WO2024049391A1

WO2024049391A1 - Otfs channel estimation methods and systems

Info

Publication number: WO2024049391A1
Application number: PCT/TR2023/050872
Authority: WO
Inventors: Ahmet Sacid SUMER; Huseyin Arslan; Salah Eddine ZEGRAR
Original assignee: Istanbul Medipol Universitesi
Priority date: 2022-08-31
Filing date: 2023-08-28
Publication date: 2024-03-07

Abstract

The invention is related to a computer-implemented OTFS channel estimation method for dispersive channels with residual delays and/or residual shift.

Description

OTFS CHANNEL ESTIMATION METHODS AND SYSTEMS

Technical Field

Prior Art

One of the main concerns of next generation wireless communication systems is providing highly reliable communication links in high mobility environments such as high-speed railway mobile communications where the channels are fast time-varying with high Doppler spreads. Recently, orthogonal time-frequency space (OTFS) modulation is proposed as a robust waveform suitable for doubly dispersive channels as in high mobility scenarios [1]. OTFS modulation parameterizes the effect of the time-varying channels for any waveform by representing the channel in the delay-Doppler domain where the real reflectors distributed in the propagation environment corresponds to the channel seen at the receiver, and thus, for a relatively short time frame the channel can be considered invariant [2] .

The Doppler shifts are induced by the mobile reflectors and delays come from the reflectors. However, the Doppler shifts might not necessarily integer multiples of the Doppler resolution of the OTFS.

As mentioned above, delays are occurred by reflectors. However, the delays might not necessarily come synchronized with the delay resolution of the OTFS waveform and come with fractional delay shifts relatively to the sampling frequency.

Additionally, even if the Doppler shifts or delays are integers, samplings might not be perfect as well causing residual time delays due to hardware impairments or carrier frequency offset can cause residual frequency shifts due to hardware impairments. This means that fractional delay channels or fractional Doppler channels will always be there even if the wireless channel causes integer delays.

In delay-Doppler domain, the fractional time delays cause inter-delay interference and likewise in delay-doppler domain, the Doppler shifts causes inter-Doppler interference (IDI). So, inter-delay interferences are introduced by the fractional Doppler channel and/or the fractional delay channel harms the performance of OTFS systems.

P. Raviteja et al [3] proposed a low complexity message passing algorithm which mitigates the highest IDI components for OTFS channel estimation. This study was followed by another work of the author [4], where embedded pilot symbols are adopted for channel estimation using the threshold method. Furthermore, in another study of the P. Raviteja et al [5], pilot, guard, and data are arranged such that the interference is avoided.

Delay-Doppler domain embedded pilot-based time domain channel estimation method is proposed S. S. Das et al. [6] by considering carrier frequency offset, residual frame timing offset, and fractional Doppler shifts which is further used to construct channel estimation and equalization methods.

Shi et al. [7] investigated MIMO OTFS systems and proposed a modified sensing matrixbased channel estimation with a deterministic pilot design for a downlink CSI acquiring scheme.

N. Hashimoto et al. [8] teaches OTFS channel is estimated using pilots in the delay-Doppler domain with a cross-correlation based algorithm. This method has lower computational complexity than the traditional channel estimation methods with pseudo sequences.

H. B. Mishra et al. [9] proposed two superimposed pilot- aided channel estimation methods. The first method uses data as interference and estimates the channel, however, it degrades the SNR. The second method reduces the degradation of SNR by exploiting the iterations between data detection and channel estimation.

F. Liu et al. [10] adopted Bayesian learning which formulates the problem as sparse signal recovery then, the channel gains along with the fractional Doppler shifts are estimated rather than estimating the delay-Doppler domain channel directly.

Furthermore, Wei et al. [11] suggested employing Dolph-Chebyshev windowing on either transmitter or receiver side for channel estimation with the consideration of multiple fractional Doppler shifts. The same authors adopted sparse Bayesian learning for off-grid original delay-Doppler domain channel response estimation rather than effective channel response which is commonly investigated in the literature [12]. The OTFS channel estimation is formulated as sparse signal recovery where both delay and Doppler shifts are estimated separately

There is no known study for fractional delay channel estimation and equalization in OTFS systems.

Future networks need to support new wireless technologies like 5G-Tactile Internet, Internet of Things (loT), ULLRC, remote surgery. However, the known devices used in the abovementioned applications are naturally power-limited, processing-restricted and delaysensitive which make complex estimation algorithms not feasible solution.

