CN104917714A

CN104917714A - Method for reducing peak-to-average power ratio of large-scale MIMO-OFDM down link

Info

Publication number: CN104917714A
Application number: CN201510309345.XA
Authority: CN
Inventors: 方俊; 包恒耀
Original assignee: University of Electronic Science and Technology of China
Current assignee: University of Electronic Science and Technology of China
Priority date: 2015-06-08
Filing date: 2015-06-08
Publication date: 2015-09-16
Anticipated expiration: 2035-06-08
Also published as: CN104917714B

Abstract

The invention belongs to the field of signal processing for wireless communication, and particularly relates to a method for reducing a signal peak-to-average power ratio (PAPR) in a large-scale MIMO-OFDM down link. The method comprises the steps of: expressing precoding constraint and OFDM modulation jointly into an underdetermined equation set; establishing a prior model which can promote low PAPR characteristics; and utilizing an Expectation-Maximization (EM) and Generalized Approximate Message Passing (GAMP) algorithm to design an algorithm capable of solving a low PAPR solution. The method provided by the invention utilizes the degree of freedom provided by a large number of antennas at a base station side in a MIMO-OFDM system, and reduces the PAPR of signal transmission of the downlink. The energy of the obtained transmitted signals is concentrated, and the signals tend to be in a constant envelope under the condition that the transmission antennas are enough, so that an RF circuit does not require an expensive linear power amplifier, thereby the construction cost of base stations in future can be effectively reduced.

Description

Method for reducing large-scale MIMO-OFDM downlink power peak-to-average ratio

Technical Field

The invention belongs to the field of signal processing of wireless communication, and particularly relates to a method for reducing a Peak-to-Average Power Ratio (PAPR) of a signal in a large-scale MIMO-OFDM downlink.

Background

Massive MIMO has received widespread attention in the industry as it is able to meet the ever-increasing communication rate and capacity requirements. MIMO-OFDM has been defaulted to the air interface scheme of next generation wireless communication systems because OFDM technology can be easily applied to MIMO systems. OFDM modulation is a technique for mapping different data onto mutually orthogonal subcarriers, can effectively combat frequency selective fading, is simple to implement, and is widely used in various communication systems, for example: LTE and WIFI. However, the OFDM modulated signal is a linear superposition of multiple independent carriers, and usually has a high PAPR, so that a high-cost linear amplifier is required for the radio frequency circuit of the OFDM system.

In the conventional SISO-OFDM system, there are many mature methods for reducing PAPR, which usually compress the original high PAPR signal into a low PAPR signal at the transmitting end for transmission, and at the same time transmit an additional information to the user, which can demodulate the signal correctly. However, in the multi-user MIMO system, it is impossible for a user at a receiving end to cooperatively demodulate a compressed PAPR signal, so that the conventional method is difficult to be extended to the multi-user MIMO system.

In a large-scale MIMO system, the number of antennas owned by a base station is far larger than the number of users served by the base station, so that an underdetermined equation set can be jointly established by multi-user precoding constraint and OFDM modulation of the MIMO-OFDM system, and infinite modulation signals without interference among users can be met. Thus, the large-scale transmit antennas provide an additional degree of freedom to find OFDM modulated signals with low PAPR characteristics. At present, an optimal solution is generally found by using a convex optimization scheme, but the complexity is high and the convergence speed is slow.

Disclosure of Invention

In view of the deficiencies of the prior art, the present invention provides a low complexity algorithm for reducing the PAPR of a signal using the statistical properties of a low PAPR signal.

The idea of the invention is as follows: firstly, precoding constraint and OFDM modulation are jointly expressed into an underdetermined equation set, then a prior model capable of promoting low PAPR characteristics is established, and finally an algorithm capable of solving a low PAPR solution is designed by utilizing an Expectation-Maximization (EM) algorithm and a Generalized Approximation Message Passing (GAMP) algorithm.

For convenience of describing the contents of the present invention, terms used in the present invention are first defined.

Massive MIMO-OFDM downlink: as shown in FIG. 1, s_nQAM modulated signals transmitted for N subcarriers, N1，Is a vector after precoding without interference among users,(M1.., M) is a frequency domain signal transmitted on M base station transmit antennas,the time domain signals transmitted on the antennas are transmitted by M base stations, K is the number of users in the large-scale MIMO, K is less than M,representing a complex field.

Pre-coding: in the MIMO-OFDM system, in order to ensure the interference-free receiving signals among a plurality of users in the same time-frequency domain resource, the transmitting signal s needs to be transmitted_nAnd carrying out precoding. The channel isThen the encoded vectorShould satisfy s_n＝H_nw_n. Thus, the signal received by the user is free of interference from other users.

The power peak-to-average ratio: the PAPR of the mth transmitting antenna is defined asI.e., the ratio of the peak to average energy of the transmitted signal, wherein,representing the real part of the parameter,representing the imaginary part of the parameter,is an operator two-norm.

Normal distribution: mean μ and variance σ²Is defined as a probability density function of a normal distribution (Gaussian distribution)The cumulative distribution function of a standard normal distribution is defined as Φ (f), where f represents an argument.

