A wireless mobile communication method based on generalized orthogonal chirp spread multiplexing

Abstract

The application discloses a wireless mobile communication method based on generalized orthogonal chirp division multiplexing, and relates to the field of wireless mobile communication. The method comprises the following steps: GOCDM modulation, double-selected channel modeling, received signal modeling, GOCDM demodulation under the double-selected channel, and channel equalization. The GOCDM communication system is applicable to a double-selected channel (i.e. a time-varying multipath channel). Each orthogonal base wave of the GOCDM is a Zadoff-Chu (ZC) sequence. The ZC sequence is determined by a sequence length N and a root coefficient l. The waveform of the GOCDM can be regarded as a digital chirp signal. When the N is fixed, the root coefficient l determines the chirp rate, namely the digital frequency modulation rate. The root coefficient l increases the flexibility of system design. By changing the l, the digital frequency modulation rate can be changed. When the l of the GOCDM is 1, the GOCDM is equivalent to a conventional OCDM system. Since the orthogonal base wave of the GOCDM is a digital chirp signal, the GOCDM has the characteristics of time-frequency domain double diffusion. The application improves the reliability of high-speed wireless communication on the double-selected channel.

Description

Technical Field

[0001] This invention relates to the field of wireless mobile communication, and more particularly to a wireless mobile communication method based on generalized orthogonal chirp multiplexing. Background Technology

[0002] With the explosive growth of mobile data traffic in wireless networks, wireless communication continues to pursue high speeds and reliability. Higher speeds mean shorter symbol durations, thus the same channel delay spread introduces more severe inter-symbol interference (ISI). The frequency selectivity of wireless channels becomes more pronounced. Furthermore, relatively high transceiver mobility, oscillator drift, and rapid environmental changes all contribute to the rapid time-varying nature of wireless channels. The time selectivity of wireless channels further degrades communication performance. Addressing the frequency and time selectivity of wireless channels (i.e., dual-selective channels) is a challenging task. The modulation scheme proposed in this paper aims to improve the reliability of high-speed wireless communication on dual-selective channels.

[0003] Recently, orthogonal chirp division multiplexing (OCDM) has been introduced into high-speed communication [1]. In OCDM systems, symbols are transmitted by orthogonal chirp waveforms. Therefore, OCDM symbols spread in both the time and frequency domains. This unique double-spreading characteristic makes OCDM more robust to burst interference in both the time and frequency domains. Therefore, OCDM systems have received widespread attention in various fields such as wireless communication, optical fiber communication, power line communication and underwater acoustic communication systems. [2] A comprehensive performance analysis of OCDM in frequency-selective channels shows that uncoded OCDM transmission can achieve unit diversity gain in the worst case. The performance of OCDM in frequency-selective channels is similar to that of single carrier (SC) communication with frequency domain equalization (FDE), but much better than orthogonal frequency division multiplexing (OFDM), which can only achieve unit diversity gain. However, most OCDM communication system schemes are only for frequency-selective channels, and the potential of OCDM in dual-selective channels has not been fully utilized, and the full advantages of OCDM have not been realized. [3] A block multiplexing-orthogonal chirp division multiplexing (BM-OCDM) system for dual-selective channels is proposed. The dual-selective channel experienced by each sub-block is decomposed into time-invariant (frequency-selective) and time-varying (time-selective) parts. The time-invariant part is estimated by interpolation method, which requires accurate knowledge of channel statistics, while the time-varying part is regarded as noise. Therefore, if no countermeasures are taken for the time-varying part of the channel, this system is difficult to cope with the fast time-varying dual-selective channel.

