Description:FIELD OF THE INVENTION
[0001] Embodiments of the present disclosure relates generally to channel estimation and symbol detection for orthogonal time frequency space-based systems impaired with impulsive noise, and more specifically to channel estimation and symbol detection for orthogonal time frequency space-based systems impaired by non-Gaussian impulsive noise.
BACKGROUND OF THE INVENTION
[0002] Multicarrier OFDM is a type of digital transmission that uses multiple carrier frequencies to encode binary data. Each carrier frequency, also called a subcarrier carries a part of the data stream in parallel. The subcarriers are chosen to be orthogonal to each other such that they do not interfere with each other over the symbol duration, allowing the subcarriers to overlap in the frequency domain, thereby increasing the spectral efficiency of transmission. Multicarrier OFDM can normally be implemented using inverse fast Fourier transform (IFFT) and fast Fourier transform (FFT) algorithms, which essentially are used to reduce the computational complexity of the modulation and demodulation processes. Multicarrier OFDM is also resistant to inter-symbol interference (ISI) caused due to multipath propagation, as long as the guard interval between the symbols is longer than the delay spread of the channel. Multicarrier OFDM is widely used in various wireless and wired communication standards, such as WiMAX, WLAN, DVB, DSL, and 5G.
[0003] Typically, such conventional multi-carrier schemes like orthogonal frequency division multiplexing (OFDM) that have been used in various wireless and wired communication standards, such as WiMAX, WLAN, DVB, DSL, and 5G are not suitable under high mobility scenarios, where there is a presence of high inter-carrier interference (ICI). Thus there is a need in the art for a better, efficient and cost effective sensing device.
SUMMARY OF THE INVENTION
[0004] Embodiments of the present disclosure related to system and method for channel estimation and symbol detection for orthogonal time frequency space based systems impaired by non-Gaussian impulsive noise, the system comprising at least a transmitter for transmitting data over a transmission channel and at least a receiver for receiving the transmitted data. In an embodiment, the transmitter is configured to receive information (data/content) as input and transmit the information to a receiver over a wireless network, wherein the information is encoded with pilot symbols to form transmission data. In an embodiment, the transmission channel is configured to transmit the transmission data from the transmitter to the receiver, wherein during the process of transmission from the transmitter to the receiver, noise, which is impulsive noise, from the transmission channel and/or surroundings is integrated with the transmission data.
[0005] In an embodiment, the receiver is configured to receive received data, wherein the received data comprises the transmission data and impulsive noise. In an embodiment, the receiver is configured to decode the received data, wherein the receiver is also provided with the pilot symbols and decoding the received data comprises filtering the impulsive noise from the received data, and provide the information at a receiver.
[0006] In an exemplary embodiment, the most widely used conventional message passing detector (MPD) requires channel state information and delivers
suboptimal performance for orthogonal time frequency space (OTFS) systems in the presence of non-Gaussian impulsive noise (IN). To circumvent this limitation, the present disclosure proposes a L0-norm constrained maximum Versoria criterion (L0-MVC) based sparse channel estimation methodology with an optimal adaptive tuning of sparsity regularization parameter for OTFS systems. In an exemplary embodiment, further, the maximum Versoria criterion-based message passing (MP-MVC) symbol detection scheme for OTFS is proposed, which is robust under non-Gaussian impulsive noise. Other embodiments are also disclosed.
BRIEF DESCRIPTION OF THE DRAWINGS
[0007] The detailed description is described with reference to the accompanying figures. Features, aspects, and advantages of the subject matter of the present disclosure will be better understood with regard to the following description and the accompanying drawings. The figures are intended to be illustrative, not limiting, and are generally described in context of the embodiments, and it should be understood that it is not intended to limit the scope of the disclosure to these particular embodiments. In the figures, the same numbers may be used throughout the drawings to reference features and components. In order that the present disclosure may be readily understood and put into practical effect, reference will now be made to exemplary embodiments as illustrated with reference to the accompanying figures. The figures together with detailed description below, are incorporated in and form part of the specification, and serve to further illustrate the embodiments and explain various principles and advantages.
[0008] Figure 1 is an exemplary illustration of a transmission system in accordance with an embodiment of the present disclosure.
[0009] Figure 2 is an exemplary illustration of a transmitter of the transmission system of Figure 1 in accordance with an embodiment of the present disclosure.
[0010] Figure 3 is an exemplary illustration of a receiver of the transmission system of Figure 1 in accordance with an embodiment of the present disclosure.
[0011] Figure 4 is an exemplary illustration of a plot showing the normalized mean deviation error message versus t? in accordance with an embodiment of the present disclosure.
[0012] Figure 5A is an exemplary illustration of a plot showing the MSD versus number of iterations under a Gaussian mixture noise condition in accordance with an embodiment of the present disclosure.
[0013] Figure 5B is an exemplary illustration of a plot showing the MSD versus number of iterations under a-stable noise condition in accordance with an embodiment of the present disclosure.
[0014] Figure 6A is an exemplary illustration of a plot showing the BER versus SNR comparison in the presence of Gaussian mixture noise condition and a Rayleigh channel in accordance with an embodiment of the present disclosure.
[0015] Figure 6B is an exemplary illustration of a plot showing the BER versus SNR comparison in the presence of a-stable noise condition and a Rayleigh channel in accordance with an embodiment of the present disclosure.
[0016] Figure 7A illustrates an exemplary method for transmission of information received at transmitter to a receiver over a transmission channel in accordance with an embodiment of the present disclosure.
[0017] Figure 8A illustrates an exemplary method implemented at the transmitter by encoding the information at the transmitter into transmission data prior to transmission over the transmission channel in accordance with an embodiment of the present disclosure.
[0018] Figure 8B illustrates an exemplary method implemented at the receiver on receiving the received data at the receiver, where the received data includes the transmission data and non-impulsive noise and decoding the received data at the receiver in accordance with an embodiment of the present disclosure.
DETAILED DESCRIPTION
[0019] The following describes technical solutions in exemplary embodiments of the subject matter of the present disclosure with reference to the accompanying drawings. In this application as disclosed herein, "at least one" means one or more, and "a plurality of" means two or more. The term "and/or" describes an association relationship for describing associated objects and represents that three relationships may exist. For example, A and/or B may represent the following cases: Only A exists, both A and B exist, and only B exists, where A and B may be singular or plural. The character "/" usually indicates an "or" relationship between the associated objects. "At least one item (piece) of the following" or a similar expression thereof means any combination of the items, including any combination of singular items (piece) or plural items (pieces). For example, at least one item (piece) of a, b, or c may represent a, b, c, a and b, a and c, b and c, or a, b, and c, where a, b, and c each may be singular or plural.
[0020] It should be noted that in this application articles “a”, “an” and “the” are used to refer to one or to more than one (i.e., to at least one) of the grammatical object of the article. The terms “comprise” and “comprising” are used in the inclusive, open sense, meaning that additional elements may be included. It is not intended to be construed as “consists of only”. Throughout this specification defined above, unless the context requires otherwise the word “comprise”, and variations such as “comprises” and “comprising”, will be understood to imply the inclusion of a stated element or step or group of elements or steps but not the exclusion of any other element or step or group of elements or steps. The term “including” is used to mean “including but not limited to”. “Including” and “including but not limited to” are used interchangeably. In the structural formulae given herein and throughout the present disclosure, the following terms have been indicated meaning, unless specifically stated otherwise.
[0021] Unless otherwise defined, all terms used in the disclosure, including technical and scientific terms, have meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. By means of further guidance, term definitions are included for better understanding of the present disclosure. The term ‘about’ as used herein when referring to a measurable value such as a parameter, an amount, a temporal duration, and the like, is meant to encompass variations of ±10% or less, preferably ±5% or less, more preferably ±1% or less and still more preferably ±0.1% or less of and from the specified value, insofar such variations are appropriate to perform the present disclosure. It is to be understood that the value to which the modifier ‘about’ refers is itself also specifically, and preferably disclosed.
