of spectral plot is not concentrated and that there are numerous peaks that are close to each other. As shown, the first peak is at value of 120 and the second peak is at value of 220. Thus, these values are close within a factor of 2. For enhancing the efficiency of the said system, it is required that one sharp peak is obtained along with very low value of other peaks.
The invention as disclosed in the present disclosure can overcome the said drawback of the typical communication system.
FIG. 3A illustrates an exemplary representation of a method for transmitting a sequence of symbols, in accordance with an exemplary embodiment of the present disclosure.FIG. 3B illustrates an exemplary architecture of a system for transmitting a sequence of symbols, in accordance with an exemplary embodiment of the present disclosure. As illustrated in FIG. 3B, the proposed system can include a binary converter (352), a frequency generator (354), a modulator (356) and a summer (358).
To provide clarity in explanation of the system and method, embodiments of the present disclose are explained taking an example of a cosine wave of the form cos(2*pi*n*f0*t), where “pi” is a constant having a value “3.14…”, “f0” is a fundamental frequency, “n” is the harmonic number, and “t” is time instant. A cosine waveform starts at a value of 1,interchangeably referred as peak, when the argument in degree is 0-degree and transitions or reaches a value of -1, interchangeably referred as valley, when argument is 180 degrees. Thus, this transition can be considered as peak-to-valley (P/V) part. Similarly, a cosine waveform has valley-to-peak (V/P) part when argument varies from 180 degrees to 360 degrees or 0 degree. It is to be appreciated that, if the frequency of the argument increases, the P/V part and V/P part can be compressed in time. For example, if n=2, the P/V part is compressed to half the time interval when compared with that of n=1.
In an embodiment, the proposed method can include a step (302) that enables the proposed system to convert a sequence of symbols (that can be data to be transmitted) in the form of bits (0,1). The step (302) can be performed using the binary convertor (352). For example, a decimal representation [0 0 2] can be converted to [0 0 0 0 0 0 0 0 0 0 1 0].
In an aspect, the proposed method can include a step (304) at which the system identifies a fundamental frequency (f0) and uses the fundamental frequency (f0) to form a plurality of higher harmonic frequencies (f1, f2, f3….fN-1), wherein N identified frequencies (f0, f1, f2, f3….fN-1) are orthogonal to each other over a time interval of 1/f0 seconds. The step (304) can be performed using the frequency generator (354). In the said step (304), if Bandwidth B is provided and fundamental frequency f0 is identified, N can be computed as N=B/f0, based on which other harmonic frequencies can be determined. For example, if B=10 MHz and f0=1 Hz, then N=10^7=10 Million. For simplicity, a harmonic parameter “n” is taken, whose value can change from 1 to N.
In an aspect, the proposed method can include a step (306) for dividing the sequence of symbols in the form of bits (0, 1) in ratio 1:2:3:...:N to give N partitions, and a step(308) for transmitting each of the N partitions. The steps (306 and 308) can be performed using the modulator (356). For clear explanation of these steps, N=3 can be considered. Thus, harmonic parameter n=1, 2, 3. If N=3, in accordance with the step (306), the sequence of symbols in binary form can be divided in the ratio 1:2:3 to give 3 partitions. For example, when N=3, the binary representation [0 0 0 0 0 0 0 0 0 0 1 0] of sequence of symbols [0 0 2] in decimal form can be divided as [0 0], [0 0 0 0], [0 0 0 0 1 0] to give 3 partitions. Thus, when n=1, partition [0 0] can be considered, when n=2, partition [0 0 0 0] can be considered and when n=3, the partition [0 0 0 0 1 0] can be considered. Each of the N partitions (n=1, 2, 3) can be then transmitted. In an aspect, the transmission of each of the N partitions can be performed for a same transmission duration.This means, in the above-mentioned example, the third partition is transmitted 3 times faster than the first partition, and the second partition is transmitted 2 times faster than the first partition.
The transmission of step (308) can be performed using following technique. The transmission can be done in volts or in some equivalent electrical signal. If the first symbol is 1, P/V part can be transmitted, else V/P part can be transmitted. For the second and subsequent symbols, if the current symbol is same as previous symbol, last voltage level in maintained, otherwise, if the current symbol is not same as the previous symbol and if the current symbol is 1, P/V part can be transmitted else V/P part can be transmitted. For clarity, if previous symbol was “1”, after transmitting P/V part the voltage at last instant of transmission is -1 volt. If the current symbol is also “1”, voltage of -1 volt can be retained for duration of transmission of the current symbol. Thus, transmission is accomplished by performing modulation in a non-linear fashion.
