CN102624670B

CN102624670B - Wireless OFDM (Orthogonal Frequency Division Multiplexing) signal peak to average power ratio inhibiting method based on amplitude distribution optimization

Info

Publication number: CN102624670B
Application number: CN201210120688.8A
Authority: CN
Inventors: 王勇; 王丽花; 葛建华; 李毅; 宫丰奎; 李靖; 杨超
Original assignee: Xidian University
Current assignee: Xidian University
Priority date: 2012-04-23
Filing date: 2012-04-23
Publication date: 2014-04-02
Anticipated expiration: 2032-04-23
Also published as: CN102624670A

Abstract

The invention discloses a wireless OFDM (Orthogonal Frequency Division Multiplexing) signal peak to average power ratio inhibiting method based on amplitude distribution optimization, which mainly solves the problems of inconstant average power and larger influence on error code rate performance of the prior art. The wireless OFDM signal peak to average power ratio inhibiting method comprises the steps of: 1, carrying out OFDM modulation on an input bit stream, obtaining an original OFDM signal after up-sampling; 2, constructing a companding function based on an improvement target, carrying out companding conversion on the original OFDM signal by using the companding function; 3, sending a companding conversion signal; 4, calculating a de-companding function, carrying out de-companding conversion on a received signal; and 5, carrying out down-sampling on a de-companding conversion signal, and reducing to obtain an original bit stream after OFDM demodulation. The invention is capable of ensuring constancy of an average power after and behind signal companding, has little influence to the error code rate performance of the system while the OFDM signal peak to average power ratio is remarkably lowered, and can be widely applied to various kinds of new generation of broadband wireless OFDM communication systems.

Description

Wireless OFDM signal peak-to-average power ratio suppression method based on amplitude distribution optimization

Technical Field

The invention belongs to the technical field of wireless communication, relates to a peak-to-average power ratio (PAPR) suppression method for Orthogonal Frequency Division Multiplexing (OFDM) modulation wireless transmission signals, and can be widely applied to various new-generation broadband OFDM wireless communication systems.

Background

In recent years, orthogonal frequency division multiplexing, OFDM, has gained increasing attention, particularly in wireless applications. OFDM is a multi-carrier communication system that divides an input information sequence into N parallel sequences, each of which has a lower rate and a narrower bandwidth than the original sequence. Each parallel sequence modulates one subcarrier. If N is large enough, the bandwidth occupied by each modulated subcarrier is less than the associated bandwidth of the channel. Thus, the signal experiences a frequency non-selective channel. The frequency spacing between the subcarriers should be large enough to keep the modulated subcarriers orthogonal. These orthogonal modulated subcarriers are added together to form the OFDM signal.

The superposition of the modulated subcarriers may be advantageous and may be detrimental in that the OFDM signal may deviate significantly from the average power, depending on the phase of the modulated signal. Therefore, at a time when the average power of the OFDM signal is not large and the instantaneous power is large, a saturation region of the power amplifier may be reached. The ratio of the maximum instantaneous power to the average power of the OFDM signal is called the peak-to-average ratio PAPR.

There are many methods for reducing the PAPR of the OFDM signal, such as: mu-law companding, exponential companding, trapezoidal companding and the like. Xianbin Wang proposed a mu-law Companding method in the Reduction of Peak-to-Average Power Ratio of OFDM System Using A company Technique, which can reduce the PAPR of OFDM signals but at the cost of increasing the Average Power of the signals. Therefore, the mu-law companding method can enable the power of the companded signal to reach the saturation region of the power amplifier, so that the power amplification signal generates nonlinear distortion; therefore, Tao Jiang proposes an Exponential Companding method in 'explicit accompanying technology for PAPR Reduction in OFDM systems', and the basic idea is to convert the amplitude distribution of the original OFDM signal into uniform distribution, but the method can increase the distribution of small-amplitude signals and large-amplitude signals, thereby causing the performance Reduction of PAPR and BER; jun Hou proposes a Trapezoidal companding method in a 'Trapezoidal composite scheme for peak-to-average power ratio reduction of OFDM signals', and the basic idea is to convert the amplitude distribution of the original OFDM signals into Trapezoidal distribution, but the method has a great influence on the BER performance of the system.