[0022] It should be noted that in this application, the term such as "example" or "for example" or “exemplary” is used to represent giving an example, an illustration, or descriptions. Any embodiment or design scheme described as an "example" or "for example" in this application should not be explained as being more preferable or having more advantages than another embodiment or design scheme. Exactly, use of the word such as "example" or "for example" is intended to present a related concept in only a specific manner.
[0023] It should be understood that in the embodiments of the present subject matter that "B corresponding to A" indicates that B is associated with A, and B can be determined based on A. However, it should be further understood that determining B based on A does not mean that B is determined based on only A. B may alternatively be determined based on A and/or other information.
[0024] In the embodiments of this application, "a plurality of" means two or more than two. Descriptions such as "first", "second" in the embodiments of this application are merely used for indicating and distinguishing between described objects, do not show a sequence, do not indicate a specific limitation on a quantity of devices in the embodiments of this application, and do not constitute any limitation on the embodiments of this application.
[0025] Embodiments of the present disclosure related to system and method for channel estimation and symbol detection for orthogonal time frequency space-based systems impaired by non-Gaussian impulsive noise. In an embodiment, the system includes at least a transmitter for transmitting data over a transmission channel and at least a receiver for receiving the transmitted data. In an embodiment, the transmitter may be configured to receive information (data/content) as input and transmit the information to a receiver over a wireless network, wherein the information may be encoded with pilot symbols to form transmission data. In an embodiment, the transmission channel may be configured to transmit the transmission data from the transmitter to the receiver, wherein during the process of transmission from the transmitter to the receiver, noise, which is impulsive noise, from the transmission channel and/or surroundings is included/combined with the transmission data.
[0026] In an embodiment, the receiver may be configured to receive received data, wherein the received data comprises the transmission data and impulsive noise. In an embodiment, the receiver may be configured to decode the received data, wherein the receiver may also be provided with the pilot symbols and decoding the received data includes filtering the impulsive noise from the received data and provide the information at a receiver. In an embodiment, the impulsive noise includes at least one of an induced impulsive noise and/or channel noise and/or noise from channel interference.
[0027] In an embodiment, the transmitter includes at least a receiving unit, wherein the receiving unit may be configured to convert the information received at the transmitter. In an embodiment, the information received at the transmitter may be an analog signal, which needs to be transmitted from the transmitter to the receiver. In an embodiment, the receiving unit may be configured to receive the transmitted signal from the transmitter and convert the analog signal into a digital signal or input bits. In an embodiment, the digital signal for transmission from the transmitter to the receiver, also referred to as the transmission signal, during the transmission over the transmission channel gets impaired by non-Gaussian impulsive noise from the channel, and the signal received at the receiver, that is the received signals, need to be cleaned of the impulsive noise before the information is provided to a user at the receiver end.
[0028] In an embodiment, the transmitter includes at least a mapping unit configured to perform a quadrature amplitude modulation (QAM) mapping of the input bits (information) producing a modulated signal. In an embodiment, the modulated signal may be a combination of a phase modulation and an amplitude modulation of the input bits. In an embodiment, the mapping unit may be configured to convert the modulated signal to delayed Doppler domain information symbols.
[0029] In an embodiment, the transmitter further includes at least a grid formation unit, wherein the grid formation unit may be configured to convert the delayed Doppler information symbols into an orthogonal time frequency grid in a time frequency domain, and generate a N X M matrix, wherein the N X M matrix is a combination of pilot symbols and the delayed Doppler information symbols, wherein N is the number of Doppler bins and M is the number of delay bins in the N X M matrix.
[0030] In an embodiment, the pilot symbols may be pre-determined by a service provider and/or a user and the pilot symbols may be provided to the transmitter and the receiver. In an embodiment, the transmitter further includes a transformation unit, wherein the transformation unit may be configured to convert the N X M matrix containing a combination of the pilot symbols and the delayed Doppler information symbols into a time domain signal. In an embodiment, the transformation unit may be configured to first perform an Inverse Sympletic Finite Fourier Transformation (ISFFT) on the N x M matrix. In an embodiment, the transformation unit may be configured to subsequently performs a Heisenberg transformation (HT) on the N X M matrix producing a time domain signal.
[0031] In an embodiment, the time domain signal may be transmitted over a transmission channel to from the transmitter to the receiver. In an embodiment, the receiver may be configured to receive the received data, wherein the received data includes the time domain signal from the transmitter combined with impulsive noise of the transmission channel.
[0032] In a further embodiment, the system may include a receiver. In an embodiment, the receiver may include an inverse-transform unit, wherein the inverse-transform unit may be configured to perform an inverse transformation on the received data, wherein the received data includes the time domain signal coupled with impulsive noise.
[0033] In an embodiment, the inverse transformation may include transforming the time domain signals into the delay Doppler domain information symbols and the pilot symbols. In an embodiment, the inverse-transform unit may be configured to first perform a Wigner transform on the received data providing a Wigner transformed data, and subsequently perform a Sympletic Finite Fourier Transformation (SFFT) on the Wigner transformed data to obtain delayed Doppler information symbols from the received data.
[0034] In an embodiment, the receiver may include a channel estimator, which may be configured to receive the delayed Doppler domain pilot symbol from the inverse-transform unit. In an embodiment, the channel estimator may be configured to estimate a channel information and the information from the received data, wherein the pilot symbols may be provided to the channel estimator at the receiver.
[0035] In an embodiment, the channel estimator may be configured to provide the channel information estimated to a detector unit. In an embodiment, the channel estimator may be configured to apply a L0-Maximum Versoria Criteria (L0-MVC) to obtain the channel information. In an embodiment, the detector unit may be configured to receive the delayed Doppler domain information symbols from the inverse-transform unit and the channel information estimated from the channel estimator. In an embodiment, the detector unit may be configured to perform a Message Passing based Maximum Versoria Criteria (MP-MVC) on the delayed Doppler domain information symbols to identify the modulated signal.
[0036] In an embodiment, the receiver may further include a de-mapping unit, wherein the de-mapping unit may be configured to demodulate the modulated signal into the digital signal or received bits, wherein the received bits are equivalent to the input bits. In an embodiment, the received bits may be transformed back to an analog signal and provided at a receiving end to a user, wherein the analog signal provided at the receiver is equivalent to the analog signal transmitted from the receiver.
[0037] Reference is now made to Figure 1, which is an exemplary illustration of a transmission system in accordance with an embodiment of the present disclosure. As illustrated the exemplary transmission system 100, includes at least a transmitter 110, at least a receiver 130 and a transmission channel 120. Information 115 needs to be transmitted from one user at one end to another user at another end. Normally, transmission systems 100 are be used to transmit the information 115 from one end to another end, wherein transmission systems 100 may preferably include a wireless network. Information 115, which is generally an analog signal, is received by transmitter 110. Information 115 is processed by transmitter 110 and encoded at transmitter 110, converting information 115 into transmission data 117, wherein transmission data 117 include original information 115 and pilot symbols. The pilot symbols are predetermined by a service provided or by a user of the transmission system.
[0038] Transmission data 117 is transmitter from transmitter 110 to receiver 130 over transmission channel. In an exemplary embodiment, transmission channel 120 may be a wireless network. It should be obvious to a person of ordinary skill in the art that various other transmission channels may be used, and all such transmission channels fall within the scope of the present disclosure. In an exemplary embodiment, transmission channel 120 may be a carrier of transmission data 117 from transmitter 110 to receiver 130.
