A low peak-to-average ratio LACO-OFDM method and system based on constellation expansion

Abstract

The present invention discloses a low peak-to-average ratio LACO-OFDM method and system based on constellation expansion, which performs a point inverse frequency domain transformation operation on a frequency domain signal to generate a time domain signal with sampling moments, and repeats the time domain signal in the time domain times to generate a time domain signal with sampling moments. Constellation expansion is performed on the subcarrier-carrying symbols of the th layer of the LP-LACO-OFDM signal to obtain a time domain signal after the LP-LACO-OFDM constellation expansion. The time domain signal after the LP-LACO-OFDM constellation expansion is subjected to digital-to-analog conversion and then input into an LED to generate a transmitted light signal. Compared with the traditional LACO-OFDM method, the present invention can effectively reduce the PAPR, thereby improving the ability of the LACO-OFDM method to resist nonlinearity and ensuring the transmission reliability of the LACO-OFDM method under nonlinear conditions.

Description

Technical Field

[0001] The invention relates to a low peak-to-average ratio LACO-OFDM method and system based on constellation expansion, belonging to the technical field of wireless optical communication. Background Art

[0002] At present, wireless spectrum communication is facing the dilemma of resource shortage. With the rapid development of the LED industry, wireless optical communication that uses light to transmit information is rapidly rising. Wireless optical communication is widely favored by researchers due to its advantages such as rich spectrum resources, diverse application scenarios, and high confidentiality. At the same time, wireless optical communication has no electromagnetic radiation and will not interfere with the radio frequency communication system. Therefore, wireless optical communication has become an effective supplement to wireless spectrum communication.

[0003] Orthogonal frequency division multiplexing (OFDM) is a multi-carrier modulation technology. Its working principle is to modulate data onto each subcarrier, and the subcarriers are used for data transmission. Each subcarrier is orthogonal, so data transmission in different frequency bands will not affect each other. OFDM technology has been widely used because of its high spectrum efficiency and its ability to effectively combat electromagnetic interference. In wireless optical communications, OFDM has also become a mainstream modulation method. On its basis, a variety of professional OFDM methods have been extended, such as DC biased optical OFDM (DCO-OFDM), asymmetric amplitude limiting optical (ACO-OFDM), hybrid ACO-OFDM (HACO-OFDM), etc., but these methods have defects in power or spectrum efficiency. For this reason, layered ACO-OFDM (LACO-OFDM) was proposed. This method can maintain the advantage of ACO-OFDM's high power efficiency. At the same time, the use of multi-layer ACO-OFDM superposition transmission effectively improves the spectrum efficiency. This method is regarded as a solution with broad application prospects in wireless optical communications.

[0004] OFDM has a high peak-to-average ratio (PAPR), which will cause signal distortion in the OFDM method under nonlinear conditions, resulting in deterioration of transmission performance. This problem is particularly prominent in the LACO-OFDM method. Since LACO-OFDM needs to use serial interference cancellation for signal detection, in nonlinear conditions, the detection errors caused by signal distortion in each layer will propagate to subsequent layers, causing serious performance deterioration. Therefore, how to effectively reduce the PAPR of LACO-OFDM has become a crucial issue. There are currently a variety of PAPR reduction technologies, including direct limiting, compression transformation, and pilot insertion, but these methods face problems such as reduced transmission performance and reduced bandwidth utilization. The PAPR method based on constellation expansion will not cause the problems of reduced performance and reduced bandwidth utilization, but the existing constellation expansion method for LACO-OFDM requires the use of a more complex convex optimization method and requires additional optimization tools such as CVX (Convex Optimization Toolbox), which is difficult to implement in actual systems.

[0005] To this end, the present invention proposes a new low peak-to-average ratio LACO-OFDM (LP-LACO-OFDM, where LP represents low peak-to-average ratio) method based on low-complexity constellation extension. Summary of the invention

[0006] Objective: To overcome the deficiencies in the prior art, the present invention provides a low peak-to-average ratio LACO-OFDM method and system based on constellation expansion, which effectively reduces the PAPR of LACO-OFDM and improves the transmission performance under nonlinear conditions. At the same time, there is no need to use a convex optimization method with high complexity to implement the constellation expansion of LACO-OFDM, thereby reducing the complexity of the system.