Disclosure of Invention

The invention aims to provide a wireless OFDM signal peak-to-average ratio restraining method based on amplitude distribution optimization aiming at the defects of the existing method, so that the influence on the system bit error rate BER performance is reduced as much as possible on the premise of obviously reducing the PAPR of the OFDM signal peak-to-average ratio, and meanwhile, the constancy of the average power before and after signal companding is ensured.

The basic idea for realizing the invention is as follows: the method is characterized in that the probability density function of the amplitude of the small signal after companding is a power function, and the probability density function of the amplitude of the large signal is a linear function, and the technical scheme comprises the following steps:

(1) orthogonal Frequency Division Multiplexing (OFDM) modulation is carried out on input bit stream, and original OFDM signals are obtained through up-samplingx_nWhere N is 0,1, …, JN-1, J denotes an upsampling factor, and N denotes the number of subcarriers included in the OFDM system;

(2) constructing a companding function:

wherein x is an input signal of the companding function, z is an output signal of the companding function, m > 0 is a power of a power function, k is a slope of a linear function, b is a longitudinal intercept of the linear function, c is a transition point factor, A is a peak amplitude of the output signal z, σ is a standard deviation of an original OFDM signal xn, exp (·) is a natural exponential function, ln (·) is a natural logarithmic function, sign (·) is a sign function,

is a root operator, | · | is a modulo operator,indicating that the input signal x satisfying this condition is a small signal,

indicating that the input signal x satisfying this condition is a large signal;

(3) according to the peak-to-average power ratio (PAPR) required by a system, selecting a conversion point factor c which minimizes the system Bit Error Rate (BER) in an interval (0,1), selecting a power m which minimizes the system Bit Error Rate (BER) in a positive integer range, and then sequentially solving a peak amplitude A, a slope k and a longitudinal intercept b of an output signal z according to the following formula:

fA^m+3+gA²-σ²＝0，

k = \frac{2 [1 - c^{m} A^{m + 1} (1 - \frac{mc}{m + 1})}{A^{2} {(1 - c)}^{2}},

b＝(cA)^m-kcA

wherein,

f = [g (\frac{mc}{m + 1} - 1) + \frac{m + 3 - {mc}^{3}}{3 (m + 3)}] c^{m}, g = \frac{c^{4} - 4 c + 3}{6 {(1 - c)}^{2}};

(4) by expanding letterPairs of original OFDM signals x_nPerforming companding conversion to obtain companding conversion signal y_n：

(5) Computing a companded transformed signal y from a peak-to-average ratio (PAPR) definition_nPAPR of;

(6) will companded the transformed signal y_nSending to channel, and transmitting to obtain received signal r_n：

<math> <mrow> <msub> <mi>r</mi> <mi>n</mi> </msub> <mo>=</mo> <msub> <mi>y</mi> <mi>n</mi> </msub> <mo>&CircleTimes;</mo> <msub> <mi>h</mi> <mi>n</mi> </msub> <mo>+</mo> <msub> <mi>w</mi> <mi>n</mi> </msub> <mo>,</mo> </mrow> </math>

Wherein,

is the convolution operator, h_nIs the channel impulse response, w_nIs additive white gaussian noise;

(7) and (3) solving an inverse function of the companding function to obtain a companding function as follows:

wherein z 'is the input signal of the despreading function and x' is the output signal of the despreading function;

(8) using pairs of companding functionsReceived signal r_nDecompression and expansion conversion is carried out to obtain a decompression and expansion conversion signal x'_n：

(9) To decompress and expand converted signal x'_nDownsampling is carried out, and bit streams are restored through OFDM demodulation;

(10) and matching the restored bit stream with the input bit stream, and counting the BER of the system, wherein the BER is closer to the BER of the original OFDM system, and the BER performance of the peak-to-average ratio suppression method is better.

The invention constructs a companding function, optimizes the probability density function of small signal amplitude into power function and optimizes the probability density function of large signal amplitude into linear function, thus not only ensuring the constancy of average power before and after signal companding, but also obviously reducing the PAPR of OFDM signal and having little influence on the BER performance of system.