[0039] Transmission system 100 includes receiver 1`30, which is configured to receive, received data 119. Received data 119 includes transmission data 117 and non-Gaussian impulsive noise that is picked up by transmission data 117, which being transmitted over transmission channel 120. In an exemplary embodiment, received data 119, typically includes transmission data 117 that is faded by transmission channel 120 and the non-Gaussian impulsive noise in and around transmission channel 120, wherein the non-Gaussian impulsive noise may be difficult to detect and remove from received data 119. Receiver 130 is configured to estimate the channels using the pilot information provided to transmitter 110 and receiver 130, wherein the pilot symbols provided to transmitter 110 and receiver 130 are identical. Receiver 130 is further configured to implement an L0-Maximum Versoria Criteria (L0-MVC) to obtain the channel information, and perform a Message Passing based Maximum Versoria Criteria (MP-MVC) on received data 119 to identify the modulated signal, and then demodulate the signal and provide data 135 to user at receiver 130. It should be obvious to a person of ordinary skill in the art, that various modifications of transmission system 100 may be made, but all such variation of transmission systems 100 using pilot symbols, L0-MVC and MP-MVC fall within the scope of the present disclosure.
[0040] Reference is now made to Figure 2, which is an exemplary illustration of a transmitter 110 of the transmission system of Figure 1 in accordance with an embodiment of the present disclosure. It should be obvious to a person of ordinary skill in the art that various modifications may be made to the transmitter, and all such transmitters fall within the scope of the present disclosure. As illustrated an exemplary transmitter 110 has receiving unit 210, mapping unit 220, pilot unit 235, grid formation unit 230 and transformation unit 240, wherein transmitter 110 is configured to receive information 205 and prepare the information 205 into transmission data 117 which can be transmitted from transmitter 110 to receiver 130.
[0041] As illustrated, information 205 to be transmitted from a first end (one end) to a second end (another end) is first received at transmitter 110. Information 205 is normally an analog signal that needs to be encoded and prepared to be in a certain format for transmission. Information 205 is received as an input at receiving unit 210 of transmitter 110. Information 205 received at the receiving unit 210 is sent to mapping unit 220. Mapping unit 220 is configured to perform a quadrature amplitude modulation (QAM) mapping on the input bits producing a modulated signal. The modulated signal is a combination of a phase modulation of the input bits and an amplitude modulation of the input bits. Mapping unit 220 is further configured to convert the modulated signal into delayed Doppler domain information symbols.
[0042] Pilot unit 235 stores the pilot symbols, wherein the pilot symbols are provided by a service provided of the transmission system or the user of the transmission system. Pilot symbols are pre-defined or pre-determined and a-priori stored in pilot unit 235. It should be obvious to a person or ordinary skill in the art that the pilot symbols may vary between service providers and there could be various variation of the pilot symbols, and all such variations fall within the scope of the present disclosure.
[0043] Transmitter 110 further comprises a grid formation unit 230. Grid formation unit 230 is configured to take an input the Doppler domain information symbols from mapping unit 220 and pilot symbols from the pilot unit 235 and convert the delayed Doppler information symbols into an orthogonal time frequency grid in a time frequency domain. Converting the delayed Doppler information symbols into an orthogonal time frequency grid in a time frequency domain essentially includes generate an N X M matrix, wherein the N X M matrix is a combination of the pilot symbols from pilot unit 235 and the delayed Doppler information symbols from mapping unit 220, and wherein N is the number of Doppler bins and M is the number of delay bins in the N X M matrix created at transmitter 110 by grid formation unit 230. As discussed previously, the pilot symbols are pre-determined or pre-defined by a service provider and/or a user and the pilot symbols are provided to both transmitter 110 and the receiver 130 of transmission system 100.
[0044] Transmitter 110 a transformation unit 240, the transformation unit 240 configured to convert the N X M matrix containing a combination of the pilot symbols 235 and the delayed Doppler information symbols into a time domain signal. Transformation unit 240 is essentially configured to first perform an Inverse Sympletic Finite Fourier Transformation (ISFFT) on the N x M matrix. After performing ISFFT on the N X M matrix containing the delayed Doppler information symbols and the pilot symbols, transformation unit 240 is configured to subsequently perform a Heisenberg transformation (HT) on the N X M matrix thereby producing a time domain signal. The time signal produced by transmitter 110 is referred to as transmission data 117, which will then be transmitted over a transmission channel 120 of the transmission system 100 to receiver 130 also on the same transmission system 100 or on a coupled transmission system, which may be a different network coupled to this system.
[0045] The time domain signal (transmission data 117) is transmitted over the transmission channel 120 to the receiver 130, wherein 130 receiver is configured to receive, received data 119, wherein received data 119 includes the time domain signal from transmitter 110 which is combined with impulsive noise 125 picked up along the transmission channel 120. In an exemplary embodiment, noise 125 may be non- Gaussian impulsive noise, but it should be obvious to a person or ordinary skill in the art that other noise may also be coupled with the time domain signal during transmission and all such variations fall within the scope of the present disclosure.
[0046] Reference is now made to Figure 3, which is an exemplary illustration of a receiver 130 of the transmission system 100 of Figure 1 in accordance with an embodiment of the present disclosure. It should be obvious to a person of ordinary skill in the art that various modifications may be made to the receiver, and all such receiver implementing a L0-Maximum Versoria Criteria (L0-MVC) to obtain the channel information, and performing a Message Passing based Maximum Versoria Criteria (MP-MVC) on received data 119 to identify the modulated signal, and then demodulate the signal and provide data 135 to user at receiver 130 fall within the scope of the present disclosure.
[0047] Exemplary receiver 130 includes inverse-transform unit 310 (also referred to as I-transform unit), wherein received data 119 is received. Received data 119 include the transmission data 117 transmitted over transmission channel 120 and impulsive noise 125 picked up by transmission data 117 on the transmission channel 120. Received data 119 is faded transmission data 117, as the transmission data 117 gradually fades over distance on transmission channel 120. I-transform unit 310 is configured to first receive received data 119. I-transform unit 310 is then configured to perform an inverse transformation on received data 119, wherein received data 119 is in the time domain, and may essentially be a time domain signal. I transform unit 310 is configured to transform the time domain signals into the delay Doppler domain information symbols and the pilot symbols, thereby obtaining a N X M matrix.
[0048] I-transform unit 310 is configured to first perform a Wigner transform on received data 119 providing a Wigner transformed data of received data 119. I-transform unit 310 is then configured to perform a Sympletic Finite Fourier Transformation (SFFT) on the Wigner transformed data to obtain delayed Doppler information symbols and the pilot symbols.
[0049] Channel estimator 325 of receiver 130 is configured to receive the delayed Doppler domain information symbols and the pilot symbol from I-transform unit 310, and estimate a channel information and the information 205 from received data 119, wherein the pilot symbols are provided to channel estimator 325 at the receiver 130, and the pilot symbols provided to receiver 130 are similar to the pilot symbols provided to transmitter 110. Channel estimator 325 is configured to estimate channel information and provide the channel information estimated to detector unit 320. Channel estimator 325 is configured to apply a L0-Maximum Versoria Criteria (L0-MVC) to the channel information.
[0050] Receiver 130 has detector unit 320, which is configured to receive the delayed Doppler domain information symbols from the I-transform unit 310 and the channel information estimated from channel estimator 325. Detector unit 330 is configured to perform a Message Passing based Maximum Versoria Criteria (MP-MVC) on the delayed Doppler domain information symbols to identify the modulated signal.
[0051] Receiver 130 further includes de-mapping unit 330, wherein de-mapping unit 330 is configured to demodulate the identified modulated signal into the digital signal or received bits 340, wherein the received bits are equivalent to the input bits. De-mapping unit 330 may be further configured to transform the received bits back to an analog signal and provide the signal at a receiving end (not shown in this Figure).
[0052] In an exemplary embodiment, information symbols xd[k, l] (Tx bits after quadrature amplitude modulation (QAM) mapping) and pilot symbols xp[k, l] are multiplexed to form an OTFS grid, denoted by the relationship
, where k = 0, …,N-1; and l = 0, …,M-1, which has a size of N X M, where N and M are the number of Doppler bins and delay bins. In the exemplary embodiment, T is reference to as symbol duration and ?f is reference to subcarrier spacing. The DD (delayed Doppler) domain symbols x[k, l] may be converted to the time domain signal x(t) by performing the inverse symplectic finite Fourier transform (ISFFT) followed by the Heisenberg transform. The received symbol at (k’, l’)th DD resource element is obtained by performing the Wigner transform followed by symplectic finite Fourier transform (SFFT) is given by the Equation