[0004] Domestic application CN202110270028.7, entitled "Multi-symbol Quasi-Orthogonal OCDM Radar-Communication Integrated Signal Modulation Method," provides a multi-symbol quasi-orthogonal OCDM radar-communication integrated signal modulation method. The method includes: determining parameters according to application requirements to obtain the symbolic expression of the OCDM integrated baseband signal; changing the frequency modulation slope in the symbols of the OCDM integrated baseband signal to obtain the symbolic expression of an orthogonal OCDM that is quasi-orthogonal to the symbols of the OCDM integrated baseband signal; performing time-division selection on the symbols of the OCDM integrated baseband signal and the orthogonal OCDM to obtain a one-frame OCDM baseband signal expression containing M symbols, and determining the radar-communication integrated signal. This invention enables the coded sequence modulated by each OCDM symbol to have excellent aperiodic autocorrelation and cross-correlation characteristics, solving the problem of the sensitivity of the ambiguity function of radar-communication integration to the communication modulation information. This invention, which addresses the radar-communication integration problem by proposing to change the frequency modulation slope in the symbols of the OCDM integrated baseband signal, is a special case of this invention. This invention allows for flexible adjustment of the digital modulation frequency and provides a complete GOCDM communication system design. Domestic application CN202010708335.4, entitled "A Low-Complexity Frequency-Selective Channel Estimation Method for Orthogonal Chip Multiplexing Modulation," provides a low-complexity frequency-selective channel estimation method for OCDM. This method reduces the complexity of channel estimation in frequency-selective fading channels while maintaining channel estimation accuracy, achieving low-complexity, high-precision frequency-selective channel estimation for OCDM systems. However, this invention only addresses frequency-selective channels; the potential of OCDM in dual-selective channels has not been fully utilized. This invention, however, focuses on dual-selective channels, maximizing the advantages of OCDM. Domestic application CN202110923441.9, entitled "An Orthogonal Chip Multiplexing Optical Transmission Method and System," provides an OCDM optical transmission method that uses a convolutional bidirectional long short-term memory neural network to filter and equalize discrete modulated signals to adapt to time-varying nonlinear channels. This method has stronger anti-interference capabilities and greatly improves the performance of the transmission system. However, the generalization ability of neural network methods remains a problem.

[0005] Therefore, those skilled in the art are dedicated to developing a wireless mobile communication method based on generalized orthogonal chirp division multiplexing (GOCDM). This invention proposes a novel GOCDM wireless mobile communication system. The GOCDM communication system of this invention is suitable for dual-select channels. Each orthogonal fundamental wave in GOCDM is a Zadoff-Chu (ZC) sequence. The ZC sequence is determined by the sequence length N and the root coefficient l. The waveform of GOCDM can be viewed as a digital chirped signal. When N is constant, the root coefficient l determines the chirp rate, i.e., the digital modulation frequency. The root coefficient l increases the flexibility of system design. By changing l, the digital modulation frequency can be changed. When l = 1 in GOCDM, it is equivalent to a traditional OCDM system. Since the orthogonal fundamental wave of GOCDM is a digital chirped signal, GOCDM possesses the characteristic of time-frequency domain double diffusion.

[0006] [1]X.Ouyang and J.Zhao, "Orthogonal chirp division multiplexing," IEEETrans.Commun., vol.64, no.9, pp.3946–3957, Jul.2016.

[0007] [2]MSOmar and

[0008] [3] R.Bomfin, M.Chafii, A.Nimr, and G.Fettweis, “A robust basebandtransceiver design for doubly-dispersive channels,” IEEE Trans.WirelessCommun., pp.1–1, 2021. Summary of the Invention

[0009] In view of the aforementioned shortcomings of the prior art, the technical problem to be solved by the present invention is to improve the reliability of wireless communication on dual-selection channels, providing communication system developers with greater design freedom. It is applicable to a wider range of scenarios for more general dual-selection channels.

[0010] To achieve the above objectives, the present invention provides a wireless mobile communication method based on generalized orthogonal chirp division multiplexing, comprising the following steps:

[0011] Step 1, GOCDM modulation: The GOCDM waveform consists of a modulated Zadoff-Chu (ZC) sequence, which is the superposition of modulated digital chirps. The chirp rate is also a digital modulation frequency that depends on the root exponent and the block size.

[0012] Step 2: Dual-selection channel modeling;

[0013] Step 3: Received signal modeling;

[0014] Step 4: Dual-selection channel GOCDM demodulation and shifting;

[0015] Step 5: Channel equalization.

[0016] Further, step 1 includes the following steps:

[0017] Step 1.1: Construct the generalized discrete Fresnel transformation matrix of GOCDM;

[0018] Step 1.2: Perform the inverse generalized discrete Fresnel transform at the transmitting end;

[0019] Step 1.3: Add a cyclic prefix to eliminate inter-block interference.

[0020] Furthermore, the generalized discrete Fresnel transformation matrix is ​​both a cyclic matrix and a unitary matrix, with properties including orthogonality, diagonalizability, and the ability to perform cyclic convolution.

[0021] Furthermore, step 1.3, the technique for eliminating inter-block interference, includes the application of zero-filling technique and cyclic prefix technique.

[0022] Furthermore, in step 2, the time-varying multipath channel is characterized by time selectivity and frequency selectivity.

[0023] Furthermore, in step 2, a basis function expansion model is used to simulate the dual-selection channel.

[0024] Furthermore, the basis function expansion model is used to describe the channel on the time-delay Doppler plane, using a small number of parameters to approximate the dual-selection channel.

[0025] Furthermore, in step 3, the transmitted GOCDM signal is passed through a time-varying multipath channel and sampled periodically to obtain the received signal model.