[0007] Technical solution: To solve the above technical problems, the technical solution adopted by the present invention is:

[0008] In a first aspect, a low peak-to-average ratio LACO-OFDM method based on constellation extension comprises the following steps:

[0009] Step 1: The subcarriers are layered according to the sequence number, and the QAM symbols are allocated to the subcarriers used in each layer to generate frequency domain signals. Layer, The frequency domain signal corresponding to the subcarrier is expressed as , , is the number of layers used, .

[0010] Step 2: Frequency domain signal implement Point inverse frequency domain transform operation is performed to generate The time domain signal at the sampling moment and repeat the time domain signal in the time domain times, generating The time domain signal at the sampling moment , .

[0011] Step 3: For the LP-LACO-OFDM signal Layered The subcarriers carry symbols for constellation expansion to obtain the time domain signal after the LP-LACO-OFDM constellation expansion.

[0012] Step 4: After the time domain signal after the LP-LACO-OFDM constellation expansion is converted into digital-to-analog format, it is input into the LED to generate a transmitted optical signal.

[0013] As a preferred solution, it also includes:

[0014] Step 5: Pass the received signal through The point frequency domain is transformed to generate a frequency domain signal, the frequency domain signal is subjected to limiting distortion removal, modulo operation and QAM symbol detection to obtain a QAM symbol, and the QAM symbol is subjected to constellation expansion, inverse frequency domain transformation, asymmetric limiting and frequency domain transformation to obtain the transmitted information.

[0015] As a preferred solution, the step 3 specifically includes:

[0016] Step 3.1: Get the LP-LACO-OFDM signal Layered subcarriers carry symbols, and calculate the Layer The sequence number of the moment Corresponding constellation extension signal ,in, The sequence number of the part to be expanded.

[0017] Step 3.2: Set the initial value of the LP-LACO-OFDM signal peak to , will be The time domain signal after constellation expansion in the sub-cycle operation is expressed as , where the initial value . , Indicates The maximum value of the sequence of labels.

[0018] Step 3.3: For Expand the constellation of each subcarrier in each layer, and calculate the minimum peak value after the subcarrier constellation expansion , the minimum value corresponds to The value of .

[0019] Step 3.4: Calculate the sequence The minimum value of The value of , and update The value of .

[0020] Step 3.5: If ,but ,Will The value of is updated to , and continue to step 3.3, step 3.4, if , jump out of the loop, and the output LP-LACO-OFDM constellation expanded time domain signal .

[0021] in, express Second cycle operation Peak value, express After the constellation is expanded in the second cycle operation Tier The time domain signal at the sampling moment, express After the constellation is expanded in the second cycle operation Tier The time domain signal at the sampling moment, Indicates Layer The sequence number of the moment Corresponding constellation extension signal.

[0022] As a preferred embodiment, the Layer The sequence number of the moment Corresponding constellation extension signal The calculation formula is as follows:

[0023]

[0024] in, represents the distance that the QAM symbol constellation extends, Indicates The first layer The real part of the QAM symbol of the subcarriers, Indicates The first layer The imaginary part of the QAM symbol of the subcarriers, Represents the sign-taking operation, Represents pi.

[0025] As a preferred solution, the subcarrier constellation expanded peak minimum value The calculation formula is as follows:

[0026]

[0027] in, Indicates is the minimum value in the sequence of labels, Indicated in After the constellation is expanded in the second cycle operation Tier The time domain signal at a sampling moment.

[0028] As a preferred embodiment, the The calculation formula is as follows:

[0029]

[0030] in, express The peak value of LACO-OFDM signal in the second cycle operation, Indicates The minimum value in the numbered sequence.

[0031] As a preferred solution, the distance of the QAM symbol constellation extension is The calculation formula is as follows:

[0032]

[0033] in, represents the order of QAM modulation, Indicates the minimum distance of constellation points.

[0034] In a second aspect, a low peak-to-average ratio LACO-OFDM system based on constellation extension includes a transmitting end, wherein the transmitting end performs the following steps:

[0035] Will The subcarriers are layered according to the sequence number, and the QAM symbols are allocated to the subcarriers used in each layer to generate frequency domain signals. Layer, The frequency domain signal corresponding to the subcarrier is expressed as , , is the number of layers used, .

[0036] For frequency domain signals implement Point inverse frequency domain transform operation is performed to generate The time domain signal at the sampling moment and repeat the time domain signal in the time domain times, generating The time domain signal at the sampling moment , .

[0037] For LP-LACO-OFDM signal Layered The subcarriers carry symbols for constellation expansion to obtain the time domain signal after the LP-LACO-OFDM constellation expansion.