As a result, all of the problems mentioned above has made it necessary to provide a novelty in the related field.

Brief Description and Objects of the Invention

The main aim of the invention is to introduce more feasible and less complicated way to estimate the fractional channels, and mitigating the interference caused by the fractional channels in the OTFS systems.

Another aim of the invention is to introduce a method that provides finer resolution of the fractional channels.

Another aim of the invention is to introduce a method that can be applied to estimate the integer and fractional components of each channel tap in parallel reducing the processing time.

Another aim of the invention is to introduce a method that can be applied both of a single tap and multiple taps dispersive channels.

Another aim of the invention is to introduce a method that provides enough flexibility to change the estimation resolution depending on the computational complexity required. This makes it implementable even in low-cost limited power devices such as internet of things (loT) devices.

To accomplish above mentioned aims, a computer-implemented OTFS channel estimation method for dispersive channels with residual delay is provided. The method (method I) comprises steps of; - Extracting received symbols which are used for channel estimation from delay- Doppler domain signal received by the receiver,

- Converting the received symbols to time domain from delay-Doppler after that to frequency domain,

- Estimating the integer and fractional shift induced by the channel with domain pilot signal and maximum power value,

- Computing a^Lh power of the pilot signal for each channel tap, until a does not exceed the maximum power value, wherein a is a power value, and converting it to time domain after that to delay- Doppler domain,

- Computing Doppler index of the maximum power bin for each channel tap for each channel tap, until a does not exceed the maximum power value, and converting it to frequency domain after that to delay-Doppler domain,

- Computing difference between each successive Doppler index of the maximum power bin and using the differences to compute the fractional delay shifts,

- Generating a matrix, according the fractional delay shifts,

- Calculating a time domain channel matrix by the matrix generated according the fractional delay shifts,

- Equalizing the channel effects.

In another aspect, for the general purpose of providing a computer implemented OTFS channel estimation method, the invention further provides a method for the cases where dispersive channels have residual shift, therefore an embodiment of the invention relates to a computer-implemented OTFS channel estimation method for dispersive channels with residual shift, wherein said method (method II) comprises the steps of;

- Extracting received symbols, which are used for channel estimation from delay- Doppler domain signal, received by the receiver,

- Converting the received symbols to time domain from delay-Doppler,

- Estimating the integer and fractional Doppler shift induced by the channel with domain pilot signal and maximum power value,

- Computing a^Lh power of the pilot signal for each channel tap, until a does not exceed the maximum power value, wherein a is a power value, and converting it to delay- Doppler domain, - Computing Doppler index of the maximum power bin for each channel tap, until a does not exceed the maximum power value, and converting it to delay- Doppler domain,

- Computing difference between each successive Doppler index of the maximum power bin and using the differences to compute the fractional Doppler shifts,

- Generating a matrix, according the fractional Doppler shifts,

- Calculating a time domain channel matrix by the matrix generated according the fractional Doppler shifts,

- Equalizing the channel effects.

Description of the Figures of the Invention

The figures and related descriptions necessary for the subject matter of the invention to be understood better are given below.

Figure 1. A pilot design for fractional delay channel.

Figure 2. A graphical presentation of the carrier wave for fractional delay channel.

Figure 3. A flow chart for fractional delay channel.

Figure 4. A pilot design for fractional Doppler channel.

Figure 5. A flow chart for fractional Doppler channel.

Detailed Description of the Invention

The invention is related to an OTFS channel estimation method for dispersive channels with residual delays.

The invention is a method to estimate channel of OTFS systems. As such, it is applicable to industry which is interested to using OTFS modulation scheme in their in wireless communication.

Any wireless communication technology can utilize this invention to provide protection to data, pilots or jointly data and pilots against eavesdroppers. However, standards like 3GPP- based cellular and IEEE 802.11 based Wi-Fi networks, or any wireless network are particularly relevant to the invention due to the support of multipoint coordination provided in both standards. Furthermore, the described method in this invention can be implemented on any device, system or network capable of supporting any of the aforementioned standards, for instance: code division multiple access (CMDA), frequency division multiple access (FDMA), Global System for Mobile communications (GSM), GSM/General Packet Radio Service (GPRS), Enhanced Data GSM Environment (EDGE), Wideband-CDMA (W- CDMA), Evolution Data Optimized (EV-DO), High Speed Packet Access (HSPA), High Speed Downlink Packet Access (HSDPA), High Speed Uplink Packet Access (HSUPA), Evolved High Speed Packet Access (HSPA+), Long Term Evolution (LTE), AMPS, 5G New Radio (NR), or other known signals that are used to communicate within a wireless, cellular or internet of things (loT) network

A system for carrying out the methods (Method I and Method II) of the present invention comprises a receiver. The receiver is configured to receive delay-doppler domain signal.

