CN105553526B - Extensive mimo system pilot length and power combined allocation method - Google Patents

Abstract

The invention discloses a joint allocation method of pilot frequency length, pilot frequency power and data power in a massive MIMO system. This method is based on maximizing the reachability and rate of the massive MIMO system, and uses the one-dimensional search method to obtain the optimal pilot length when the pilot power and data power are fixed, and the optimal pilot length when the pilot length is fixed. Next, use the one-dimensional search method to obtain the optimal pilot power and data power, and iterate each search result until the reachability and rate converge, and at the same time obtain the joint optimal value of the pilot length, pilot power and data power . The joint allocation method provided by the invention can improve the reachability and rate of the receiver, has low computational complexity, and is easy to implement.

Description

Joint Allocation Method of Pilot Length and Power in Massive MIMO System

technical field

The present invention relates to a joint allocation method of pilot length, pilot power and data power of a large-scale multiple-input multiple-output (MIMO) system, especially relates to the field of 5G (five-generation mobile communication system) standardization process Joint allocation method of pilot length, pilot power and data power for massive MIMO system.

Background technique

In order to meet the demand for higher data transmission rates in future mobile communication systems, massive MIMO wireless transmission schemes have attracted extensive attention. As a common way for the receiving end to obtain channel state information, the pilot-assisted method sends pilots at the sending end and then estimates the channel according to the received pilot signals. In a massive MIMO system using pilot-assisted methods, the channel estimator (MMSE estimator) based on the minimum mean-square error (MMSE) criterion has the same performance as the maximum a posteriori probability estimator, The MMSE-based signal detector (MMSE detector) has the advantage of maximizing the posterior signal-to-interference-plus-noise ratio (SINR) in the same linear detector, and has important application value .

The joint allocation method of pilot length, pilot power and data power is an effective way to optimize the receiving performance of wireless communication systems. As one of the important performance indicators, reachability and rate can be used as optimization objects for the joint allocation method. On the premise that the channel coherence time is determined and the total power is limited, the transmission pilot length and transmission power are allocated based on the criterion of maximizing reachability and rate. The traditional joint allocation method is proposed for an independent and identical distribution (i.i.d.) channel model, which cannot describe the spatial correlation fading characteristics. The channel statistical model obtained by modeling the antenna array topology in the physical angle domain is more suitable for evaluating reachability and rate than the idealized i.i.d. channel model. Consider a linear antenna array (ULA) spaced at half wavelength. In the angle domain description mode, the correlation matrix of the user's receiving end is a diagonal matrix, and each element of the channel matrix therefore presents a statistical model of independent and non-identical distribution (i.n.d.). However, there is no precedent disclosure of a joint allocation method for i.n.d. channel models. In addition, the traditional joint allocation method only considers the case of the maximum-ratio combining (MRC) detector, and does not consider the case of using the MMSE detector with better performance. The traditional method is equivalent to the power allocation method, because the optimal pilot length is equal to the number of single-antenna users under any SNR situation. This conclusion about the length of the pilot does not necessarily hold in the case of the MMSE detector.

The invention provides a pilot length and power joint allocation method for a massive MIMO system. The presented method is particularly well suited for the case of employing MMSE detectors. Compared with the allocation method of equal power allocation and the pilot length is fixed to the number of single-antenna users, the provided method obtains higher reachability and rate. This method has low computational complexity and is easy to implement.

Contents of the invention

Purpose of the invention: Aiming at the problems and deficiencies in the prior art, the present invention provides a joint allocation method of pilot length, pilot power and data power of a large-scale MIMO system with low computational complexity and easy implementation, so as to obtain pilot Joint optimal value of length, pilot power and data power.