[0026] Furthermore, step 4 includes the following steps:

[0027] Step 4.1: Obtain the demodulated signal;

[0028] Step 4.2: Equivalent channel matrix modeling;

[0029] Step 4.3: Determine the cyclic shift amount;

[0030] Step 4.4: Determine the number of non-zero elements in the first column of the equivalent channel matrix;

[0031] Step 4.5: Determine the equivalent channel broadening of the dual-selection channel in the generalized discrete Fresnel domain;

[0032] Step 4.6: The demodulated signal is cyclically shifted and then dropped to obtain the pre-processed waveform.

[0033] Furthermore, in step 4.3, the shift amount depends on the Doppler widening, multipath channel length, root coefficient, and block size.

[0034] In a preferred embodiment of the present invention, existing OCDM lacks modulation flexibility, and the frequency change rate of the orthogonal chirped signal it employs is fixed. The potential of OCDM in dual-select channels has not been fully utilized. This invention proposes a new GOCDM waveform. It consists of a modulated Zadoff-Chu (ZC) sequence and can be considered as a superposition of modulated digital chirps. Its chirp rate, i.e., the digital modulation frequency, depends on the root exponent l and the block size N. In the GOCDM system, symbols are transmitted through a generalized orthogonal chirped waveform. The fundamental transformation of the GOCDM system is the generalized discrete Fresnel transform (GDFnT). An N×N GDFnT matrix Φ(l) is defined, which is related to the positive integer root coefficient l, where l and N are coprime and l < N. The (m, n)th element of Φ(l) can be represented as...

[0035]

[0036]

[0037] The columns of Φ(l) are cyclic shifts of the Zadoff-Chu (ZC) sequence. Different l values ​​determine different chirp rates. When l = 1, matrix Φ(1) is the Discrete Fresnel Transform (DFnT) matrix of traditional OCDM. Since it is a digital implementation, there is no bandwidth expansion. GDFnT inherits all the characteristics of DFnT and provides system developers with more design freedom. Moreover, GOCDM, including OCDM schemes, naturally has double diffusion characteristics. The diffusion mode of GOCDM is determined by the root exponent l and the block size N. Compared with other modulation schemes, GOCDM waveforms have a natural advantage in resisting burst interference in any domain.

[0038] Existing OCDM communication systems only consider frequency-selective channels, rarely taking into account the impact of dual-selective channels. This invention presents a received signal model for a generalized orthogonal chirp-division multiplexing (OCDM) communication system based on the Basis Expansion Model (BEM). Time-varying multipath channels are characterized by time selectivity and frequency selectivity. The BEM model describes the channel in the delay-Doppler plane, using a small number of parameters to approximate the dual-selective channel, thus facilitating channel estimation. It is assumed that the maximum delay spread τ... max and maximum Doppler broadening f max It is known that a basis function expansion model (BEM) is used to simulate a dual-select channel. The transmitted GOCDM signal passes through a time-varying multipath channel and is transmitted periodically T. s Sampling is performed to obtain the received signal model. This invention also presents an equalization design for the receiver in a generalized orthogonal chirp-division multiplexing communication system under dual-selection channels. Based on the received signal model, a corresponding equalizer is designed to effectively balance the effects of dual-selection channels, helping the receiver to correctly demodulate information symbols.

[0039] The novel Generalized Orthogonal Chip Division Multiplexing (GOCDM) wireless mobile communication system proposed in this invention has the following implementation steps:

[0040] (1) Step 1: GOCDM modulation

[0041] (11) Step 11: Generalized Discrete Fresnel Transform (GDFnT) Matrix of GOCDM

[0042] Let x(k) be the k-th symbol block of length N, and let [x(k)] be the n-th element of x(k) n = x(kN+n). In GOCDM systems, symbols are transmitted via generalized orthogonal chirped waveforms. The fundamental transform of a GOCDM system is the generalized discrete Fresnel transform (GDFnT). Define an N×N GDFnT matrix Φ(l), which is related to the positive integer root coefficients l, where l is coprime to N and l < N. The (m, n)th element of Φ(l) can be represented as...

[0043]

[0044] The columns of Φ(l) are cyclic shifts of the Zadoff-Chu (ZC) sequence, where l is the root coefficient of the ZC sequence. They can also be viewed as digital chirped signals. Different l values ​​determine different chirp rates. When l = 1, matrix Φ(1) is the Discrete Fresnel Transform (DFnT) matrix of the traditional OCDM. GDFnT inherits all the characteristics of DFnT, as shown below.

[0045] 1) Orthogonality: All basis vectors of Φ(l) (i.e. all columns of Φ(l)) are orthogonal to each other, due to the excellent autocorrelation property of the ZC sequence.