A system also comprises a processing unit capable of carrying out below mentioned steps;

- Extracting a received symbols which are used for channel estimation from delay-doppler domain signal received by the receiver,

- Converting the received symbols to time domain from delay-Doppler after that to frequency domain.

- Estimating the integer and fractional shift induced by the channel with domain pilot signal and maximum power value.

- Computing power of the pilot signal for each channel tap, until a does not exceed the

maximum power value, wherein a is a power value, and converting it to time domain after that to delay-Doppler domain,

- Computing Doppler index of the maximum power bin for each channel tap for each channel tap, until a does not exceed the maximum power value, and converting it to delay-Doppler domain,

- Computing difference between each successive Doppler index of the maximum power bin and using the differences to compute the fractional shifts,

- Generating a matrix, according the fractional shifts,

- Calculating a time domain channel matrix by the matrix generated according the fractional shifts,

- Equalizing the channel effects. In a preferred embodiment of the invention, a system comprises a processing unit capable of carrying out below mentioned steps;

- Converting the received symbols to time domain from delay-Doppler,

maximum power value, wherein a is a power value, and converting it to delay-Doppler domain,

- Generating a matrix, according the fractional shifts,

- Equalizing the channel effects

The above-mentioned method steps of the invention, for example Method I and Method II, in broadest term, can be used prevent for inter-delay interferences are introduced by the fractional delay channel or fractional Doppler channel.

Referring to the Fig 3 which is a flow-chart for fractional delay channel according to Method I of the invention;

In the second embodiment, the channel matrix will be examined in the integer delay and integer Doppler scenario. This embodiment is designed for estimating fractional delay shift. From here, we will show the fractional Doppler scenario. In case of having both integer delay and Doppler shifts, the input-output relationship can be derived as

where w, H G (JMNXMN , , y and x denote the AWGN vector with variance cr², the time equivalent and delay-Doppler domain channel matrices, received delay-Doppler symbols, and transmitted delay-Doppler symbols respectively. and are represent the unitary

discrete Fourier transform (DFT) matrix and M x M identity matrix. M and N corresponds to delay and Doppler number of delay and Doppler bins. Moreover, H in above equation can be expressed as

where h_t, L, fc^and denote the channel coefficients, number of channel tap, integer Doppler and integer delay indices, respectively. _Nexpresses delay shift matrix which is corresponds

to the forward cyclic shifted permutation matrix as

and ^refers to the Doppler shift matrix and can be represented as

with

In case of having fractional delays and integer Doppler shifts in the system is equivalent of having integer delays channel but downsampled at the receiver side. So, the fractional delay channel matrix is a downsampled version of a larger matrix with integer delays. Specifically, the L tap fractional delay time-domain channel matrix can be given as

where (1 is the upsampling factor such that all the delay shifts are integers. Therefore, the upsampled received time-domain signal can be found as

where w_up is the oversampled time-domain AWGN noise vector, A is the D.MN X MN zero padding matrix, and B = BlkDiag(F_MW, 0_MN, OMN) ^ar|d ®MN i^s the MN X MN zeros matrix. Therefore, the time domain received signal can be computed as follows

where

The received signal in delay-Doppler domain is then found as

where T*-¹-* is a known phase term that denotes the type of prefix/suffix used and W(l, k) represents the noise. We will use reduced-CP OTFS configuration, therefore F^(Z, fc) can be found as

Due to fractional shifts of the two-dimensional sine pulse in delay-Doppler domain in the delay directional causing inter-delay interference since these sine pulses are no more sampled at their zero-crossings. The fractional delay shifts induce spreading of all the symbols in delay dimension. Thus, to avoid the inter-delay interference the pilot arrangement is chosen to be as shown in Fig. 1, which is given by

where k_p and l_p correspond to pilot locations on delay-Doppler grid. At the receiver side, the received symbols are used for channel estimation where