[0038] The time domain signal after the LP-LACO-OFDM constellation expansion is converted into digital and analog form and then input into the LED to generate the transmitted optical signal.

[0039] As a preferred solution, the invention further includes a receiving end, wherein the receiving end performs the following steps:

[0040] The received signal passes through The point frequency domain is transformed to generate a frequency domain signal, the frequency domain signal is subjected to limiting distortion removal, modulo operation and QAM symbol detection to obtain a QAM symbol, and the QAM symbol is subjected to constellation expansion, inverse frequency domain transformation, asymmetric limiting and frequency domain transformation to obtain the transmitted information.

[0041] Beneficial effect: Compared with the traditional LACO-OFDM method, the low peak-to-average ratio LACO-OFDM method and system based on constellation expansion provided by the present invention can effectively reduce PAPR, thereby improving the ability of the LACO-OFDM method to resist nonlinearity and ensuring the transmission reliability of the LACO-OFDM method under nonlinear conditions.

[0042] The method of the present invention uses constellation expansion to reduce PAPR. Compared with direct limiting, compression transformation, pilot insertion and other methods, it does not cause problems such as reduced transmission performance and reduced frequency band utilization. At the same time, compared with the traditional constellation expansion method, there is no need to use a convex optimization method to select constellation expansion, which effectively reduces the complexity of implementation. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 The figure is a block diagram of the transmitter of the LP-LACO-OFDM method based on low-complexity constellation extension.

[0044] Figure 2 The figure is a receiving block diagram of the LP-LACO-OFDM method based on low-complexity constellation extension.

[0045] Figure 3 The figure is the simulation result of the complementary cumulative distribution function of PAPR of the method of the present invention.

[0046] Figure 4 The bit error rate (BER) performance of the method of the present invention and LACO-OFDM under nonlinear conditions. DETAILED DESCRIPTION

[0047] The following is a clear and complete description of the technical solutions in the examples of the present invention in conjunction with the accompanying drawings in the examples of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work are within the protection scope of the present invention.

[0048] The present invention will be further described below in conjunction with specific embodiments.

[0049] Embodiment 1:

[0050] This embodiment introduces a low peak-to-average ratio LACO-OFDM method based on constellation expansion, such as Figure 1 As shown, the following steps are included:

[0051] Step 1: Record the number of subcarriers as , the subcarriers are layered according to the sequence number, and the QAM symbols are allocated to the subcarriers used in each layer to generate frequency domain signals, where the first Layer, The frequency domain signal corresponding to the subcarrier is expressed as , , is the number of layers used, .

[0052] Step 2: For frequency domain signals implement Point IFFT operation, generating Time domain signal at sampling time , , and repeat in the time domain times, generating The time domain signal at the sampling moment , .in, and The relationship is expressed as ,in, express about Remainder operation.

[0053] Step 3: For the LP-LACO-OFDM signal layers, total subcarriers carry symbol transmission, so, considering the real part and imaginary part of the subcarrier, there are Parts to be expanded by constellation, definition is the serial number of the part to be expanded, ,when Time, serial number The corresponding The first layer subcarrier real part, when Time, serial number The corresponding The first layer subcarrier imaginary part, calculate the Layer The sequence number of the moment Corresponding constellation extension signal .

[0054] Constellation extension signal Calculated by the following formula:

[0055] in, represents the distance that the QAM symbol constellation extends, represents the order of QAM modulation, represents the minimum distance of the constellation points, Indicates The first layer The real part of the QAM symbol of the subcarriers, Indicates The first layer The imaginary part of the QAM symbol of the subcarriers, Represents the sign-taking operation, Represents pi.

[0056] Initialize the relevant parameters and set the initial value of the LP-LACO-OFDM signal peak to , , Indicates is the maximum value of the sequence of labels, which will be The time domain signal after constellation expansion in the sub-cycle operation is expressed as , where the initial value , execute the following loop algorithm:

[0057] (1) For Layers are formed, and the constellation is expanded subcarrier by subcarrier. The minimum peak value after the subcarrier constellation expansion is calculated. The minimum value corresponds to The value of ; That is, calculated by the following formula:

[0058]

[0059] in, Indicates In the next cycle, for the The minimum value after subcarrier constellation expansion is performed layer by layer, Indicated in After the constellation is expanded in the second cycle operation Tier The time domain signal at the sampling moment, Indicates The minimum value in the sequence of labels.