where (.)N is modulo-N operation. The non-Gaussian noise Z[K’, l’] is characterized by both Gaussian mixture and a-stable distributions. The corresponding probability density functions (pdfs) can be written as

where , with L being the total number of components in Gaussian mixture, and s2i is the variance of ith component. {zr}Rr=1 are the R noise samples drawn from arbitrary statistical data, and s is the kernel width for non-parametric (NP) Parzen window approximation of a-stable distribution.
[0053] The received symbol vector may be written as y = Xh + z (which is an alternative form of y = Hx + z),where h ? C MNX1, which is the equivalent to the DD-domain sparse channel vector, and z ? C MNX1 is non-Gaussian noise vector, where C denotes the set of complex numbers. X ? C MNXMN is the equivalent transmit symbol matrix whose elements contain both pilots symbols xp(k, l) for channel estimation and information symbols xd(k, l) taken from modulation alphabet A ? {aq}Qq=1, where Q denotes modulation order. In the exemplary case, the middle Np rows of X are considered as pilot symbols for ensuring time invariancy throughout the OTFS grid, and the remaining MN - Np rows consist of information symbols. The received symbol vector corresponding to the pilots may be written as yp= Xph+zp, where yp ? CNp×1, Xp ? C CNp×MN, and zp ? C CNp×1.
[0054] In an exemplary embodiment, the proposed l0-MVC scheme for channel estimation, followed by the MP-MVC-based symbol detection algorithm under non-Gaussian noise for OTFS is illustrated. In the exemplary embodiment, the conventional minimization problem min E(h) {|| yp(i) – Xp(i) h(i)||2 is not robust under non-Gaussian noise due to high error terms arising by imperative noise transients. In the exemplary case, therefore, a robust MVC-based channel estimation optimization problem is formulated as

