Efficient OTFS time delay-Doppler domain symbol detection method

Abstract

The invention relates to an efficient OTFS time delay-Doppler domain symbol detection method, and belongs to the technical field of wireless communication. According to the method, firstly, a matrix is used for representing an OTFS modulation process, a matrix is used for representing a wireless channel transmission process, and a matrix is used for representing an OTFS demodulation process; then, the time delay-Doppler domain equivalent transmission matrix is used for representing OTFS time delay-Doppler domain equivalent transmission; and finally, calculating an estimated time delay-Doppler domain sending symbol by using the time delay-Doppler domain symbol of the receiving end, the time delay-Doppler domain equivalent transmission matrix and the variance of the Gaussian white noise, thereby completing symbol detection. When decimal time delay / Doppler exists in a channel or transmitter / receiver formed pulses cannot meet ideal orthogonal conditions, the method is more suitable for the decimal time delay of the channel, and the complexity is lower.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to an efficient OTFS delay-Doppler domain symbol detection method. Background Art

[0002] OTFS (Orthogonal Time Frequency Space) is a new two-dimensional modulation technology that modulates information symbols in the delay-Doppler domain. Many studies have shown that OTFS performs better than OFDM (Orthogonal Frequency Division Multiplexing) technology in high-speed mobile scenarios. Channel estimation and detection are two key technologies for OTFS reception. Among them, OTFS channel estimation often uses a data-assisted method, that is, the transmitter inserts known pilot symbols in the delay-Doppler domain, and the receiver estimates CSI (Channel State Information) based on the response of the pilot symbols affected by the channel in the delay-Doppler domain; OTFS detection estimates information symbols based on the CSI and the response of information symbols in the delay-Doppler domain. Since the pilot symbols and information symbols of OTFS are both in the delay-Doppler domain, the equivalent transmission representation of the delay-Doppler domain, that is, constructing the equivalent input-output relationship of OTFS in the delay-Doppler domain, is the basis for OTFS channel estimation and detection.

[0003] Raviteja P et al. published a paper titled "Interference Cancellation and Iterative Detection for Orthogonal Time Frequency Space Modulation" in the IEEE Transactions on Wireless Communications in 2018. The paper analyzes the signal processing and transmission process of OTFS in detail and proposes an OTFS delay-Doppler domain equivalent transmission representation method that can adapt to fractional delay channels. This method has a high complexity when the transmitter and receiver shaped pulses are not ideally orthogonal, or when fractional delay / Doppler exist simultaneously (Method 1).

[0004] Raviteja P et al. published a paper titled "Practical Pulse-Shaping Waveforms for Reduced-Cyclic-Prefix OTFS" in IEEE transactions on vehicular technology in 2018. The equivalent channel transmission matrix is ​​divided into two matrices multiplied by one, where one matrix represents Doppler and the other represents channel delay. This method is only unsuitable for fractional delay channels (method 2).

[0005] In summary, when the channel has fractional delay / Doppler, or the transmitter / receiver shaped pulse cannot meet the ideal orthogonal condition, the existing OTFS delay-Doppler domain symbol detection method has the problem of being unable to adapt to the channel fractional delay or having high complexity. Therefore, how to provide an efficient OTFS delay-Doppler domain symbol detection method that can adapt to the fractional delay / Doppler channel is a technical problem that technicians in this field are very concerned about. Summary of the invention

[0006] The present invention provides an efficient OTFS delay-Doppler domain symbol detection method for the situation where a channel has fractional delay / Doppler and a pulse shaping waveform is not ideally orthogonal.

[0007] The technical solution adopted by the present invention is:

[0008] An efficient OTFS delay-Doppler domain symbol detection method, in which, is the delay-Doppler domain symbol to be sent, is the delay-Doppler domain symbol at the receiving end, and the oversampling rate at the transmitting end and the receiving end is N s , the sampling period is T s The pulse shaping waveforms at the transmitter and receiver are g tx (·), g rx (·); The method comprises the following steps:

[0009] Step 1: Represent the OTFS modulation process as matrix M T :

[0010]

[0011] Among them, F M and F N Represents the Fourier transform matrix of M and N points respectively, and its m rows and n columns are M and N represent the number of grid points in frequency and time dimensions, respectively; express The first M columns of Respectively represent F N, The conjugate transpose of ; represents the Kroneth product; G tx is a diagonal matrix, T represents the symbol period;