Technical solution: In order to achieve the above-mentioned purpose of the invention, the present invention adopts the following technical solution:

A joint allocation method of pilot length and power for a massive MIMO system. The method is based on maximizing the reachability and rate of the massive MIMO system, and uses a one-dimensional search method when the pilot power and data power are fixed. Obtain the optimal pilot length, and use the one-dimensional search method to obtain the optimal pilot power and data power when the pilot length is fixed, and iterate each search result until the reachability and rate converge, so as to obtain Joint optimal value of optimal pilot length, pilot power and data power.

The reachable and rate of the massive MIMO system is K is the total number of users at the sending end, R _k is the average uplink achievable rate of user k, in And it is a concave function under the condition of K≤T _t <T, and it is also a concave function under the condition of 0≤pt _≤P /T _t , where T _t is the pilot length, K is the number of users, T is the channel coherence time, p _t is the power of the user sending the pilot, and P is the user's sending energy.

The specific steps for obtaining the optimal pilot length using the one-dimensional search method include:

(11) Initialize the pilot length T _t ⁽⁰⁾ = K, the pilot power p _u and data power p _t are the optimal pilot power and data power obtained in the last round of iterations, the initial values of p _u and p _t The value is any positive number that satisfies T _t p _t +(TT _t )p _u =P; calculates the approximate value of the reachable sum rate

(12) Under the given p _u and p _t , using the one-dimensional linear search method to obtain the optimal solution T _t ^* with the criterion of maximizing the reachable sum rate;

(13) Select based on the criterion of maximizing reachability and speed or T _t is the optimal pilot length for this round of iteration.

The specific steps for obtaining the optimal pilot power and data power using the one-dimensional search method include:

(21) Initialize pilot power p _u and data power p _t , The value of the pilot length T _t is the optimal pilot length obtained in the last round of iterations, and the initial value of T _t is any integer satisfying K≤T _t <T; calculate the approximate value of the reachable sum rate

(22) Under a given T _t , with the maximization of reachability and speed as the criterion, the optimal solution p _t is obtained by using the one-dimensional linear search method, and p is calculated according to T _t p _t +(TT _t )p _u =P _u , as the optimal pilot power and data power of the current iteration.

The joint allocation method for iteratively obtaining the optimal pilot length, pilot power and data power based on the above-mentioned one-dimensional search results specifically includes the following steps:

(1) Initialize pilot length T _t ⁽⁰⁾ = K, pilot power and data power The number of iterations is numbered i = 1, and an approximation of the reachability and rate is calculated

(2) Under the given p _u and p _t , the optimal solution T _t ^*(i) is obtained by using the one-dimensional linear search method based on the criterion of maximizing the reachable sum rate;

(3) Select based on the criterion of maximizing reachability and speed or T _t ⁽ⁱ⁾ , as the optimal pilot length of the current iteration;

(4) Under the given T _t ⁽ⁱ⁾ , the optimal solution is obtained by using the one-dimensional linear search method based on the criterion of maximizing the reachable sum rate Calculated according to T _t p _t +(TT _t )p _u =P As the optimal pilot power and data power for this round of iteration;

(5) According to and T _t ⁽ⁱ⁾ calculation

(6) If is less than the threshold ε, the output and T _t ⁽ⁱ⁾ is the final optimal pilot length, pilot power and data power; otherwise, update i=i+1, and go to step (2).

Beneficial effects: Compared with the prior art, the pilot length and power allocation method provided by the present invention adopts the angle domain i.n.d. channel model of spatial correlation fading characteristics, and is especially suitable for the case of using the MMSE detector. Compared with the allocation method of equal power allocation and the pilot length is fixed to the number of single-antenna users, the provided method obtains higher reachability and rate. This method has low computational complexity and is easy to implement.

Description of drawings

Figure 1 is a block diagram of joint allocation of pilot length and power in a massive MIMO uplink system;

Figure 2 is a comparison diagram of the cumulative distribution of reachability and speed under equal power allocation and optimal power allocation;

Fig. 3 is a comparison diagram of reachability and rate under joint allocation, pilot length allocation (equal power) and fixed pilot length (equal power).