Now we to introduce the lemma on the OTFS waveform carrier. The OTFS waveform carrier holds its shape under the operations of time delay and Doppler shift, where it extends quasi- periodically in the delay-Doppler grid. The time domain OTFS waveform carrier can be seen as a frequency modulated pulse train as depicted in Fig. 2, thus it is expressed as

The OTFS waveform carrier is self-dual between time and frequency, such that applying Fourier transform to the OTFS waveform carrier results in the OTFS waveform carrier as well and vice-versa. The frequency representation of the OTFS waveform carrier can be found by DFT as follows

The frequency shifting property states that the Fourier transform of the modulated signal in time is the shifted version of its Fourier transforms in frequency [1]. Then, we find

The second term in the equation is periodic over f 6 [0, MN — 1], with period N as follows

Also, for the summation becomes equivalent to the DFT which results in

Then, the frequency representation of a OTFS waveform carrier becomes

we see that the frequency representation of the OTFS waveform carrier is indeed the OTFS waveform carrier.

The OTFS waveform carrier /pilot location is delay-Doppler domain can be chosen randomly, therefore, for the rest of this patent it is assumed that

and .

For simplicity, we first explain the proposed method considering a single tap with fractional delay shift, and then, the proposed method is generalized for any doubly-dispersive channel.

To estimate fractional Doppler shifts in the channel, the received signal is exploited.

Using lemma, the time domain signal r_p(n) can be found by setting as follows

According to lemma, it is found that the transmitted pilot impulse is self-dual between time and frequency, such that applying Fourier transform to it results in another OTFS carrier. However, the only change is that the delay and Doppler shifts will exchange places. Therefore, the frequency representation of the whole received time pilot signal can be found as

To estimate fractional delay shifts in the channel we are assuming a single tap channel, the a- th power of given by

Consequently, the time-domain single of [#p(/)] can be found by taking the inverse DFT as follows

Furthermore, the delay-Doppler representation of is found as

It is possible to convert the fractional delay shift into integer just by ensuring the following condition

Then, we have

It is concluded that trying different a until the condition fulfilled can give us the exact integer and fractional delay shift.

We propose a single algorithm to find all integer and fractional delay shifts at once. Initially, is computed for Then, for each a and Doppler shift Zc_£ values, the

Doppler index of the max power bin is found After that, the

difference between each successive is calculated as follows

Finally, the integer and fractional Doppler shifts are found by taking the mean of the differences as follows

After finding the fractional delay shifts in the channel, the G matrix can be found. After that, the time domain channel matrix H, can be calculated from G to generate delay-Doppler channel matrix

Then, the MMSE detector [1] can be used to equalize the channel effects, subsequently, the estimated data symbols X are obtained as

Referring to the Fig 5, which is a flow chart for fractional Doppler channel related to Method II of the invention;

In the first embodiment, the channel matrix will be examined in the integer delay and integer Doppler scenario. This embodiment is designed for estimating fractional Doppler shift. From here, we will show the fractional Doppler scenario. In case of having both integer delay and Doppler shifts, the input-output relationship can be derived as

where , y and x denote the AW GN vector with variance , the time

equivalent and delay-Doppler domain channel matrices, received delay-Doppler symbols, and transmitted delay-Doppler symbols respectively. F_w and I_M are represent the Nx N unitary discrete Fourier transform (DFT) matrix and M x M identity matrix. M and N corresponds to delay and Doppler number of delay and Doppler bins. Moreover, H in above equation can be expressed as

where h_t, L, fc^and denote the channel coefficients, number of channel tap, integer Doppler and integer delay indices, respectively. expresses delay shift matrix which is corresponds

to the forward cyclic shifted permutation matrix as

and refers to the Doppler shift matrix and can be represented as

with

In case of having integer delays and fractional Doppler shifts, the channel matrix becomes

with

and denotes the fractional Doppler shifts. Consequently,

the received signal becomes

where is a known phase term that denotes the type of prefix/suffix used and

represents the noise. We will use reduced-CP OTFS configuration, therefore can be

found as

Due to fractional shift of the two-dimensional sine in delay-Doppler domain in the Doppler directional causing inter-Doppler interference since sampling is no more at zero-crossings. As seen from