[0046] 2) Circular matrices and diagonalizability: The GDFnT matrix Φ(l) is a circular matrix. Therefore, Φ(l) = F H Γ(l)F, where F is a discrete Fourier transform (DFT) matrix of size N×N, and Γ(l) is a diagonal matrix collecting the eigenvalues ​​of Φ(l), i.e., Γ(l)=diag(F[Φ(l)]:,1)=FΦ(l)F H .

[0047] 3) Circular Convolution: Due to the circular structure of Φ(l), it has the properties of circular convolution, as shown below:

[0048]

[0049] in This represents circular convolution, where a and b are vectors of length N.

[0050] 4) Unitary matrix: The GDFnT matrix Φ(l) is a unitary matrix, i.e.

[0051] (12) Step 12: Execute the inverse GDFnT (inverse generalized discrete Fresneltransform, IGDFnT) at the transmitting end.

[0052] By performing IGDFnT at the transmitter, the modulated GOCDM symbol block u(k, l) can be given, where

[0053]

[0054] Where [u(k, l)] n = u(kN+n, l). Therefore, the emitted block u(k, l) consists of superimposed orthogonal digital chirped waveforms.

[0055] (13) Step 13: Eliminate inter-block interference (IBI)

[0056] Zero-padding (ZP) or cyclic prefix (CP) techniques can be applied to eliminate IBI. A ZP-based modulation block can be converted to a CP-based modulation block through time-domain aliasing, but the noise vector will be slightly different.

[0057] (2) Step 2: Dual-selection channel modeling

[0058] Time-varying multipath channels are characterized by time selectivity and frequency selectivity. Assume the maximum delay spread τ... max and maximum Doppler broadening fmax It is known that the Basis Function Extended Model (BEM) is used to simulate a dual-selection channel, as shown below:

[0059]

[0060] Where ω q = 2πq / N, Where T s It is the sampling period, which is equal to the symbol period, NT. s It is the time interval of the modulated GOCDM symbol block u(k, l). The sequence index i is related to the block index k by i = kN + n, where n ∈ [0, N-1]. Therefore, the length of CP is set to be longer than L to accommodate IBI from the previous symbol block. Further assumptions are made about the channel as follows:

[0061] Assumption 1: Channel parameter f max and τ max It is bounded, and the time-varying multipath channel is underspread, i.e., 2f max τ max <1.

[0062] Assumption 2: Coefficient h q (k;l) is a zero-mean complex Gaussian random variable with variance . They remain unchanged within a symbol block, but may change in different blocks.

[0063] A parameterized BEM model is used to describe the channel in the time-delay Doppler plane. It uses a small number of parameters to approximate a dual-selection channel, thus facilitating channel estimation.

[0064] (3) Step 3: Received signal modeling

[0065] The transmitted GOCDM signal passes through a time-varying multipath channel and is transmitted periodically T. s Sampling is performed. Subsequently, the i-th received sample can be modeled as

[0066]

[0067] Where w(i) is independent and identically distributed zero-mean additive white Gaussian noise (AWGN) with variance σ. 2 After synchronization and removal of the cyclic prefix, the k-th received symbol block of length N can be represented as y(k, l) = [y(kN, l), y(kN+1, l), ..., y(kN+N-1, l)]. T Since the inter-block interference is removed by the received cyclic prefix, the block index k is omitted in the following paragraphs to simplify the symbolic representation. Therefore, the received data block y(l) can be modeled as

[0068] y(l)=Hu(l)+w,

[0069] Where w is the corresponding noise vector, and H is the channel matrix, [H] m，n = h(kN+m; rN+mn), where r∈{0,1} and m,n=1,...,N. Based on the BEM model of the dual-selection channel, H can be modeled as...

[0070]

[0071] in

[0072] D q := diag(d q ),

[0073]

[0074] And H q It is a circular matrix, and its first column is h q =[h q (0), ..., h q (L)] T , where h q (l), l=0,1,...,L are channel coefficients.

[0075] (4) Step 4: The impact of dual-selection channels on GOCDM modulation and demodulation

[0076] (41) Step 41: Obtain the demodulated signal

[0077] The GDFnT is carried on the received signal block y(l). The demodulated signal is defined. Result signal block of length N It can be modeled as:

[0078]

[0079] in It is the equivalent channel matrix that includes modulation and demodulation operations. In addition, the noise vector... Since Φ(l) is a unitary matrix, the noise is still a variable with variance σ. 2 The zero-mean joint Gaussian vector.