[0060] (2) Calculation sequence The minimum value of The value of , and update The value of

[0061]

[0062] in, express The peak value of LACO-OFDM signal in the second cycle operation, Indicates that The minimum value in the numbered sequence.

[0063] (3) If , express The peak value of the LACO-OFDM signal in the second cycle operation is ,Will The value of is updated to , and continue the loop if , jump out of the loop, then the output LP-LACO-OFDM constellation expansion signal can be expressed as .in, express After the constellation is expanded in the second cycle operation Tier The time domain signal at the sampling moment, express After the constellation is expanded in the second cycle operation Tier The time domain signal at the sampling moment, Indicates Layer The sequence number of the moment Corresponding constellation extension signal.

[0064] Step 4: After the LP-LACO-OFDM constellation expansion signal is converted into digital-to-analog format, it is input into an LED to generate a transmission optical signal;

[0065] Step 5: The receiver of the proposed LP-LACO-OFDM solution still uses the traditional LACO-OFDM receiver structure. First, the received signal is Point FFT transformation is performed to generate a frequency domain signal. After removing the limiting distortion, the influence of constellation expansion is removed by modulo operation, and QAM symbol detection is performed. Further, based on the detected QAM symbols, constellation expansion, IFFT operation, asymmetric limiting and FFT operation are performed to restore the limiting distortion for subsequent layered limiting distortion removal.

[0066] from Figure 2 It can be seen from the figure that the method proposed in the present invention still adopts the same receiver structure as the traditional LACO-OFDM, and before symbol detection, the influence of constellation expansion is removed by means of modulo operation.

[0067] Embodiment 2:

[0068] This embodiment introduces a low peak-to-average ratio LACO-OFDM system based on constellation extension, including a transmitting end and a receiving end.

[0069] The transmitting end performs the following steps:

[0070] The number of subcarriers is , the subcarriers are layered according to the sequence number, and the QAM symbols are allocated to the subcarriers used in each layer to generate frequency domain signals, where the first Layer, The frequency domain signal corresponding to the subcarrier is expressed as , , is the number of layers used, .

[0071] For frequency domain signals implement Point IFFT operation, generating Time domain signal at sampling time , , and repeat in the time domain times, generating The time domain signal at the sampling moment , .in, and The relationship is expressed as ,in, express about Remainder operation.

[0072] For LP-LACO-OFDM signal layers, total subcarriers carry symbol transmission, so, considering the real part and imaginary part of the subcarrier, there are Parts to be expanded by constellation, definition is the serial number of the part to be expanded, ,when Time, serial number The corresponding The first layer subcarrier real part, when Time, serial number The corresponding The first layer subcarrier imaginary part, calculate the Layer The sequence number of the moment Corresponding constellation extension signal .

[0073] Constellation extension signal Calculated by the following formula:

[0074] in, represents the distance that the QAM symbol constellation extends, represents the order of QAM modulation, represents the minimum distance of the constellation points, Indicates The first layer The real part of the QAM symbol of the subcarriers, Indicates The first layer The imaginary part of the QAM symbol of the subcarriers, Represents the sign-taking operation, Represents pi.

[0075] Initialize the relevant parameters and set the initial value of the LP-LACO-OFDM signal peak to , , will be The time domain signal after constellation expansion in the sub-cycle operation is expressed as , where the initial value , execute the following loop algorithm:

[0076] (1) For Layers are formed, and the constellation is expanded subcarrier by subcarrier. The minimum peak value after the subcarrier constellation expansion is calculated. The minimum value corresponds to The value of ; That is, calculated by the following formula:

[0077]

[0078] in, Indicates In the next cycle, for the The minimum value after subcarrier constellation expansion is performed layer by layer, Indicated in After the constellation is expanded in the second cycle operation Tier The time domain signal at a sampling moment.

[0079] (2) Calculation sequence The minimum value of The value of , and update The value of

[0080]

[0081] in, express Peak value of LACO-OFDM signal in the second cycle operation.

[0082] (3) If , express The peak value of the LACO-OFDM signal in the second cycle operation is ,Will The value of is updated to , and continue the loop if , jump out of the loop, the output LP-LACO-OFDM signal can be expressed as .in, express After the constellation is expanded in the second cycle operation Tier The time domain signal at the sampling moment, express After the constellation is expanded in the second cycle operation Tier The time domain signal at the sampling moment, Indicates Layer The sequence number of the moment Corresponding constellation extension signal.