Detailed ways

Below in conjunction with specific embodiment, further illustrate the present invention, should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention, after having read the present invention, those skilled in the art will understand various equivalent forms of the present invention All modifications fall within the scope defined by the appended claims of the present application.

In order to better understand the content of the embodiment of the present invention, firstly, the channel model based on the method of the embodiment of the present invention is introduced in detail. Figure 1 shows a block diagram of the pilot length and power allocation of uplink multi-user transmission links in a massive MIMO system. Consider the case of a single cell. The receiving end is equipped with a linear array with a half-wavelength interval, and the number of antennas is M. All users at the sending end are equipped with a single antenna, and the number of users is K. The channel expression between the receiver and user k is

where k=1,2,...,K, β _k is the large-scale fading factor, is the fast fading channel vector, is the diagonalized variance spectrum of the channel from user k to the receiving end, its diagonal elements are v _km , m=1,2,...,M. The expression of v _km is

In the formula, ψ _n =n/M, n=1,...,M; S _k (θ) is the channel angle domain power distribution, and its normalization condition is The covariance matrix of the vector g _k is is a diagonal matrix. Define the channel matrix from all users to the receiver and the correlation matrix of G It is a diagonal matrix with [R] _kk =β _k tr{V _k }=β _k M as diagonal elements, and its expression is R=Mdiag{β ₁ ,...,β _k ,...,β _K }.

In the pilot transmission phase, the user sends the orthogonal pilot sequence synchronously, and the receiving end uses the MMSE as the criterion to estimate G by using the received signal. The pilot symbol power sent by each user is p _t , the pilot length measured by the number of sent symbols is T _t , and the pilot matrix is S satisfies the orthogonal condition: SS ^H =I _K . The base station receives the signal The expression is

In the formula, is additive complex Gaussian noise with mean zero and variance 1 per element. Taking MMSE as the criterion, the estimation formula for G is

In the formula, is additive complex Gaussian noise with mean zero and variance 1 per element. definition and covariance matrix of obeys a complex Gaussian distribution, that is,

【Formula 6】

During the data transfer phase, supplemented by The detector uses MMSE as the criterion to detect the data symbols transmitted by the user. The channel coherence time measured by the number of transmitted symbols is T. Therefore, the data transmission time is TT _t . is the data vector sent by the user, p _u is the power of data sent by each user, the mean value of x is zero, and the variance is I _K . receive vector The expression is

In the formula, is additive complex Gaussian noise with zero mean and variance _IM . Define a cyclic symmetric complex Gaussian random vector Its covariance matrix K _w is expressed as

definition The posterior signal-to-interference ratio (SINR) of user k is

The average uplink achievable rate of user k is

【Formula 10】

In the formula, is the coherence time scaling factor. The reachability and rate expressions of the system are

The sending energy of each user is P, and the satisfying conditions are shown in the following formula.

T _t p _t +(TT _t )p _u ＝P. 【Formula 12】

From the above formula, the average signal-to-noise ratio of users can be determined as SNR=P/T.

A massive MIMO system pilot length and power joint allocation method disclosed in the embodiment of the present invention mainly includes the following steps:

Step 1. Calculate the reachability and rate of the massive MIMO system according to the specific channel model. For the i.n.d. channel model of the spatial correlation fading characteristics described in this embodiment, the specific calculation process is as follows:

The expression of ρ _k is

【Formula 14】

The expression is

In the formula, is a Gaussian vector with mean zero and variance 1 for each element. ρ _k obeys the Gamma distribution. The shape parameters and scale parameters of the probability density function are α _k and ζ _k , respectively. In order to calculate α _k and ζ _k , first calculate The Stieltjes transformation of the empirical distribution of the eigenvalues of T(z). Using numerical iterative method, according to the following expression to solve.