), the range of motion of the Doppler bins is the whole Doppler dimension as demonstrated as Therefore, the channel spreads all Doppler dimensions

as . Since the delay propagation is still integer, it would still be sufficient to

put guard as around the pilot in the delay dimension as depicted in Fig. 1

and the pilot arrangement for fractional Doppler scenario can be represented as

where and _p correspond to pilot locations on delay-Doppler grid. At the receiver side, the received symbols

are used for channel estimation where

Now we introduce the lemma on the OTFS waveform carrier. The OTFS waveform carrier holds its shape under the operations of time delay and Doppler shift, where it extends quasi- periodically in the delay-Doppler grid. The time domain OTFS waveform carrier can be seen as a frequency modulated pulse train as depicted in Fig. 2, thus it is expressed as

After passing through a doubly-dispersive channel, the received signal can be found as

where q 6 [—0.5, 0.5] denotes fractional delay shifts and for M > lj + q, there is no intersymbol interference between r_p(n) samples meaning that the double summation in above equation denotes the shifts only. For simplicity, we first explain the proposed method considering a single tap with fractional Doppler shift, and then, the proposed method is generalized for any doubly-dispersive channel.

To estimate fractional Doppler shifts in the channel, the received Y_p(l, k) signal is exploited.

In fact, Y_p(l, k) is delay-Doppler representation of a the OTFS waveform carrier that passed through a one-tap doubly-dispersive channel. Then, using lemma the time domain signal r_p(n)can be found from lemma equation by setting q = 0 as follows

Consider the a-th power of given by

Lemma states that for

, which is true, there is no inter- symbol interference between r_p(n) samples. Thus, powers of can be found by taking the power of each element

ignoring the double summation. Therefore, we find

Note that the term limits the potential of the proposed method for a » 1, such that

Therefore, instead of taking the powers of r_p(n), we consider the powers of the phase of the received signal Zr_p(n) since it is the one containing the Doppler shift information. Then, we find

Consequently, the delay-Doppler representation of is found as

It is possible to convert the fractional Doppler shift into integer just by ensuring the following condition

Then, we have

It is concluded that trying different a until the condition fulfilled can give us the exact integer and fractional Doppler shift. In case of multi-tap doubly-dispersive channel with fractional Doppler shifts, the same process in the one-tap case can be followed. The only difference is that all Doppler bins are monitored in parallel for each value of a. For instance, the first tap can turn to integer for a = 2, where the second tap becomes integer at a = 5. The delay-Doppler representation of the received pilot signal is given by

Instead of checking each Doppler bin separately, we propose a single algorithm to find all integer and fractional Doppler shifts at once. Initially, is computed for

1,2, ... , a_max- Then, for each a and delay Z_£ values, the Doppler index of the max power bin is found

After that, the difference between each successive is

calculated as follows Finally, the integer and fractional Doppler shifts

are found by taking the mean of the differences as follows

Another embodiment of the invention is related to a system for OTFS channel estimation which comprises, (i) a receiver that is configured to receive delay-doppler domain signal and (ii) a processing unit that is configured to perform the computer-implemented OTFS channel estimation method for dispersive channels with residual delay (method I) or computer- implemented OTFS channel estimation method for dispersive channels with residual shift (method II).

Another embodiment of the invention is related to a computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the computer-implemented OTFS channel estimation method for dispersive channels with residual delay (method I) or the computer-implemented OTFS channel estimation method for dispersive channels with residual shift (method II). Another embodiment of the invention is related to A computer-readable storage medium comprising instructions which, when executed by a computer, cause the computer to carry out the computer-implemented OTFS channel estimation method for dispersive channels with residual delay (method I) or computer-implemented OTFS channel estimation method for dispersive channels with residual shift (method II).

References

1. S. Dogan-Tusha, and H. Arslan, “6g vision: An ultra-flexible perspective,” ITU Journal on Future and Evolving Technologies, vol. 1, no. 1, pp. 121-140, 2020.

2. R. Hadani, S. Rakib, A. Molisch, C. Ibars, A. Monk, M. Tsatsanis, J. Delfeld, A. Goldsmith, and R. Calderbank, “Orthogonal time frequency space (OTFS) modulation for millimeter-wave communications systems,” in IEEE MTT-S International Microwave Symposium (IMS). IEEE, 2017, pp. 681-683.