where t and c are the spread parameter for the Versoria function and regularization errors.
[0055] To reach the optimal point (zero error) along the gradient ascent at a faster rate, the steepness of the Versoria function that depends on t must be at the lower side. h(i) is the estimate of channel vector at ith instant with h(0) being initialized channel vector. Using the convex approximation for L0-norm, overall Lagrangian is formulated as

where ? is the Lagrange multiplier. Using the stochastic sub gradient as disclosed previously the estimated channel coefficients for the proposed algorithm can be adaptively determined by

Where [e(i) = yp(i) - Xp(i) h(i)] denotes the prediction error and ? is SRP, ? is the step size, and u(h(i)) may be determined by

where sgn(·) is the component-wise sign function and ? is a constant. In the exemplary case, observations indicate that the proposed L0-MVC model selectively shrinks those filter taps whose magnitude are comparable or smaller than 1/? for || h(i)|| = 1/? and provides less-attraction to the coefficients for || h(i)|| >> 1/?, thereby resulting in better convergence performance as compared to L1-MVC model which uniformly attracts filter taps towards zero.
[0056] In an exemplary case, the optimal choice for ? is the proper selection of SRP ? which is crucial for a generic sparsity-aware adaptive filtering algorithm, and its improper selection may result in degraded performance. In addition, ? is sensitive to different noise distributions and time-varying scenarios, necessitating repetitive estimations for various deployment scenarios. On the basis of minimizing the mean square deviation (MSD) between the filter weights, the loss function for ? optimization can be expressed as

where h(i+1) = h - h(i+1), is the deviation of channel from actual channel at (i + 1)th instant of time.
[0057] Using the previously disclosure equation for computing h(i+1), and assuming independence between e(i) and Xp(i) the expectation term in the cost function may be obtained as

where .
[0058] In the exemplary case, by partially differentiating the above expression w.r.t ?(i+1) and putting equals to zero, the optimal ? at (i + 1)th instant of time is obtained as

where, the expectations involved in the above expression can be easily computed using the unbiased time average approximations method. The parameter updates in are not affected by transients due to large outliers. This is attributed to the presence of nonlinear error term fMVC (e(i)), which is finite/small even for large values of error as opposed to e(i) alone in MMSE-based approaches. Hence, the proposed L0-MVC model as disclosed herein provides improved robustness to non-Gaussian noise as compared to the MMSE-based model.
[0059] The exemplary pseudo-code for the proposed channel estimation approach is detailed below:

[0060] In an exemplary embodiment, conventional MPD assumes impulsive noise and interference as Gaussian distribution. For an iteration, observation nodes y[n] compute the mean µnm and variance s2nm of the received symbols and pass it to variable node x[m] where m, n = 1, 2, . . . , S, where S being the number of non-zero rows out of MN rows in the channel matrix. The non-zero elements of the estimated channel vector in the previous subsection are denoted by h[n]. Therefore, a log-likelihood corresponding to the probability mass function (pmf) of the message propagated from x[m] to y[n] for the conventional MPD is given as

Where the energy of the error message for the conventional MPD is not guaranteed to be bounded in the presence of non- Gaussian impulsive noise. Hence, in the present disclosure it is proposed to propagate the energy of the gradients of messages formulated using MVC, which is a robust learning criterion for mitigating outliers caused by non-Gaussian impulsive noise. Therefore, the propagated message for the proposed
MP-MVC symbol detector is given by

where tv is the spread parameter of MVC. The MVC based multiplicative term in the above equation suppresses message error energy, resulting in improved performance over MPD. The pseudo-code for the proposed detection technique is detailed methodology given below.

[0061] Reference is now made to Figure 4, which is an exemplary illustration of a plot showing the normalized mean deviation error message versus t? in accordance with an embodiment of the present disclosure. The mean deviation in the instantaneous error messages for the proposed MP-MVC-based detector in the presence of generic Gaussian mixture and a-stable distributed noise may be computed by Equation below:

where gd are the roots and wd are the weights of a Hermite polynomial H(D-1)(gd), and ? is the mean deviation of the a conventional message passing detector (MPD). The MP-MVC detector as proposed in the present disclosure has a lower mean deviation than the conventional MPD since E[??mn]/? = 1 for a wide range of Versoria shape parameter tv as illustrated in Figure 4. Further, the proposed MP-MVC detector has a lower mean deviation than the existing MP-MCC algorithm because it has a erfc(·) function that decays faster than the exp(·) function of the MP-MCC model. Thereby, the MP-MVC detector is more robust to non-Gaussian noise than MPD and MP-MCC. ‘
[0062] In exemplary Figure 4, which is a plot of normalized deviation of error message E[??mn]/? versus the Versoria shape parameter tv, the decay line 410 is for an a-stable MP-MCC, while delay line 430 is for an a-stable MP-MVC. The delay in the a-stable MP-MVC is faster compared to the a-stable MP-MCC. The delay line 420 is for a Gaussian mixture MP-MCC, whereas the decay line 440 is for a Gaussian mixture MP-MVC, and again the Gaussian mixture almost follows the a-stable shapes parameters. In both case the decay of the MP-MCC is slower than the MP-MCC.
[0063] Figure 5A is an exemplary illustration of a plot showing the MSD versus number of iterations under a Gaussian mixture noise condition in accordance with an embodiment of the present disclosure. The measurements were made for LMS, L1-LMS, MCC, L1-MCC, L0-MCC, MVC, L1-MVC and the proposed L0-MVC. The outlier in this case was observed for the LMS and L1-LMS as indicated in line 510, showing large variations with respect to the number of iterations between MSD values of 10-2 to about 100.5. The line 512 is the result for the proposed L0-MVC, with the MSD dropping from 1 to about 10-3 for about 1000 iterations and then remains stable. All other cases were found to be follow the L0-MVC curve, but stabilized at higher values that L0-MVC after about 1000 iterations.
[0064] Figure 5B is an exemplary illustration of a plot showing the MSD versus number of iterations under a-stable noise condition in accordance with an embodiment of the present disclosure. The measurements were made for LMS, L1-LMS, MCC, L1-MCC, L0-MCC, MVC, L1-MVC and the proposed L0-MVC. Again, the outlier in this case was observed for the LMS and L1-LMS as indicated in line 520, showing large variations with respect to the number of iterations between MSD values of 10 to about 103. The line 522 is the result for the proposed L0-MVC, with the MSD dropping from 1 to about 10-3 for about 1000 iterations and then remains stable. All other cases were found to be follow the L0-MVC curve, but stabilized at higher values that L0-MVC after about 1000 iterations.
[0065] Figure 6A is an exemplary illustration of a plot showing the BER versus SNR comparison in the presence of Gaussian mixture noise condition and a Rayleigh channel in accordance with an embodiment of the present disclosure. The bit error rate versus the signal to noise ratio is illustrated, wherein line 610 indicated the BER vs SNR for single tap case, line 615 indicates the BER versus SNT for LMMSE and line 620 indicates the BER vs SNR for MRC. The lines are almost flat for a SNT from 0 to 20 db and then show a small dip in the BER, which may be negligible. Line 625 illustrated the BER to SNT for the proposed MP-MVC and it shows a linear decrease from 10-0.5 at an SNR of 0 to about 10-3 at SNR of 30. For proposed MP-MVC line 635, simulated with perfect CSI, it shows a linear decrease from 10-1.5 at an SNR of 0 to about 10-3.5 at SNR of 30. For proposed MP-MVC line 630, simulated with estimated CSI, it shows a linear decrease from 10-1 at an SNR of 0 to about 10-3.5 at SNR of 30.
[0066] Figure 6B is an exemplary illustration of a plot showing the BER versus SNR comparison in the presence of a-stable noise condition and a Rayleigh channel in accordance with an embodiment of the present disclosure.
[0067] Form Figure 6A and Figure 6B it may be inferred that the proposed MP-MVC based detection model of the present disclosure delivers 2 dB and 8 dB gain at BER of 10-3 over the existing MP-MCC and MPD Models. The inferior performance of MPD is attributed to the erroneous likelihood messages in the presence of non-Gaussian distortions. It is also observed that the BER performance of the proposed MP-MVC detector using estimated CSI (by the proposed l0-MVC) closely overlaps with the performance of the perfect CSI scenario, which highlights the viability of the proposed channel estimation
algorithm. Furthermore, the analytical lower bound (LB) on BER agrees well with the simulated BER under a high SNR regime, which highlights the accuracy of the derived BER. The BER’s LB of the proposed MP-MVC detector for generic non-Gaussian noise is close to the LB for the AWGN scenario, which makes the proposed algorithm feasible for practical deployments of OTFS systems impaired by non-Gaussian noise. However, other low complexity detectors, including Linear MMSE (LMMSE), single-tap, and maximum ratio combining, provide poor performance under non-Gaussian noise, making them unsuitable for non- Gaussian impulsive noise scenarios. The proposed MP-MVC detector provides 5 dB gain using the channel estimates from l0-MVC algorithm as compared to the channel estimates using the iterative scheme as disclosed. This is attributed. to the incapability of the scheme in handling non-Gaussian noise.
[0068] Figure 7A illustrates an exemplary method for transmission of information received at transmitter to a receiver over a transmission channel in accordance with an embodiment of the present disclosure. In step 710 information is received at a transmitter, wherein the information to be transmitted is received as analog signals and the analog signals to are converted to digital signals. In step 720, transmission data is created by multiplexing the digital signal with pilot symbols, and the data is processed to create a time domain signals which is transmitted over a transmission channel. In step 730, the transmission data, which is the input bits and the pilot symbols are transmitted over the transmission channel to a receiver. In step 740, as the transmission data is being transmitted from the transmitter to the receiver, the transmission data faded in intensity and also pick-up random non-Gaussian impulsive noise. In step 750, the receiver, receives received data, wherein the received data contains the transmission data and impulsive noise. In step 760, the receiver does an inverse transformation and performs a channel estimation and filters the impulsive noise and provides the information that was initially received at the transmitter to the user at the receiver end. The steps have been discussed elaborately with respect to the previous figures in the present disclosure.
[0069] Figure 8A illustrates an exemplary method implemented at the transmitter by encoding the information at the transmitter into transmission data prior to transmission over the transmission channel in accordance with an embodiment of the present disclosure. In step 810 an analog signal for transmission is received at the transmitter. In step 812, the analog signal is converted to a digital signal for transmission over a wireless network. In step 814, the transmitter performs a QAM on the digital signal to obtained delayed Doppler domain information symbols. In step 816, the delayed Doppler domain information is converted to an orthogonal time frequency grid and a N X M matrix is generated with pilot symbols inserted into the matrix and a ISFFT and HT performed on the matrix. In step 826, the matrix is converted to a time domain signal for transmission over a wireless network. The steps of the method have been discussed in the previous Figures.
[0070] Figure 8B illustrates an exemplary method implemented at the receiver on receiving the received data at the receiver, where the received data includes the transmission data and non-impulsive noise and decoding the received data at the receiver in accordance with an embodiment of the present disclosure. In step 822, the receiver receives received data, which includes the transmission data and impulsive noise embedded into the transmission data, and the transmission data has also faded in intensity. In step 824, an inverse transformation is performed on the received data, first a Wigner transform and then a SFFT to convert the time domain signal into delayed Doppler domain information symbols (DDDIS). In step 826, the channel estimator receives the pilot symbols, which may be provided by the service provider. In step 828, a channel information is estimated. In step 830, a L0-MVC and MP-MVC is applied to estimate the channel information. In step 832 from channel information and DDDIS detect information symbols using MP-MVC and converting information symbols to received bits, where received bits at receiving end are similar to transmitted bits
[0071] Although the present disclosure has been described with reference to several preferred embodiments, it should be understood that the present disclosure is not limited to the preferred embodiments disclosed here. Embodiments of the present disclosure are intended to cover various modifications and equivalent arrangements within the spirit and scope of the appended claims. Although the foregoing disclosure has been described in some detail for purposes of clarity of understanding, it will be apparent that certain changes and modifications may be practised within the scope of the appended claims. Examples of the present disclosure have been described in language specific to structural features and/or methods. It should be noted that there are many alternative ways of implementing both the process and apparatus of the present invention. Accordingly, embodiments of the present disclosure are to be considered illustrative and not restrictive, and the invention is not to be limited to the details given herein but may be modified within the scope and equivalents of the appended claims. It should be understood that the appended claims are not necessarily limited to the specific features or methods described. Rather, the specific features and methods are disclosed and explained as examples of the present disclosure. , Claims:We Claim:
1. A system 100, the system 100 comprising a transmitter 110 and a receiver 130 for transmitting data over a transmission channel 120, wherein
the transmitter 110 configured to receive information 115 as input, and transmit the information 115 to a receiver 130, wherein the information 115 is encoded with pilot symbols 235 to form transmission data 117;
the transmission channel 120 configured to transmit the transmission data 117 from the transmitter 110 to the receiver 130, wherein noise 125 from the transmission channel 120 is integrated with the transmission data 117;
the receiver106 configured to receive a received data 119, wherein the received data 119 comprises:
the transmission data 117 and the noise 125, and the receiver 106 configured to decode the received data 119, wherein the receiver 106 is provided with the pilot symbols 235 and decoding the received data 119 comprises filtering the impulsive noise 125 from the received data 119 and provide the information 115 at a receiver 130.

2. The system 100 as claimed in claim 1, wherein the noise 125 comprise:
at least one of an induced impulsive noise and/or channel noise and/or noise from channel interference.

3. The system as claimed in claim 1, wherein the transmitter 110 comprises:
a receiving unit 210, wherein the receiving unit 210 is configured to convert the information 115 received at the transmitter 110, wherein the information 115 is an analog signal, and the receiving unit 210 is configured to convert the analog signal into a digital signal or input bits.