[0083] After the LP-LACO-OFDM signal is converted from digital to analog, it is input into the LED to generate a transmitted optical signal.

[0084] The receiving end performs the following steps:

[0085] The receiver of the proposed LP-LACO-OFDM scheme still uses the traditional LACO-OFDM receiver structure. First, the received signal is Point FFT transformation is performed to generate a frequency domain signal. After removing the limiting distortion, the influence of constellation expansion is removed by modulo operation, and QAM symbol detection is performed. Further, based on the detected QAM symbols, constellation expansion, IFFT operation, asymmetric limiting and FFT operation are performed to restore the limiting distortion for subsequent layered limiting distortion removal.

[0086] Embodiment 3:

[0087] This embodiment introduces the data comparison of the transmission effects of LP-LACO-OFDM of the present invention and LACO-OFDM of the prior art at different layers.

[0088] Figure 3 The complementary cumulative function of the peak-to-average ratio with different number of layers is given, that is, the peak-to-average ratio PAPR is greater than the threshold PAPR 0 The probability of .from Figure 3 It can be seen that the peak-to-average ratio (PAPR) of the traditional LACO-OFDM is greater than a threshold PAPR. 0 The probability of is much higher than that of the method of the present invention, indicating that the method of the present invention can obtain a lower PAPR than the traditional LACO-OFDM method. Therefore, the method of the present invention has a stronger ability to resist nonlinear distortion. At the same time, as the number of layers increases, the PAPR of LP-LACO-OFDM gradually decreases.

[0089] Figure 4 The results of different signal-to-noise ratios under nonlinear transmission are given. The corresponding bit error rate (BER) performance is Figure 4 It can be observed that the method of the present invention has the same signal-to-noise ratio It has a lower BER, indicating that the method of the present invention has a lower probability of bit transmission errors in the case of linear transmission, and therefore has higher transmission reliability than the traditional LACO-OFDM method.

[0090] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A low peak-to-average ratio LACO-OFDM method based on constellation extension, characterized by: The steps include: Step 1: Layer the N subcarriers according to the sequence number, assign QAM symbols to the subcarriers used in each layer, and generate frequency domain signals, where the frequency domain signal corresponding to the kth subcarrier in the lth layer is represented as X l,k , l=1,2,…,L, L is the number of layers used, k=0,1,2,3,…,N-1; Step 2: For the frequency domain signal X l,k Execute N / 2 l-1 Point inverse frequency domain transform operation generates N / 2 l-1 The time domain signal at the sampling moment and repeat the time domain signal in the time domain 2 l-1 times, generating a time domain signal x with N sampling moments l,n , n=0,1,…,N-1; Step 3: For the LP-LACO-OFDM signal Layered Subcarriers carry symbols to perform constellation expansion, and obtain the time domain signal after LP-LACO-OFDM constellation expansion; Step 4: After the time domain signal after the LP-LACO-OFDM constellation expansion is converted into digital-to-analog format, it is input into the LED to generate a transmission optical signal; The step 3 specifically includes: Step 3.1: Get the LP-LACO-OFDM signal Layered subcarriers carry symbols, and calculate the The sequence number of the nth moment of the layer Corresponding constellation extension signal in, is the serial number of the part to be expanded; Step 3.2: Set the initial value of the LP-LACO-OFDM signal peak to The time domain signal after constellation expansion in the i-th cycle operation is expressed as Among them, the initial value It represents the maximum value of a sequence numbered by n; Step 3.3: For Expand the constellation of each subcarrier in each layer, and calculate the minimum peak value after the subcarrier constellation expansion The minimum value corresponds to The value of Step 3.4: Calculate the sequence The minimum value of The value of and update The value of Step 3.5: If but Update the value of i to i+1 and continue with steps 3.3 and 3.

4. If Jump out of the loop, and the output is the time domain signal after the LP-LACO-OFDM constellation expansion in, Indicates i-1 times of loop operation Peak value, Indicates the constellation after expansion in the i-th cycle operation The time domain signal of the nth sampling moment of the layer, represents the first The time domain signal of the nth sampling moment of the layer, Indicates The sequence number of the nth moment of the layer Corresponding constellation extension signal.

2. The low peak-to-average ratio LACO-OFDM method based on constellation expansion according to claim 1, characterized in that: Also includes: Step 5: Transform the received signal through N-point frequency domain to generate a frequency domain signal. Remove the limiting distortion from the frequency domain signal, perform modulo operation and QAM symbol detection to obtain the QAM symbol. Perform constellation expansion, inverse frequency domain transformation, asymmetric limiting and frequency domain transformation on the QAM symbol to obtain the transmitted information.