[0080] (42) Step 42: Equivalent channel matrix decomposition

[0081] In dual-selection channel mode, the equivalent channel matrix It can be decomposed into the following form:

[0082]

[0083] Where parameter c q，l for

[0084]

[0085] And the permutation matrix P q (l) then captured The position of a non-zero element is specifically defined as:

[0086]

[0087] m, n=1,...,N, q=-Q,...,Q,

[0088] and

[0089] in, The values ​​of q need to be chosen appropriately so that m, n and q are within their respective ranges.

[0090] (43) Step 43: Determine the cyclic shift amount

[0091] Permutation matrix P q (l) Make matrix D q H q Circular shift along the column. The shift amount depends on the Doppler broadening q, the root index l, and the block size N, and can be expressed as...

[0092] Δ q (l) = mod((q+v) q N) / l, N), q∈[-Q, Q],

[0093] Where Δ q (l) and v q It is a non-negative integer, Δ q (l)∈[0, N-1]. Parameter v q The smallest non-negative integer is chosen such that (q+v) q N) / l is an integer. When q = 0, Δ0(l) = 0. For q1 = -q2, we have Therefore, only calculation is needed. Integer Δ q (l) can be determined as follows based on Δ1(l):

[0094] Δ q (l)=mod(qΔ1(l),N), q∈[1,Q],

[0095] Where Δ1(l) = mod((1+v1N) / l, N).

[0096] (44) Step 44: Determine The number of non-zero elements in the first column

[0097] H q It is a cyclic matrix, and its approximate bandwidth is L+1. Matrix c q，l P q (l)D q H q It is a "pseudo-circular matrix" because It is a circular matrix, where ⊙ represents element-wise multiplication. When non-zero elements and The non-zero elements overlap. Since the equivalent channel matrix H(l) is 2Q+1 "pseudo-cyclic matrices". The sum of each column The number of non-zero elements is the same. Let ρ(l) represent... The number of non-zero elements in the first column. Due to the dual-selection channel, GOCDM modulation and demodulation scheme, a single symbol is spread across ρ(l) received samples. A larger ρ(l) indicates a wider spread. On the one hand, it helps GOCDM communication resist burst interference in the time or frequency domain. On the other hand, it makes ISI more pronounced.

[0098] The value of ρ(l) is determined by the quadruple (N, l, L, Q). First, they are arranged in ascending order. Since Δ0(l)=0, the resulting sequence is collected in a vector of length 2Q+2. Then, the value of ρ(l) can be calculated as follows:

[0099]

[0100] Where c = min(a, b) is compared element-wise, the matrix J of size (2Q+1) × (2Q+2) is given by the following formula.

[0101]

[0102] ρ can be derived min ≤ρ(l)≤ρ max , where ρ min =ρ(1)=L+2Q+1,ρ max = (L+1)(2Q+1). A larger ρ(l) means that the symbol is propagated more widely. When the maximum ρ max When preferred, given L and Q, a pair (N, l) can be designed to satisfy the following two conditions in a sequential manner.

[0103] 1) To avoid overlap caused by cyclic shifts, the block size N should not be less than (L+1)(2Q+1), that is, N≥(L+1)(2Q+1).

[0104] 2) The parameter l should be chosen so that the non-zero value ρ(l) reaches its maximum value, that is, ρ(l) = ρ max = (L+1)(2Q+1).

[0105] There may be multiple l that satisfy condition 2). Define a set. It includes all l that satisfy condition 2), that is

[0106] (45) Step 45: Determine the equivalent channel broadening L(l) in the generalized discrete Fresnel domain.

[0107] Define another important parameter for quantization. The characteristic of L(l), namely the equivalent channel broadening in the generalized discrete Fresnel domain, is as follows:

[0108] L(l)=N+L-[JΔ(l)] τ(l) ,

[0109] Where τ(l) is given by the following formula:

[0110] τ(l)=max(arg max τ∈[1，...，2Q+1] [JΔ(l)] τ ),

[0111] And [JΔ(l)] τ(l) This represents the maximum difference between adjacent shifts in Δ(l). There may be multiple τ values ​​that can reach [JΔ(l)]. τ The maximum value. In this case, the largest τ is chosen as τ(l). Therefore, the parameter L(l) represents the minimum channel broadening including all channel fading, ρ(l)≤L(l)+1≤N. Define the set when When this occurs, τ(l) = 2Q + 1, L(l) + 1 = ρ(l) = L + 1 + 2QΔ1(l), and the equivalent channel length is most efficient. Definition Or Δ1(l)=NL-1}.