[0012] Step 2: Represent the wireless channel transmission process as matrix H t :

[0013]

[0014] Where P represents the number of transmission paths of the channel, h i represents the path gain corresponding to the i-th path, Δ i is a diagonal matrix, ν i represents the Doppler corresponding to the i-th path; k represents the Doppler index; κ i represents the fractional delay of the ith path; K i represents the integer delay of the ith path;

[0015] P is the forward shift matrix, expressed as:

[0016]

[0017] c i [l,κ i ] is expressed as:

[0018]

[0019] Step 3: Represent the OTFS demodulation process as matrix M R :

[0020]

[0021] in, express The first M rows of G rx is a diagonal matrix,

[0022] Step 4: Use the delay-Doppler domain equivalent transmission matrix H e Represents OTFS delay-Doppler domain equivalent transmission:

[0023] H e =M R H t M T ;

[0024] Step 5: Use the delay-Doppler domain symbol at the receiving end Delay-Doppler domain equivalent transmission matrix He and the variance σ of Gaussian white noise 2 , calculate the estimated delay-Doppler domain transmitted symbol

[0025]

[0026] Where I represents the identity matrix;

[0027] Complete symbol detection.

[0028] The following beneficial effects can be obtained by adopting the present invention:

[0029] 1. The present invention uses matrix T i represents the channel delay, T i The calculation process combines the integer delays of the four adjacent channels to achieve the representation of the channel fractional delay. Although the methods 1 and 2 in the prior art can also achieve the representation of the channel fractional delay, this method is better than method 2 in representation accuracy and error performance, and is similar to method 1; the representation complexity is lower than that of method 1.

[0030] 2. N in the present invention s It is configurable, while the existing methods 1 and 2 can only adapt to N s =1. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is a comparison chart of the bit error performance of the present invention, method 1, and method 2;

[0032] Figure 2 It is a complexity comparison chart between the present invention and method 1. DETAILED DESCRIPTION

[0033] In order to better understand the present invention, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0034] An efficient OTFS delay-Doppler domain symbol detection method is proposed, where T and Δf represent the symbol period and subcarrier spacing, respectively, and M and N represent the number of grid points in the frequency and time dimensions, respectively. is the delay-Doppler domain symbol to be sent, is the delay-Doppler domain symbol at the receiving end, σ 2 is the variance of Gaussian white noise, and the oversampling rates of the transmitter and receiver are both N s , the sampling period is T s The pulse shaping waveforms at the transmitter and receiver are g tx (·), g rx (·), P represents the number of transmission paths of the channel, h i , τ i , νi They represent the path gain, delay, and Doppler corresponding to the i-th path respectively. The specific steps are:

[0035] The first step is to use the matrix M T represents the OTFS modulation process, M T The calculation method is Among them, F M and F N Represents the Fourier transform matrix of M and N points respectively, and the calculation method of its m rows and n columns is express The first M columns of Respectively represent F N , The conjugate transpose of ; represents the Kroneth product; G tx is a diagonal matrix, and

[0036] The second step is to use the matrix H t Represents the wireless channel transmission process, and the calculation method is where Δ i is a diagonal matrix, and Δ i =diag[z(0),…,z(k),…,z(N s MN-1)], k represents the Doppler index; κ i represents the fractional delay of the ith path; K i represents the integer delay of the ith path; Π is the forward shift matrix, expressed as

[0037]

[0038] c i [l,κ i ] is expressed as

[0039]

[0040] The third step is to use the matrix M R represents the OTFS demodulation process, M R The calculation method is in express The first M rows of G rx is a diagonal matrix,

[0041]

[0042] The fourth step is to use the delay-Doppler domain equivalent transmission matrix H erepresents the OTFS delay-Doppler domain equivalent transmission, H e The calculation method is H e =M R H t M T .

[0043] Step 5: Use the delay-Doppler domain symbol at the receiving end Delay-Doppler domain equivalent transmission matrix H e and the variance σ of Gaussian white noise 2 Compute the estimated delay-Doppler domain transmitted symbol The calculation method is Where I represents the identity matrix.