And (3) protecting the bandwidth: in order to protect the frequency band used in OFDM modulation from interference of adjacent frequency bands, subcarriers located at both ends of the frequency band are not generally used. Thus, the N subcarriers are divided into two sets:andfor sub-carriersThe transmitted signal is a QAM modulated signal,for sub-carrierss_nIs an M-dimensional zero vector.

Maximum expectation: an iterative algorithm for finding a maximum likelihood estimate. And continuously establishing a lower bound of the likelihood function, and optimizing the lower bound so as to maximize the likelihood function.

Generalized approximate messaging: an algorithm for solving a variable approximation a posteriori distribution function.

The Digamma function: defined as the derivative of the natural logarithm of the Gamma function, i.e.

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The method for reducing the power peak-to-average ratio of the large-scale MIMO-OFDM downlink comprises the following specific steps:

s1, calculating a signal model y of joint precoding and OFDM modulation as Ax, specifically:

s11, jointly representing precoding constraint of massive MIMO-OFDM downlink and OFDM modulation of massive MIMO-OFDM downlink into a linear equation systemWherein, is a block diagonal momentArray, theByA channel matrix H_nAndthe unit matrix of M dimension is formed,t is a permutation matrix for allocating the precoded signals to the respective transmit antennas,is a block diagonal matrix, saidConsists of M N-dimensional inverse discrete Fourier transform matrixes,as an unknown quantity [. sup. ] [. ]]^TRepresenting the transpose of the matrix, | represents the number of elements in the set;

s12, using the complex equation set of S11Transformation to the real number domain: let x be dimension I and y be dimension J, where,

s2, introducing a prior model, specifically:

s21, making each element of the x in S1 independent, and introducing a truncated Gaussian mixture model prior to the xWherein i is 1,., I, the ith element x of said x_i∈[-v,v]，α_i1And alpha_i2Is the inverse Gaussian variance, κ_iFor discrete variables with values of 0 and 1, v is a priori boundary, normalization factor

Normalization factor

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S22, linear equation for S11Introducing a Gaussian noise with a mean value of zero and an inverse variance of beta;

s3, iterative updating and outputtingThe method comprises the following specific steps:

s31, initializing, and for all J ═ 1.1, for all I:α_i1(0)＝α_i2(0)＝1，κ_i(0)＝1/2，v(0)＝||y||_∞/||A||_∞，making the iteration number t equal to 1;

s32, calculating approximate posterior distribution by using GAMP, which comprises the following steps:

j is equal to 1, J,

wherein, the upper mark^pThe function of distinguishing is realized,representing the function, A, associated with x as stated at S12_jiThe jth row and ith column elements of the matrix a are represented S12,represents S12 the square of the element of the ith column of the jth row of the matrix a,

wherein,as an intermediate parameter, the parameter is,

wherein, the upper mark^zThe function of distinguishing is realized,

wherein,as an intermediate parameter, the parameter is,

wherein,as an intermediate parameter, the parameter is,

wherein, the upper mark^sThe function of distinguishing is realized,

for all I1, 1., I,

wherein, the upper mark^rThe function of distinguishing is realized,

wherein,is an intermediate parameter;

s33, updating signal x_iAnd parameter alpha_i1，α_i2And kappa_i：

κ_i(t+1)＝q(κ_i＝1)，

Wherein,

for kappa_iA posterior probability q (k) of_i) Is provided with

S34, updating the inverse variance beta of S22:

s35, updating the boundary v of S21: v (t +1) ═ v (t) + Δ v, where,

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s36, judging, if T is T, jumping out iteration and outputtingIf T < T, then let T +1 go to S31, where T is the maximum number of iterations and T is an empirical threshold.

The invention has the beneficial effects that:

the invention reduces the PAPR of the downlink sending signal by utilizing the degree of freedom provided by a large number of antennas at the base station end in a large-scale MIMO-OFDM system. The energy of the obtained transmission signal is very concentrated, and the signal tends to a constant envelope state under the condition that the transmission antenna is enough, so that an expensive linear power amplifier is not needed in a radio frequency circuit, and the construction cost of a future base station can be effectively reduced.

Drawings

Fig. 1 is a downlink block diagram of a MIMO-OFDM system.

Fig. 2 shows a transmitted time domain signal and a corresponding frequency domain signal, (a) the time domain signal, and (b) the frequency domain signal, where EM-TGM-gam represents the invented method, and ZF is a conventional precoding method without PAPR processing.

FIG. 3 is a complementary cumulative distribution graph of the PAPR.

Detailed Description

The technical solution of the present invention will be described in detail below with reference to the embodiments and the accompanying drawings.

The base station end is provided with 100 transmitting antennas; the number of service users is K equal to 10; the number of OFDM subcarriers is 128, wherein the effective number of subcarriers is

Assuming that the channel is perfectly known, a 16QAM modulation scheme is selected.