In an aspect, the proposed method can include a step (310) for adding all the N transmitted partitions for further processing. The step (310) can be performed using the summer (358) that can be a summer-amplifier for voltage addition or a junction node for current addition. It can further be used to transmit the summed waveform onto the transmission channel.
In an aspect, the further processing includes transmission over a transmission channel or decoding, detecting and/or estimating at the receiver. The receiver can decode, detect and/or estimate the sequence of symbols from the transmitted waveform.
In an aspect, the receiver can be enabled to perform distance and/or difference computation.At the receiver, all possible transmitted waveforms for a given length of sequence of symbols can be generated. Each of the generated waveforms can be compared with the received and amplified waveform; this operation is also known as distance/difference computation. The generated waveform which has lowest aggregate difference or is closest in shape to the received waveform can be the estimate of transmitted waveform.
It is to be appreciated that the present disclosure pertains to a modulation technique that provides improved data rate and reduced spectral leak, which can be evidently made clear by explanation of the following figure.
FIG. 4 illustrates an exemplary representation of a spectral plot obtained from a system and method using a modulation technique in accordance with the embodiments of the present disclosure. For clear comparison, an example similar to that of FIG. 1 is considered. Hence, it is considered that a decimal of value “2” is transmitted. However, 12 bits instead of 6 bits of the prior example can be transmitted for the same power and still be able to give a very concentrated spectrum plot. For enhancing the efficiency of the prior art, it was required that one sharp peak is obtained along with very low value of other peaks. It can be seen that the spectrum plot has the second peak at about 20 times lower than first peak. Also, at the same time, the system has an ability to transmit twice the bits or information for the same power as compared to the prior art. Thus, the system reduced spectral leak and improved data rate or provided higher throughput.
In the view of the foregoing, as it has been mentioned above that the proposed system can transmit twice the bits as compared to the prior art, when there are N harmonics, then the system can transmit 2 bits over f0, 4 bits over f1, 6 bits over f2, and so on upto 2N bits over f(N-1) frequencies. Thus, the total transmitted bits over a time period of 1/f0 seconds are:
2+4+6+?+2N = 2(1+2+3+N) =2*N*(N+1)/2
After further simplification,
2*N*(N+1)/2= 2*N*N/2=N*N
Thus, N*N bits are transferred over a time period of 1/f0 seconds.
For clarity, it is assumed that N = 1000 and bandwidth is1000 Hz, then
f0=B/N= 1Hz
Time Period = 1/f0=1sec
Thus, N*N bits can be transferred in 1 sec = 10^6 bits/sec. Hence, the spectral efficiency can be calculated as:
Spectral efficiency = (data rate)/(bandwidth in Hz)=(?10?^6 bps)/1000Hz = 1000 bps/Hz

As it was assumed that N=1000, it can be said that the data rate increases N times. When N = 3 (i.e. B = 3 Hz and f0= 1 Hz) and Signal power = 1 unit of Noise power, then current scheme will obtain 3*3*log2(1+1) = 9 bps with three units of signal power, one unit per orthogonal frequency. For the same total signal power (i.e. SNR = 3), Hartley-Shannon formula would result in 3*log2(1+3) = 3*2 = 6 bps < 9 bps. The inequality becomes prominent as N increases, for example when N = 1000, Hartley-Shannon would give 1000*log2(1+1000) ~ 10,000 bps << 1000*1000*log2(1+1) = 1000,000 bps. Thus, it can be inferred that the present invention gives higher spectral efficiency and higher throughput than the prior art or the Hartley-Shannon formula.
Therefore, it can be appreciated that embodiments of the present disclosure provides an ability to transmit large number of bits for same power. Thus, it is advantageous that the proposed system uses less number of components, consumes low power and therefore is cost effective.

ADVANTAGESOF THE INVENTION
The present disclosure provides a system and method for transmitting a sequence of symbols.
The present disclosure provides a system and method for transmitting a sequence of symbols that has low spectral leakage.
The present disclosure provides a system and method for transmitting a sequence of symbols that provides higher throughput than Hartley-Shannon formula.
The present disclosure provides a system and method for transmitting a sequence of symbols that uses less number of components, consumes low power and therefore is cost effective.