3. The low peak-to-average ratio LACO-OFDM method based on constellation expansion according to claim 1, characterized in that: The said The sequence number of the nth moment of the layer Corresponding constellation extension signal The calculation formula is as follows: Where D represents the distance that the QAM symbol constellation extends, Indicates The first layer The real part of the QAM symbol of the subcarriers, Indicates The first layer The imaginary part of the QAM symbol of the subcarrier, sgn(·) represents the sign operation, and π represents pi.

4. The low peak-to-average ratio LACO-OFDM method based on constellation expansion according to claim 1, characterized in that: The subcarrier constellation after the peak minimum value is extended The calculation formula is as follows: in, Indicates is the minimum value in the sequence of labels, Indicates the first number after the constellation is expanded in the i-1th cycle operation. The time domain signal of the nth sampling moment of the layer.

5. The low peak-to-average ratio LACO-OFDM method based on constellation expansion according to claim 1, characterized in that: Said The calculation formula is as follows: in, represents the peak value of LACO-OFDM signal in the i-th cycle operation, Indicates The minimum value in the numbered sequence.

6. The low peak-to-average ratio LACO-OFDM method based on constellation expansion according to claim 5, characterized in that: The calculation formula for the distance D of the QAM symbol constellation extension is as follows: Among them, M QAM represents the order of QAM modulation, and d represents the minimum distance between constellation points.

7. A low peak-to-average ratio LACO-OFDM system based on constellation extension, characterized by: The method comprises a transmitting end, wherein the transmitting end performs the following steps: N subcarriers are layered according to the sequence numbers, and QAM symbols are allocated to the subcarriers used in each layer to generate frequency domain signals, where the frequency domain signal corresponding to the kth subcarrier in the lth layer is represented as X l,k , l=1,2,…,L, L is the number of layers used, k=0,1,2,3,…,N-1; For the frequency domain signal X l,k Execute N / 2 l-1 Point inverse frequency domain transform operation generates N / 2 l-1 The time domain signal at the sampling moment and repeat the time domain signal in the time domain 2 l-1 times, generating a time domain signal x with N sampling moments l,n , n=0,1,…,N-1; For LP-LACO-OFDM signal Layered Subcarriers carry symbols to perform constellation expansion, and obtain the time domain signal after LP-LACO-OFDM constellation expansion; After the time domain signal after the LP-LACO-OFDM constellation expansion is converted into digital-to-analog format, it is input into the LED to generate a transmission optical signal; The first Layered Subcarriers carry symbols for constellation expansion to obtain a time domain signal after LP-LACO-OFDM constellation expansion, specifically including: Step 3.1: Get the LP-LACO-OFDM signal Layered subcarriers carry symbols, and calculate the The sequence number of the nth moment of the layer Corresponding constellation extension signal in, is the serial number of the part to be expanded; Step 3.2: Set the initial value of the LP-LACO-OFDM signal peak to The time domain signal after constellation expansion in the i-th cycle operation is expressed as Among them, the initial value It represents the maximum value of a sequence numbered by n; Step 3.3: For Expand the constellation of each subcarrier in each layer, and calculate the minimum peak value after the subcarrier constellation expansion The minimum value corresponds to The value of Step 3.4: Calculate the sequence The minimum value of The value of and update The value of Step 3.5: If but Update the value of i to i+1 and continue with steps 3.3 and 3.

4. If Jump out of the loop, and the output is the time domain signal after the LP-LACO-OFDM constellation expansion in, Indicates i-1 times of loop operation Peak value, Indicates the constellation after expansion in the i-th cycle operation The time domain signal of the nth sampling moment of the layer, represents the first The time domain signal of the nth sampling moment of the layer, Indicates The sequence number of the nth moment of the layer Corresponding constellation extension signal.

8. The low peak-to-average ratio LACO-OFDM system based on constellation extension according to claim 7, characterized in that: The invention also includes a receiving end, wherein the receiving end performs the following steps: The received signal is transformed in the N-point frequency domain to generate a frequency domain signal. The frequency domain signal is subjected to the limiting distortion removal, and then the modulo operation and QAM symbol detection are performed to obtain the QAM symbol. The QAM symbol is subjected to constellation expansion, inverse frequency domain transformation, asymmetric limiting and frequency domain transformation operations to obtain the transmitted information.

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