[0112] (46) Step 46: After the cyclic shift descent, we obtain

[0113] To aid in subsequent channel estimation and equalization, the demodulated signal... After the cyclic shift descends, we obtain

[0114]

[0115] Where q ＊ ∈[-Q, Q] satisfies the following equation

[0116]

[0117] definition pass Perform a circular shift. The first element of the first column is always a non-zero value, and a window of length L(l)+1 can cover all non-zero elements in its first column. The shifted demodulated signal can be... Rewritten as

[0118]

[0119] here,

[0120]

[0121] and It is a circular matrix, and its first column is in It is a zero-padded channel vector of length L(l)+1, defined as in

[0122]

[0123] Its size is (L(l)+1)×(L+1). Zero-filled It has different numbers of zeros at its head and tail, by Confirmed. However, the length of its non-zero elements is fixed at L+1. Noise vector. It remains a joint Gaussian random vector with zero mean and variance σ. 2 Because the arrangement does not change its randomness.

[0124] (5) Step 5: Channel equalization

[0125] The equalized signal is represented as:

[0126]

[0127] Where F is the normalized DFT matrix. G(l) is the equilibrium matrix, whose diagonal elements are [G(l)]. k，k Specifically, the ZF equalizer is [G(l)]. ZF =[Λ(l)] -1 ,in MMSE equalizer is Where ρ is the signal-to-noise ratio (SNR).

[0128] Compared with the prior art, the present invention has the following obvious substantive features and significant advantages:

[0129] 1. This invention increases the flexibility of system design. GDFnT inherits all the characteristics of DFnT and provides system developers with more design freedom. Moreover, GOCDM, including the OCDM scheme, inherently possesses double diffusion characteristics. The diffusion mode of GOCDM is determined by the root exponent and the block size. Compared with other modulation schemes, GOCDM waveforms have a natural advantage in resisting burst interference in any domain.

[0130] 2. This invention uses the BEM model to simulate a dual-selection channel, which uses a small number of parameters to approximate the dual-selection channel, thus facilitating channel estimation.

[0131] 3. This invention can effectively balance the impact of dual-selection channels and help the receiver correctly demodulate information symbols.

[0132] 4. The modulation scheme of the present invention improves the reliability of wireless communication on dual-select channels.

[0133] The following will further explain the concept, specific structure, and technical effects of the present invention in conjunction with the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0134] Figure 1 This is a comparison diagram of a preferred embodiment of the present invention, GOCDM, with other popular modulation schemes;

[0135] Figure 2 This is a flowchart illustrating the execution of a preferred embodiment of the present invention. Detailed Implementation

[0136] The following description, with reference to the accompanying drawings, illustrates several preferred embodiments of the present invention to make its technical content clearer and easier to understand. The present invention can be embodied in many different forms, and the scope of protection of the present invention is not limited to the embodiments mentioned herein.

[0137] In the accompanying drawings, components with the same structure are indicated by the same numerical designation, and components with similar structures or functions are indicated by similar numerical designations. The dimensions and thicknesses of each component shown in the drawings are arbitrary, and the present invention does not limit the dimensions and thicknesses of each component. To make the illustrations clearer, the thickness of some components has been appropriately exaggerated in the drawings.

[0138] Figure 1This invention provides a novel GOCDM wireless mobile communication system. Traditional OCDM can be considered a special case of GOCDM. The GOCDM communication system proposed in this invention is suitable for dual-channel selection. GOCDM includes OCDM as a special case (1=1) and inherits the dual-spread spectrum characteristics. Figure 1 Simulation results confirm that GOCDM has superior performance compared to other popular modulation schemes. BER performance comparison under BEM channel N s =48. GOCDM: Q=1, l=18, L=3, N=71. OCDM: Q=1, N=81.

[0139] like Figure 2 As shown, under the assumed conditions, the specific execution steps of this invention are as follows:

[0140] Step 1: Represent the k-th symbol block of length N as x(k), and the n-th element of x(k) as [x(k)]. n = x(kN+n). In GOCDM systems, symbols are transmitted via generalized orthogonal chirped waveforms. The fundamental transform of a GOCDM system is the generalized discrete Fresnel transform (GDFnT). Define an N×N GDFnT matrix Φ(l), which is related to a positive integer parameter l, where l is coprime to N and l < N. The (m, n)th element of Φ(l) can be represented as...

[0141]

[0142] Among them, l is designed according to specific needs.

[0143] By performing IGDFnT at the transmitter, the modulated GOCDM symbol block u(k, l) can be given, where

[0144]

[0145] Where [u(k, l)] n = u(kN+n, l). The emitted block u(k, l) consists of superimposed orthogonal digital chirped waveforms.