Drawings

FIG. 1 is a flow chart of the present invention for suppressing the peak-to-average ratio of an OFDM signal;

FIG. 2 is a graph comparing the peak-to-average ratio performance of the present invention and a prior art companding method;

FIG. 3 is a graph comparing the bit error rate performance under QPSK modulation with the prior art companding method;

fig. 4 is a graph comparing the bit error rate performance under 16QAM modulation of the present invention and the existing companding method.

Detailed Description

Embodiments of the present invention will be described in detail below with reference to the accompanying drawings. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the protection scope of the present invention is not limited to the following embodiments.

Referring to fig. 1, the specific implementation steps of the present invention are as follows:

the method comprises the following steps: OFDM modulation is carried out on input bit stream, and original OFDM signal x is obtained through up-sampling_nWhere N is 0,1, …, JN-1, J denotes an upsampling factor, and N denotes the number of subcarriers included in the OFDM system.

Step two: and constructing a companding function.

2.1) the probability density function f (| z |) defining the companding function output signal amplitude | z |:

wherein z is the output signal of the companding function, m > 0 is the power of the power function, k is the slope of the linear function, b is the longitudinal intercept of the linear function, c is the conversion point factor, a is the peak amplitude of the output signal z, | · | is the modulo operator;

2.2) determining the cumulative distribution function F (| z |) and its inverse F of the output signal amplitude | z |) of the companding function^-1(|z|)：

Wherein,

is the root operator;

2.3) F (| z |) and its inverse F^-1Substituting the operation result of (| z |) into the solving formula g ═ sign (x) F of the companding function^-1[F(|x|)]To obtain a companding function z:

where x is the input signal of the companding function, z is the output signal of the companding function, and F (| x |) ═ 1-exp (— | x |), (y |)²/σ²) Is the cumulative distribution function of the companding function input signal amplitude x, sigma is the original OFDM signal x_nExp (-) is a natural exponential function, ln (-) is a natural logarithmic function, sign (-) is a sign function,

is a root operator, | · | is a modulo operator,

indicating that the input signal x satisfying this condition is a small signal,

indicating that the input signal x satisfying this condition is a large signal.

Step three: the conversion point factor c, the power m, the peak amplitude a of the output signal z, the slope k and the vertical intercept b in the companding function are determined.

3.1) selecting a conversion point factor c which can minimize the BER of the system in an interval (0,1) according to the PAPR required by the system, and selecting a power m which can minimize the BER of the system in a positive integer range;

3.2) determining the peak amplitude A of the output signal z according to the fact that the average power of the input signal x and the average power of the output signal z of the companding function are equal, and the derivation process is as follows:

<math> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mi>E</mi> <mo>[</mo> <msup> <mrow> <mo>|</mo> <mi>x</mi> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>]</mo> <mo>=</mo> <mi>E</mi> <mo>[</mo> <msup> <mrow> <mo>|</mo> <mi>z</mi> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <mo>&DoubleRightArrow;</mo> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mo>∞</mo> </msubsup> <msup> <mrow> <mo>|</mo> <mi>x</mi> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mi>f</mi> <mrow> <mo>(</mo> <mo>|</mo> <mi>x</mi> <mo>|</mo> <mo>)</mo> </mrow> <mi>d</mi> <mrow> <mo>(</mo> <mo>|</mo> <mi>x</mi> <mo>|</mo> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mo>∞</mo> </msubsup> <msup> <mrow> <mo>|</mo> <mi>z</mi> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mi>f</mi> <mrow> <mo>(</mo> <mo>|</mo> <mi>z</mi> <mo>|</mo> <mo>)</mo> </mrow> <mi>d</mi> <mrow> <mo>(</mo> <mo>|</mo> <mi>z</mi> <mo>|</mo> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>&DoubleRightArrow;</mo> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mo>∞</mo> </msubsup> <msup> <mrow> <mo>|</mo> <mi>x</mi> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mfrac> <mrow> <mn>2</mn> <mo>|</mo> <mi>x</mi> <mo>|</mo> </mrow> <msup> <mi>σ</mi> <mn>2</mn> </msup> </mfrac> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <msup> <mrow> <mo>|</mo> <mi>x</mi> <mo>|</mo> </mrow> <mn>2</mn> </msup> <msup> <mi>σ</mi> <mn>2</mn> </msup> </mfrac> <mo>)</mo> </mrow> <mi>d</mi> <mrow> <mo>(</mo> <mo>|</mo> <mi>x</mi> <mo>|</mo> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mi>cA</mi> </msubsup> <msup> <mrow> <mo>|</mo> <mi>z</mi> <mo>|</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mo>|</mo> <mi>z</mi> <mo>|</mo> </mrow> <mi>m</mi> </msup> <mi>d</mi> <mrow> <mo>(</mo> <mo>|</mo> <mi>z</mi> <mo>|</mo> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mo>&Integral;</mo> <mi>cA</mi> <mi>A</mi> </msubsup> <msup> <mrow> <mo>|</mo> <mi>z</mi> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>z</mi> <mo>|</mo> <mo>+</mo> <mi>b</mi> <mo>)</mo> </mrow> <mi>d</mi> <mrow> <mo>(</mo> <mo>|</mo> <mi>z</mi> <mo>|</mo> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>&DoubleRightArrow;</mo> <msup> <mi>σ</mi> <mn>2</mn> </msup> <mo>=</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>cA</mi> <mo>)</mo> </mrow> <mrow> <mi>m</mi> <mo>+</mo> <mn>3</mn> </mrow> </msup> <mrow> <mi>m</mi> <mo>+</mo> <mn>3</mn> </mrow> </mfrac> <mo>+</mo> <mfrac> <mi>k</mi> <mn>4</mn> </mfrac> <msup> <mi>A</mi> <mn>4</mn> </msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>c</mi> <mn>4</mn> </msup> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mi>b</mi> <mn>3</mn> </mfrac> <msup> <mi>A</mi> <mn>3</mn> </msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>c</mi> <mn>3</mn> </msup> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>&DoubleRightArrow;</mo> <msup> <mi>fA</mi> <mrow> <mi>m</mi> <mo>+</mo> <mn>3</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>gA</mi> <mn>2</mn> </msup> <mo>-</mo> <msup> <mi>σ</mi> <mn>2</mn> </msup> <mo>=</mo> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </math>

wherein E [ | x-²]Is the average power of the input signal x, E [ | z $ -²]Is the average power of the output signal z, E [. cndot.)]Is a desired operator of the plurality of operators,

is a probability density function of the companding function input signal amplitude | x,

f = [g (\frac{mc}{m + 1} - 1) + \frac{m + 3 - {mc}^{3}}{3 (m + 3)}] c^{m}, g = \frac{c^{4} - 4 c + 3}{6 {(1 - c)}^{2}};

3.3) obtaining the slope k and the vertical intercept b of the companding function from the property F (a) of the cumulative distribution function F (| z |) 1 and the amplitude distribution optimization target:

k = \frac{2 [1 - c^{m} A^{m + 1} (1 - \frac{mc}{m + 1})}{A^{2} {(1 - c)}^{2}},

b＝(cA)^m-kcA。

step four: using companding function to original OFDM signal x_nPerforming companding transform, namely optimizing the probability density function of small signal amplitude into a power function, and optimizing the probability density function of large signal amplitude into a linear function to obtain a companding transform signal y_n：

Step five: calculating companding transform signal y according to defined formula of peak-to-average power ratio (PAPR)_nPAPR (PAPR), i.e. signal PAPR = peak power of signal/average power of signal), and the calculation result is compared with the original OFDM signal x_nThe PAPRs are compared, and the lower the PAPR is, the original OFDM signal x is indicated to be subjected to the comparison by the method_nThe better the suppression effect of the PAPR of the peak-to-average ratio,as shown in fig. 2.

Step six: will companded and expanded the converted signal r_nSending to channel, and transmitting to obtain received signal r_n：

Wherein,

is the convolution operator, h_nIs the channel impulse response, w_nIs additive white gaussian noise.

Step seven: and (5) solving an inverse function of the companding function in the step (II) to obtain a decompanding function as follows:

where z 'is the input signal of the despreading function and x' is the output signal of the despreading function.