3. P. Raviteja, K. T. Phan, Y. Hong, and E. Viterbo, “Interference cancellation and iterative detection for orthogonal time frequency space modulation,” IEEE Transactions on Wireless Communications, vol. 17, no. 10, pp. 6501-6515, 2018.

4. P. Raviteja, K. T. Phan, Y. Hong, and E. Viterbo, “Embedded Delay-Doppler Channel Estimation for Orthogonal Time Frequency Space Modulation,” in 2018 IEEE 88th Vehicular Technology Conference (VTC-Fall), 2018, pp. 1-5.

5. P. Raviteja, K. T. Phan, and Y. Hong, “Embedded pilot-aided channel estimation for OTFS in delay-Doppler channels,” IEEE Transactions on Vehicular Technology, vol. 68, no. 5, pp. 4906-4917, 2019.

6. S. S. Das, V. Rangamgari, S. Tiwari, and S. C. Mondal, “Time Domain Channel Estimation and Equalization of CP-OTFS Under Multiple Fractional Dopplers and Residual Synchronization Errors,” IEEE Access, vol. 9, pp. 10 561-10 576, 2021.

7. D. Shi, W. Wang, L. You, X. Song, Y. Hong, X. Gao, and G. Fettweis, “Deterministic Pilot Design and Channel Estimation for Downlink Massive MIMO-OTFS Systems in Presence of the Fractional Doppler,” IEEE Transactions on Wireless Communications, vol. 20, no. 11, pp. 7151-7165, 2021.

8. N. Hashimoto, N. Osawa, K. Yamazaki, and S. Ibi, “Channel Estimation and Equalization for CP-OFDM-based OTFS in Fractional Doppler Channels,” in 2021 IEEE International Conference on Communications Workshops (ICC Workshops), 2021, pp. 1-7.

9. H. B. Mishra, P. Singh, A. K. Prasad, and R. Budhiraja, “OTFS Channel Estimation and Data Detection Designs With Superimposed Pilots,” IEEE Transactions on Wireless Communications, vol. 21, no. 4, pp. 2258-2274, 2022.

10. F. Liu, Z. Yuan, Q. Guo, Z. Wang, and P. Sun, “Message Passing-Based Structured Sparse Signal Recovery for Estimation of OTFS Channels With Fractional Doppler Shifts,” IEEE Transactions on Wireless Communications, vol. 20, no. 12, pp. 7773-7785, 2021. Z. Wei, W. Yuan, S. Li, J. Yuan, and D. W. K. Ng, “Performance analysis and window design for channel estimation of OTFS modulation,” in ICC 2021 - IEEE International Conference on Communications, 2021, pp. 1-7. Z. Wei, W. Yuan, S. Li, J. Yuan, and D. W. K. Ng, “Off-grid Channel Estimation with Sparse Bayesian Learning for OTFS Systems,” IEEE Transactions on Wireless Communications, pp. 1-1, 2022.

Claims

CLAIMS 1. A computer-implemented OTFS channel estimation method for dispersive channels with residual delay wherein said method (method I) comprises steps of,

- Receiving delay-doppler domain signal,

- Extracting a received symbols which are used for channel estimation from delay- doppler domain signal received by the receiver,

- Estimating the integer and fractional delay shift induced by the channel with domain pilot signal and maximum power value.

- Computing

power of the pilot signal for each channel tap, until a does not exceed the maximum power value, wherein a is a power value, and converting it to time domain after that to delay-Doppler domain,

- Generating a matrix, according the fractional delay shifts,

- Equalizing the channel effects, according the time domain channel matrix 2. A computer-implemented OTFS channel estimation method for dispersive channels with residual shift wherein said method (method II) comprises the steps of;

- Converting the received symbols to time domain from delay-Doppler,

- Computing 01^th power of the pilot signal for each channel tap, until a does not exceed the maximum power value, wherein a is a power value, and converting it to delay- Doppler domain, - Computing Doppler index of the maximum power bin for each channel tap, until a does not exceed the maximum power value, and converting it to delay- Doppler domain,

- Generating a matrix, according the fractional Doppler shifts,

- Equalizing the channel effects.

2. A system for OTFS channel estimation comprises,

A receiver that is configured to receive delay-doppler domain signal and

A processing unit that is configured to carry out the method of claim 1 or claim 2.

3. A computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method of claim 1 or claim 2.

4. A computer-readable storage medium comprising instructions which, when executed by a computer, cause the computer to carry out the method of claim 1 or claim 2.