[0146] Step 2: Assume maximum delay spread τ max and maximum Doppler broadening f max It is known that a basis function expansion model (BEM) is used to simulate a dual-selection channel, as shown below:

[0147]

[0148] Where ω q = 2πq / N, Q: =f max NT sT s It is the sampling period, which is equal to the symbol period, NT. s It is the time interval of the modulated GOCDM symbol block u(k, l). The sequence index i and the block index k are related as i = kN + n, where n ∈ [0, N-1]. IBI is eliminated by CP technique, and the length of CP is set to be longer than L to accommodate IBI from previous symbol blocks.

[0149] Step 3: The transmitted GOCDM signal passes through a time-varying multipath channel and is periodically processed by T. s Sampling is performed. Subsequently, the i-th received sample can be modeled as

[0150]

[0151] Where w(i) is independent and identically distributed zero-mean additive white Gaussian noise (AWGN) with variance σ. 2 After synchronization and removal of the cyclic prefix, the k-th received symbol block of length N can be represented as y(k, l) = [y(kN, l), y(kN+1, l), ..., y(kN+N-1, l)]. T Since the inter-block interference is removed by the received cyclic prefix, the block index k is omitted in the following paragraphs to simplify the symbolic representation. Therefore, the received data block y(l) can be modeled as

[0152] y(l)=Hu(l)+w,

[0153] Where w is the corresponding noise vector, and H is the channel matrix, [H] m，n = h(kN+m; rN+mn), where r∈{0,1} and m,n=1,...,N.

[0154] Step 4: Determine the impact of dual-selection channels on GOCDM modulation and demodulation.

[0155] (41) Step 41: Define the demodulation signal

[0156] Define demodulation signal Result signal block of length N for:

[0157]

[0158] in It is the equivalent channel matrix that includes modulation and demodulation operations. In addition, the noise vector... Since Φ(l) is a unitary matrix, the noise is still a variable with variance σ. 2 The zero-mean joint Gaussian vector.

[0159] (42) Step 42: Equivalent channel matrix decomposition

[0160] In dual-selection channel mode, the equivalent channel matrix Decomposed into the following form:

[0161]

[0162] Where parameter c q，l for

[0163]

[0164] And the permutation matrix P q (l) then captured The position of a non-zero element is specifically defined as:

[0165]

[0166] and

[0167] in, The values ​​of q need to be chosen appropriately so that m, n and q are within their respective ranges.

[0168] (43) Step 43: Determine the cyclic shift amount

[0169] Permutation matrix P q (l) Make matrix D q H q Shift cyclically along the column. The shift amount depends on the Doppler broadening little-root index l and the block size N, and can be expressed as...

[0170] Δ q (l) = mod((q+v) q N) / l, N), q∈[-Q, Q],

[0171] Where Δ q (l) and v q It is a non-negative integer, Δ q (l)∈[0, N-1]. Parameter v q The smallest non-negative integer is chosen such that (q+v) q N) / l is an integer. Integer Δ q (l) can be determined as follows based on Δ1(l):

[0172] Δ q (l)=mod(qΔ1(l),N), q∈[1,Q],

[0173] Where Δ1(l) = mod((1+v1N) / l, N).

[0174] (44) Step 44: Determine The number of non-zero elements in the first column

[0175] Using ρ(l) to represent The number of non-zero elements in the first column. The value of ρ(l) is determined by the quadruple (N, l, L, Q). First, arrange them in ascending order. Since Δ0(l)=0, the resulting sequence is collected in a vector of length 2Q+2. Then, the value of ρ(l) can be calculated as follows:

[0176]

[0177] Where c = min(a, b) is compared element-wise, the matrix J of size (2Q+1) × (2Q+2) is given by the following formula.

[0178]

[0179] ρ can be derived min ≤ρ(l)≤ρ max , where ρ min =ρ(1)=L+2Q+1,ρ max = (L+1)(2Q+1). A larger ρ(l) means that the symbol is propagated more widely. When the maximum ρ max When it is preferred, given L and Q, design a tuple (N, l) that satisfies the two conditions in a sequential manner.

[0180] 1) To avoid overlap caused by cyclic shifts, the block size N should not be less than (L+1)(2Q+1), that is, N≥(L+1)(2Q+1).

[0181] 2) The parameter l should be chosen so that the non-zero value ρ(l) reaches its maximum value, that is, ρ(l) = ρ max = (L+1)(2Q+1).

[0182] There may be multiple l that satisfy condition 2). Define a set. It includes all l that satisfy condition 2), that is

[0183] (45) Step 45: Determine the equivalent channel broadening L(l) in the generalized discrete Fresnel domain.