Firstly, calculating A and y in a signal model according to a channel matrix and user data; then, algorithm parameters are initialized:α_i1(0)＝α_i2(0)＝1、κ_i(0)＝1/2、v(0)＝||y||_∞/||A||_∞、and (4) iteratively updating signals and model parameters according to GAMP and EM algorithms, jumping out when the maximum iteration times are reached, and outputting the solved result.

s11, jointly representing precoding constraint of massive MIMO-OFDM downlink and OFDM modulation of massive MIMO-OFDM downlink into a linear equation systemWherein, is a block diagonal matrix, saidByA channel matrix H_nAndthe unit matrix of M dimension is formed,t is a permutation matrix for allocating the precoded signals to the respective transmit antennas,is a block diagonal matrix, saidConsists of M N-dimensional inverse discrete Fourier transform matrixes,as an unknown quantity [. sup. ] [. ]]^TRepresenting the transpose of the matrix, | represents the number of elements in the set;

s12, using the complex equation set of S11Transformation to the real number domain: let x be dimension I and y be dimension J, where,since K < M, A is underdetermined, the equation has infinite solutions, and the next step is used to find the PAPR-best among themA small solution;

s2, introducing a prior model, specifically:

s21, in order to realize the low PAPR characteristic of rent solution, each element of the x is independent in S1, and a truncated Gaussian mixture model prior is introduced to the xWherein I1.. I, the ith element x of said x_i∈[-v,v]，α_i1And alpha_i2Is the inverse Gaussian variance, κ_iFor discrete variables with values of 0 and 1, v is a priori boundary, normalization factorNormalization factor

S22, linear equation for S11Introducing a Gaussian noise with zero mean value and beta inverse variance, and jointly estimating x and alpha by using the following iterative algorithm₁、α₂Kappa, v, beta, thereby obtaining a low PAPR signal;

j is equal to 1, J,

wherein,as an intermediate parameter, the parameter is,

wherein, the upper mark^zThe function of distinguishing is realized,

wherein,as an intermediate parameter, the parameter is,

wherein, the upper mark^sThe function of distinguishing is realized,

for all I1, 1., I,

wherein, the upper mark^rThe function of distinguishing is realized,

wherein,is an intermediate parameter;

s33, updating signal x_iAnd parameter alpha_i1，α_i2And kappa_i：

κ_i(t+1)＝q(κ_i＝1)，

Wherein,

for kappa_iA posterior probability q (k) of_i) Is provided with

S34, updating the inverse variance beta of S22:

s35, updating the boundary v of S21: v (t +1) ═ v (t) + Δ v, where,

After the iterative operation, the sending signal with low PAPR can be obtained, and the signal can ensure no interference among users and no signal energy on the protection bandwidth.

As shown in fig. 2, the time domain signal and its spectrum on the 1 st transmit antenna. Wherein, the curve shown by EM-TGM-GAMP is the signal obtained by the method of the invention, ZF is a common Zero Forcing (ZF) algorithm without PAPR processing. From fig. 2(a), it can be seen that most of the energy of the signal samples obtained by the present invention is concentrated in one peak, and the energy of the remaining samples is less than this peak, so the PAPR of the signal is very small, only 0.6dB, and the PAPR of the signal without PAPR processing is as high as 11.9 dB. Fig. 2(b) is a frequency spectrum of a signal, and it can be seen that on some subcarriers used as guard bandwidth, EM-TGM-gam has no energy as does ZF.

Fig. 3 shows the comparison of the complementary cumulative distribution of PAPR of signals of two schemes, and it can be seen that the PAPR of the modulated signal obtained by the present invention is basically always less than 1dB and more than 10dB better than ZF. Therefore, the scheme of the invention can effectively reduce the construction cost of the future base station antenna radio frequency.

Claims

1. The method for reducing the power peak-to-average ratio of the large-scale MIMO-OFDM downlink is characterized by comprising the following steps of:

s12, using the complex equation set of S11Transformation to the real number domain: x, and x is the dimension I and y is the dimension J, wherein，

S2, introducing a prior model, specifically:

s21, making each element of the x in S1 independent, and introducing a truncated Gaussian mixture model prior to the xWherein I1.. I, the ith element x of said x_i∈[-v,v]，α_i1And alpha_i2Is the inverse Gaussian variance, κ_iFor discrete variables with values of 0 and 1, v is a priori boundary, normalization factor

Normalization factor

j is equal to 1, J,

wherein,as an intermediate parameter, the parameter is,

wherein, the upper mark^zThe function of distinguishing is realized,

wherein,as an intermediate parameter, the parameter is,

wherein, the upper mark^sThe function of distinguishing is realized,

for all I1, 1., I,

wherein, the upper mark^rThe function of distinguishing is realized,

wherein,is an intermediate parameter;

s33, updating signal x_iAnd parameter alpha_i1，α_i2And kappa_i：

κ_i(t+1)＝q(κ_i＝1)，

Wherein,

φ_i＝Φ((v(t)-μ_i)/σ_i)-Φ((-v(t)-μ_i)/σ_i)，

for kappa_iA posterior probability q (k) of_i) Is provided with

S34, updating the inverse variance beta of S22:

s35, updating the boundary v of S21: v (t +1) ═ v (t) + Δ v, where,