The expressions of α _k and ζ _k are as follows:

【Formula 19】

The expression of R _k is

【Formula 20】

definition: When the number of users K remains unchanged and the number of antennas M at the receiving end increases without bounds, γ→0. The expression of R _k is

【Formula 21】

The reachability and rate approximations are

Step 2. Based on the criterion of maximizing reachability and rate, respectively perform one-dimensional search of optimal pilot length and optimal power allocation value, and iterate each search result until reachability and rate converge, and at the same time obtain the guide The joint optimal value of frequency length, pilot power and data power.

The one-dimensional search for the optimal pilot length in this step is to use the one-dimensional search method to obtain the optimal pilot length under the condition that the pilot power and the data power are both fixed, and the maximization of reachability and rate is taken as the criterion.

The problem of optimal pilot length is expressed as

【Formula 23】

for The second derivative with respect to T _t . because exist and condition is a concave function. Using the property that the sum of concave functions is still a concave function, is also a concave function. Therefore, the optimization problem of the optimal pilot length can be obtained by a one-dimensional linear search method to obtain the optimal solution Then use the maximum reachability and speed as the criterion in and Choose between.

For the pilot length optimization problem described in [Formula 23], the specific steps of the pilot length allocation method provided by the present invention can be summarized as follows:

The one-dimensional search of the optimal power allocation value in this step is to use the one-dimensional search method to obtain the optimal pilot power and data power under the condition that the pilot length is fixed and the maximum achievable rate is taken as the criterion.

The problem of optimal power allocation is expressed as

for The second derivative with respect to T _t . because It is a concave function under the condition of 0≤pt _≤P /T _t . Using the property that the sum of concave functions is still a concave function, is also a concave function. Therefore, for the problem of optimal power allocation, one-dimensional linear search method can be used to search for the optimal solutions p _u and p _t . For the power optimization problem described in [Formula 24], the specific steps of the power allocation method provided by the present invention can be summarized as follows:

Combining the above optimization problems of pilot length and optimal power allocation, the problem of joint allocation of pilot length and power is expressed as

【Formula 25】

The present invention provides a joint allocation method, which iteratively performs one-dimensional search of optimal pilot length and optimal allocation power until reachability and rate converge. The obtained pilot length, pilot power and data power are used as optimal values for joint allocation. For the joint optimization problem described in [Formula 25], the specific steps of the iterative algorithm provided by the present invention can be summarized as follows:

In order to verify the effectiveness of the method of the present invention and the advantages compared with the existing methods, the following simulation comparison experiments were done. Figure 2 is a comparison diagram of the cumulative distribution of reachability and rate under equal power allocation and optimal power allocation, and the total power is set to 10dB and 20dB respectively. It can be seen from the figure that the power allocation method provided by the present invention increases the mean value of reachability and rate by 4 bits/s/Hz. Fig. 3 is a comparison diagram of reachability and rate under joint allocation, pilot length allocation (equal power) and fixed pilot length (equal power). It can be seen from the figure that the joint allocation method of the present invention can achieve and increase the rate by 4 bits/s/Hz when SNR=20dB, and the optimal pilot length is close to K. When SNR=10dB, the reachability and rate can be increased by 5bits/s/Hz, and the optimal pilot length is greater than K.

Claims (7)