[0184] Define the equivalent channel stretching L(l) in the generalized discrete Fresnel domain to quantize Its characteristics are as follows:

[0185] L(l)=N+L-[JΔ(l)] τ(l) ,

[0186] Where τ(l) is given by the following formula:

[0187] τ(l)=max(arg max τ∈[1，...，2Q+1] [JΔ(l)] τ ),

[0188] And [JΔ(l)] τ(l) This represents the maximum difference between adjacent shifts in Δ(l). There may be multiple τ values ​​that can reach [JΔ(l)]. τ The maximum value. In this case, the largest τ is chosen as τ(l). Therefore, the parameter L(l) represents the minimum channel broadening including all channel fading, ρ(l)≤L(l)+1≤N. Define the set when When τ(l) = 2Q+1 and L(l)+1 = ρ(l) = L+1 + 2QΔ1(l), the equivalent channel length is most efficient.

[0189] (46) Step 46: After the cyclic shift descent, we obtain

[0190] Demodulated signal After the cyclic shift descends, we obtain

[0191]

[0192] Where q * ∈[-Q, Q] satisfies the following equation

[0193]

[0194] definition pass Perform a circular shift. The first element of the first column is always a non-zero value, and a window of length L(l)+1 can cover all non-zero elements in its first column.

[0195] The shifted demodulated signal Rewritten as

[0196]

[0197] (5) Step 5: Channel equalization

[0198] The equalized signal is represented as:

[0199]

[0200] Where F is the normalized DFT matrix, and G(l) is the equilibrium matrix, whose diagonal elements are [G(l)]. k，kSpecifically, the ZF equalizer is [G(l)]. ZF =[Λ(l)] -1 ,in MMSE equalizer is Where ρ is the signal-to-noise ratio (SNR).

[0201] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A wireless mobile communication method based on generalized orthogonal chirp division multiplexing, characterized in that, Includes the following steps: Step 1, GOCDM Modulation: The GOCDM waveform is generated by the root exponent... The Zadoff-Chu (ZC) sequence with up-parameter modulation is composed of the superposition of modulated digital chirps, and the chirp rate is also the digital modulation frequency, which depends on the root exponent and the block size. Step 2: Dual-selection channel modeling; Step 3: Received signal modeling; Step 4: Dual-selection channel GOCDM demodulation and shifting; Step 5: Channel equalization; Step 1 includes the following steps: Step 1.1: Construct the generalized discrete Fresnel transform (GDFnT) matrix of GOCDM and design the root exponents. ; Step 1.2: At the transmitting end, according to the GDFnT matrix in Step 1.1, perform the inverse generalized discrete Fresnel transform IGDFnT to modulate the information symbols; Step 1.3: Add a cyclic prefix to eliminate inter-block interference; The GDFnT matrix is ​​a circular matrix and a unitary matrix, and its properties include orthogonality, diagonalizability, and the ability to perform circular convolution. Step 4 includes the following steps: Step 4.1: Obtain the demodulated signal; Step 4.2: Using the GDFnT matrix, IGDFnT matrix and dual-selection channel model, establish the equivalent channel matrix. The structure of the equivalent channel matrix is ​​related to the root exponent in the GDFnT matrix. Step 4.3: Determine the cyclic shift amount of the received demodulated signal, which is determined by the length of the transmitted signal block, the Doppler broadening and multipath delay of the dual-select channel, and the root exponent of GDFnT; Step 4.4: Determine the equivalent channel broadening of the dual-selection channel in the generalized discrete Fresnel domain, which is determined by the number of non-zero elements in the first column of the equivalent channel matrix and their positions. Step 4.5: The demodulated signal is cyclically shifted and then descends to obtain the pre-processed waveform.

2. The wireless mobile communication method based on generalized orthogonal chirp division multiplexing as described in claim 1, characterized in that, Step 1.3, the technique for eliminating inter-block interference, includes the application of zero-filling technique and cyclic prefix technique.

3. The wireless mobile communication method based on generalized orthogonal chirp division multiplexing as described in claim 1, characterized in that, In step 2, the characteristics of time-varying multipath channels are time selectivity and frequency selectivity.

4. The wireless mobile communication method based on generalized orthogonal chirp division multiplexing as described in claim 1, characterized in that, In step 2, a basis function expansion model is used to simulate the dual-selection channel.

5. The wireless mobile communication method based on generalized orthogonal chirp division multiplexing as described in claim 4, characterized in that, The basis function expansion model is used to describe the channel on the time-delay Doppler plane, using a small number of parameters to approximate the dual-selection channel.

6. The wireless mobile communication method based on generalized orthogonal chirp division multiplexing as described in claim 1, characterized in that, In step 3, the transmitted GOCDM signal is passed through a time-varying multipath channel and sampled periodically to obtain the received signal model.

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