4. The system 100 as claimed in claim 1, wherein the transmitter 110 comprises:
a mapping unit 220 configured to perform a quadrature amplitude modulation (QAM) mapping of the input bits producing a modulated signal, the modulated signals is a combination of a phase modulation and an amplitude modulation of the input bits, and the mapping unit 220 configured to convert the modulated signal to delayed Doppler domain information symbols.

5. The system 100 as claimed in claim 1, wherein the transmitter comprises:
a grid formation unit 230, wherein the grid formation unit 230 is configured to convert the delayed Doppler information symbols into an orthogonal time frequency grid in a time frequency domain, and generate a N X M matrix, wherein the N X M matrix is a combination of the pilot symbols 235 and the delayed Doppler information symbols, wherein N is the number of Doppler bins and M is the number of delay bins in the N X M matrix.

6. The system 100 as claimed in claim 5, wherein the pilot symbols 235 are pre-determined by a service provider and/or a user and the pilot symbols 235 are provided to the transmitter 110 and the receiver 130.
7.
8. The system 100 as claimed in claim 1, wherein the transmitter 110 comprises:
a transformation unit 240, the transformation unit 240 configured to convert the N X M matrix containing a combination of the pilot symbols 235 and the delayed Doppler information symbols into a time domain signal.

9. The system as claimed in claim 7, wherein the transformation unit 240 configured to perform an Inverse Sympletic Finite Fourier Transformation (ISFFT) on the N x M matrix; and subsequently perform a Heisenberg transformation (HT) on the N X M matrix producing a time domain signal.

10. The system 100 as claimed in claim 8, wherein the time domain signal is transmitted over the transmission channel 120 to the receiver 130, wherein the receiver is configured to receive the received data, wherein the received data comprises the time domain signal from the transmitter 110 combined with impulsive noise 125 picked up along the transmission channel 125.

11. The system 100 as claimed in claim 1, wherein the receiver 130 comprises:
an inverse-transform unit 310, wherein the inverse-transform unit 310 is configured to perform an inverse transformation on the received data, wherein the received data comprises: the time domain signal.

12. The system 100 as claimed in claim 10 wherein the inverse transformation comprises: transforming the time domain signals into the delay Doppler domain information symbols and the pilot symbols.

13. The system 100 as claimed in claim 10, wherein the inverse-transform unit 310 is configured to first perform a Wigner transform on the received data providing a Wigner transformed data, and subsequently perform a Sympletic Finite Fourier Transformation (SFFT) on the Wigner transformed data to obtain delayed Doppler information symbols from the received data.

14. The system 100 as claimed in claim 1, wherein the receiver 120 comprises:
a channel estimator 325 configured to receive the delayed Doppler domain pilot symbol from the inverse-transform unit 310, and estimate a channel information and the information 117 from the received data 119, wherein the pilot symbols 235 are provided to the channel estimator 325 at the receiver 130.

15. The system as claimed in claim 13, wherein the channel estimator 325 is configured to provide the channel information estimated to a detector unit 320.

16. The system 100 as claimed in claim 13, wherein the channel estimator 325 is configured to apply a L0-Maximum Versoria Criteria (L0-MVC) to the channel information.

17. The system 100 as claimed in claim 1, wherein the detector unit 320 is configured to receive the delayed Doppler domain information symbols from the inverse-transform unit 310 and the channel information estimated from the channel estimator.

18. The system 100 as claimed in claim 16, wherein the detector unit 330 is configured to perform a Message Passing based Maximum Versoria Criteria (MP-MVC) on the delayed Doppler domain information symbols to identify the modulated signal.

19. The system 100 as claimed in claim 1, wherein the receiver 130 comprises:
de-mapping unit 330, wherein the de-mapping unit 330 is configured to demodulate the modulated signal into the digital signal or received bits 340, wherein the received bits are equivalent to the input bits.

20. The system 100 as claimed in claim 18, wherein the received bits are transformed back to an analog signal and provided at a receiving end.

21. A method of processing information from a transmitter to a receiver, the information transmitted over a transmission channel, the method comprising:
receiving information as analog signals and converting the analog signals to digital signals;
creating transmission data by multiplexing the digital signal with pilot symbols;
transmitting the transmission data from a transmitter to a receiver over a transmission channel.

22. The method as claimed in claim 20, the method comprising:
performing a QAM on the digital signals to obtain delayed Doppler domain information symbols;
converting the delayed Doppler domain information symbols to an orthogonal time frequency space signal N X M grid by combining the orthogonal time frequency space signal with pilot symbols, wherein the pilot symbols are provided by a service provider;
performing an ISFFT and HT on the time domain frequency space signal N X M grid to obtain transmission data.

23. A method for receiving information from a transmitter at a receiver, the information transmitted over a transmission channel, the method comprising:
receiving received data at a receiver, wherein the received data comprises transmission data and noise, wherein the noise is embedded into the transmission data by the transmission channel, the noise being at least one of at least one of an induced impulsive noise and/or channel noise and/or noise from channel interference;
demultiplexing the received data to obtain a digital signal from the transmission data; and
converting the digital signal into an analog signal and providing the analog signal to an end user.

24. The method as claimed in claim 22, the method comprising:
receiving pilot symbols at a channel estimator 130;
performing an inverse transformation on the received data at a inverse-transform unit 310, wherein the received data includes a time domain signal, and the inverse transformation includes transforming the time domain signal to delayed Doppler domain information symbols and pilot symbols;
estimating channel information at the channel estimator 325 using L0-MVC
performing a MP-MVC on the delayed doppler domain information symbols to obtain a modulated signal;
de-multiplexing the modulated signal to receive the digital signal, and converting the digital signal to an analog signal.

Dated this 15th day of December 2023
Indian Institute of Science
By their Agent & Attorney

(Dr. Eric W B Dias)
of Khaitan & Co
Reg No IN/PA-1058