1. A massive MIMO system pilot length and power joint allocation method is characterized in that, the method is based on maximizing the reachability and speed of the massive MIMO system as a criterion, and is carried out under the conditions that the pilot power and the data power are fixed respectively The optimal pilot length is obtained by using the one-dimensional search method, and the optimal pilot power and data power are obtained by using the one-dimensional search method when the pilot length is fixed, and the search results are iterated with each other until the sum and Rate convergence, so as to obtain the joint optimal value of the optimal pilot length, pilot power and data power at the same time; The reachable and rate of the massive MIMO system is K is the total number of users at the sending end, R _k is the average uplink achievable rate of user k, in And it is a concave function under the condition of K≤T _t <T, and it is also a concave function under the condition of 0≤pt _≤P /T _t , where T _t is the pilot length, K is the number of users, T is the channel coherence time, p _t is the power of the user sending the pilot, P is the user's sending energy; The mutual iteration of each search result refers to: when searching for the optimal pilot length with fixed pilot power and data power, the values of pilot power and data power are the optimal pilot power and data obtained from the last iteration. Power; when searching for optimal pilot power and data power with a fixed pilot length, the pilot length is the optimal pilot length obtained in the last iteration. 2. massive MIMO system pilot length according to claim 1 and power joint distribution method, it is characterized in that, under the situation that pilot frequency power and data power are all fixed in described joint distribution method, utilize one-dimensional search The specific steps for obtaining the optimum pilot length include: (11) Initialize the pilot length T _t ⁽⁰⁾ = K, the pilot power p _u and data power p _t are the optimal pilot power and data power obtained in the last round of iterations, the initial values of p _u and p _t The value is any positive number that satisfies T _t p _t +(TT _t )p _u =P; calculates the approximate value of the reachable sum rate (12) Under the given p _u and p _t , using the one-dimensional linear search method to obtain the optimal solution T _t ^* with the criterion of maximizing the reachable sum rate; (13) Select based on the criterion of maximizing reachability and speed or T _t is the optimal pilot length for this round of iteration. 3. massive MIMO system pilot length according to claim 1 and power joint allocation method, it is characterized in that, in the described joint allocation method, under the fixed situation of pilot length, utilize one-dimensional search method to obtain optimum The specific steps of pilot power and data power include: (21) Initialize pilot power p _u and data power p _t , The value of the pilot length T _t is the optimal pilot length obtained in the last round of iterations, and the initial value of T _t is any integer satisfying K≤T _t <T; calculate the approximate value of the reachable sum rate (22) Under a given T _t , with the maximization of reachability and speed as the criterion, the optimal solution p _t is obtained by using the one-dimensional linear search method, and p is calculated according to T _t p _t +(TT _t )p _u =P _u , as the optimal pilot power and data power of the current iteration. 4. massive MIMO system pilot length according to claim 1 and power joint distribution method, it is characterized in that, described method specifically comprises the steps: (1) Initialize pilot length T _t ⁽⁰⁾ = K, pilot power and data power The number of iterations is numbered i = 1, and an approximation of the reachability and rate is calculated (2) Under the given p _u and p _t , the optimal solution T _t ^*(i) is obtained by using the one-dimensional linear search method based on the criterion of maximizing the reachable sum rate; (3) Choose based on the criterion of maximizing reachability and speed or T _t ⁽ⁱ⁾ , as the optimal pilot length of the current iteration; (4) Under the given T _t ⁽ⁱ⁾ , the optimal solution is obtained by using the one-dimensional linear search method based on the criterion of maximizing the reachable sum rate Calculated according to T _t p _t +(TT _t )p _u =P As the optimal pilot power and data power for this round of iteration; (5) According to and T _t ⁽ⁱ⁾ calculation (6) If is less than the threshold ε, the output and T _t ⁽ⁱ⁾ is the final optimal pilot length, pilot power and data power; otherwise, update i=i+1, and go to step (2). 5. massive MIMO system pilot length according to claim 1 and power joint distribution method, it is characterized in that, the channel model of described MIMO system adopts independent different distribution channel model, Among them, ρ _k is the posteriori signal-to-interference ratio of user k. 6. massive MIMO system pilot length according to claim 5 and power joint distribution method, it is characterized in that, ρ _k obeys gamma distribution, the approximate formula of R _k Expressed as: where α _k and ζ _k are the shape parameters and scale parameters of the probability density function, respectively. 7. massive MIMO system pilot length and power joint allocation method according to claim 6, is characterized in that, The calculation formula is: Among them, p _u is the power of the user sending data, β _k is the large-scale fading factor formula, and v _ki is the variance of the i-th element of the channel vector of user k.