[0044] In order to illustrate that the present invention can effectively realize OTFS delay-Doppler domain symbol detection, simulation experiments are carried out on method 1, method 2 and the present invention. The simulation results are shown in FIG. Figure 1 As shown. The horizontal axis represents the signal-to-noise ratio, and the vertical axis represents the bit error rate. The simulation parameters are set as: M = 32, N = 16, Δf = 15kHz, the relative movement speed between the transmitter and the receiver v = 500km / h, and the carrier frequency f c =4GHz, symbol mapping mode is QPSK. P, h i , τ i Determined by the extended vehicle channel model, τ i After normalization, they are 0, 0.0144, 0.072, 0.1488, 0.1776, 0.3408, 0.5232, 0.8304, and 1.2048 respectively. The Doppler frequency deviation ν of each transmission path i =v max cos(θ i ), where ν max Because v, f c The calculated maximum Doppler frequency deviation, θ i is the arrival angle of the ith path and is uniformly distributed in [0,2π). Assume that P and h i , τ i , ν i Ideal estimation, since method 2 cannot adapt to fractional delays, τ i Rounded to an integer multiple of the OTFS delay resolution. Curve 1 (solid line with "+") represents method 1, curve 2 (dashed line with "*") represents method 2, and curve 3 (solid line with squares) represents the method of the present invention and N s =1, Curve 4 (solid line with circle) The method of the present invention and N s =2, Curve 5 (solid line with five-pointed star) The method of the present invention and N s =4. Figure 1 It can be seen from the figure that when the channel fractional delay exists, method 2 can no longer correctly represent the channel, resulting in a high bit error rate. s When =4, the present invention can achieve bit error performance similar to that of method 1.

[0045] To illustrate that the complexity of the present invention is lower than that of method 1, simulation experiments are conducted on the complexity of method 1 and the present invention. The simulation results are as follows: Figure 2 In the figure, the horizontal axis represents different M and N, and the vertical axis represents the minimum number of DSPs required when the development platform is FPGA. Curve 1 (solid line with "*") represents method 1, and curve 2 (solid line with diamonds) represents the present invention and N s = 1, curve 3 (dashed line with squares) represents the present invention and N s = 2, curve 4 (dashed line with circle) represents the present invention and N s =4, curve 5 (dashed line with hexagonal star) represents the present invention and N s = 8. As can be seen from the figure, the complexity of the present invention is about 1 / 10 of that of method 1, which shows that the complexity of the present invention is much lower.

[0046] In summary, the present invention is more adaptable to channel fractional delay and has lower complexity when there is fractional delay / Doppler in the channel or the transmitter / receiver shaped pulse cannot meet the ideal orthogonal condition.

Claims

1. An efficient OTFS delay-Doppler domain symbol detection method, characterized in that: is the delay-Doppler domain symbol to be sent, is the delay-Doppler domain symbol at the receiving end, and the oversampling rate at the transmitting end and the receiving end is N s , the sampling period is T s The pulse shaping waveforms at the transmitter and receiver are g tx (·), g rx (·); The method comprises the following steps: Step 1: Represent the OTFS modulation process as matrix M T : Among them, F M and F N Represents the Fourier transform matrix of M and N points respectively, and its m rows and n columns are M and N represent the number of grid points in frequency and time dimensions, respectively; express The first M columns of Respectively represent F N , The conjugate transpose of ; represents the Kroneth product; G tx is a diagonal matrix, T represents the symbol period; Step 2: Represent the wireless channel transmission process as matrix H t : Where P represents the number of transmission paths of the channel, h i represents the path gain corresponding to the i-th path, Δ i is a diagonal matrix, Δ i =diag[z(0),…,z(k),…,z(N s MN-1)], ν i represents the Doppler corresponding to the i-th path; k represents the Doppler index; κ i represents the fractional delay of the ith path; K i represents the integer delay of the ith path; P is the forward shift matrix, expressed as: c i [l,κ i ] is expressed as: Step 3: Represent the OTFS demodulation process as matrix M R : in, express The first M rows of G rx is a diagonal matrix, Step 4: Use the delay-Doppler domain equivalent transmission matrix H e Represents OTFS delay-Doppler domain equivalent transmission: H e =M R H t M T ; Step 5: Use the delay-Doppler domain symbol at the receiving end Delay-Doppler domain equivalent transmission matrix H e and the variance σ of Gaussian white noise 2 , calculate the estimated delay-Doppler domain transmitted symbol Where I represents the identity matrix; Complete symbol detection.

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