Step eight: using a de-spreading function on the received signal r_nPerforming a de-companding transformation, i.e. using the r_nReplacing the input signal z 'of the decompression and expansion function to obtain a decompression and expansion conversion signal x'_n：

Step eight: for decompressionTransform signal x'_nAnd carrying out down-sampling and then restoring bit streams through OFDM demodulation.

Step nine: matching the restored bit stream with the input bit stream, namely judging the same bits in the restored bit stream and the input bit stream as correct and judging different bits as error codes, and counting the system bit error rate BER, wherein the more the BER is close to the BER of the original OFDM system, the better the BER performance of the PAPR suppression method is, as shown in FIG. 3 and FIG. 4.

The above steps describe the preferred embodiment of the present invention, and it is obvious that those skilled in the art can make various modifications and substitutions to the present invention with reference to the preferred embodiment of the present invention and the accompanying drawings, and those modifications and substitutions should fall within the protection scope of the present invention.

The effect of the present invention can be further illustrated by simulation.

1) Simulation conditions are as follows: in the OFDM modulation, the number of selected subcarriers is 1024, and the selected modulation modes are QPSK modulation and 16QAM modulation; the transmission channel does not carry out coding processing, and the noise in the channel adopts additive white Gaussian noise.

2) Simulation content and results:

simulation 1, the original OFDM signal is companded and transformed by the present invention and the existing μ law companding method, exponential companding method and trapezoidal companding method, and the obtained PAPR performance of the peak-to-average ratio is shown in fig. 2.

Simulation 2, the bit error rate BER performance obtained by decompressing and expanding the received signal by using the method of the present invention and the existing μ law companding method, exponential companding method and trapezoidal companding method is shown in fig. 3 and 4.

As can be seen from fig. 2 and fig. 3, when a QPSK modulation scheme is adopted in an additive white gaussian noise channel, the performance of the PAPR and BER of the present invention is significantly better than that of the existing companding method.

As can be seen from fig. 2 and 4, when a 16QAM modulation scheme is employed in an additive white gaussian noise channel, compared with the μ -law companding and trapezoidal companding methods, the present invention effectively reduces the PAPR and improves the BER performance to a certain extent; compared with the exponential companding method, the invention not only greatly reduces the PAPR of the signal, but also has little influence on the BER performance of the system.

Claims

1. A wireless Orthogonal Frequency Division Multiplexing (OFDM) signal peak-to-average power ratio suppression method based on amplitude distribution optimization comprises the following steps:

(1) orthogonal Frequency Division Multiplexing (OFDM) modulation is carried out on input bit stream, and original OFDM signal x is obtained through up-sampling_nWhere N is 0,1, …, JN-1, J denotes an upsampling factor, and N denotes the number of subcarriers included in the OFDM system;

(2) constructing a companding function:

where x is the input signal of the companding function, z is the output signal of the companding function, m > 0 is the power of the power function, k is the slope of the linear function, b is the vertical intercept of the linear function, c is the conversion point factor, A is the peak amplitude of the output signal z, and σ is the original OFDM signal x_nExp (-) is a natural exponential function, ln (-) is a natural logarithmic function, sign (-) is a sign function,is a root operator, | · | is a modulo operator,

indicating that the input signal x satisfying this condition is a small signal,

indicating that the input signal x satisfying this condition is a large signal;

fA^m+3+gA²-σ²＝0，

k = \frac{2 [1 - c^{m} A^{m + 1} (1 - \frac{mc}{m + 1})}{A^{2} {(1 - c)}^{2}},

b＝(cA)^m-kcA

wherein,

f = [g (\frac{mc}{m + 1} - 1) + \frac{m + 3 - {mc}^{3}}{3 (m + 3)}] c^{m}, g = \frac{c^{4} - 4 c + 3}{6 {(1 - c)}^{2}};

(4) using companding function to original OFDM signal x_nPerforming companding conversion to obtain companding conversion signal y_n：

Wherein,

(8) using a de-spreading function on the received signal r_nDecompression and expansion conversion is carried out to obtain a decompression and expansion conversion signal x'_n：

2. The method of claim 1, wherein the step (9) of matching the restored bitstream with the input bitstream is to judge the same bits in the restored bitstream and the input bitstream as correct and judge different bits as error codes.