Multi-antenna wireless network performance analysis method

Abstract

The invention provides a multi-antenna wireless network performance analysis method, and belongs to the field of wireless communication. The method comprises the following steps: in a multi-antenna wireless network, calculating an upper bound of a network condition successful transmission probability when a given base station position is distributed; calculating a first moment and a second moment of the upper bound; on the basis of the first moment and the second moment, a complementary cumulative distribution function approximate expression of the conditional successful transmission probability is obtained through Beta function approximation, the percentage information of users capable of achieving the required link performance in the network can be obtained through the expression, and therefore fine-grained analysis of the performance of the multi-antenna wireless network is achieved. According to the invention, link-level performance analysis of the multi-antenna wireless network can be realized, and more effective information is provided for performance analysis of the multi-antenna wireless network and deployment of network base stations.

Description

Technical Field

[0001] The present invention belongs to the field of wireless communications, and in particular, relates to a multi-antenna wireless network performance analysis method. Background Art

[0002] Nowadays, with the development of mobile communication technology, the number of terminals in ground mobile networks has exploded. As a result, the demand for communication traffic in the network has also increased rapidly. Equipping ground base stations with multiple antennas has become an important solution to meet the growing demand for communication traffic. For ground operators, when deploying multi-antenna base stations in wireless networks, analyzing the performance of the network is an important process for selecting network design parameters. Therefore, how to effectively and reasonably analyze the performance of multi-antenna wireless networks is an important issue that needs to be solved in current research.

[0003] The existing performance analysis of multi-antenna wireless networks is based on the network coverage probability or successful transmission probability, that is, considering the probability that the signal-to-interference ratio (SIR) received at a certain point in the network is greater than a given threshold τ. However, the coverage probability can only reflect the average performance of the network, but cannot reflect the link performance distribution information in the network. In order to perform a more fine-grained analysis of the performance of multi-antenna wireless networks, to understand the link performance distribution in the network more carefully, and then to obtain the percentage of users in the network that can achieve the required link performance, a new multi-antenna wireless network performance analysis method needs to be proposed. Summary of the invention

[0004] In view of the defect that the existing performance analysis method of multi-antenna wireless network can only obtain the average performance information of the network, the present invention provides a multi-antenna wireless network performance analysis method. The present invention can realize fine-grained analysis of the performance distribution of multi-antenna wireless network links, thereby providing more detailed network performance information for network deployment.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A multi-antenna wireless network performance analysis method is provided. A plurality of base stations are deployed in the network. Each base station is equipped with M antennas. The spatial position of the base station is represented by a two-dimensional random point process Φ. The method comprises the following steps:

[0007] S1, calculate the conditional successful transmission probability P of the network when a realization of Φ is given s The upper bound of

[0008] S2, calculation The first moment of in, It refers to the expectation of the random variable X;

[0009] S3, calculation The second moment of

[0010] S4, based on The first-order moment and the second-order moment of are approximated by the Beta function to obtain the approximate expression of the complementary cumulative distribution function of the conditional successful transmission probability. in express The probability that the value of is greater than the given successful transmission probability threshold x∈[0,1];

[0011] S5, using the approximate expression of the complementary cumulative distribution function Analyze the distribution performance of the network's conditional successful transmission probability:

[0012] S51, with the successful transmission probability threshold x∈[0,1] as the horizontal coordinate, Draw the simulation curve for the ordinate;

[0013] S52, based on the simulation curve, take the point (x, y) on the curve, and obtain the proportion y of the number of users whose successful transmission probability can reach x in the network, thereby realizing network performance analysis.

[0014] Furthermore, the two-dimensional random point process Φ is a homogeneous Poisson point process with a parameter λ, where λ is the density of base stations.

[0015] Furthermore, the conditional successful transmission probability P s It represents the probability that the signal-to-interference ratio (SIR) received by the user is greater than the threshold τ when a realization of Φ is given.

[0016] Furthermore, given a realization of Φ, users in the network are served by the base stations that are closest to them.

[0017] Further, The calculation method is:

[0018]

[0019] Where, β = (M!) -1 / M , Φ b is the set of all interfering base stations of the user at the origin, Z is the distance between the user at the origin and its serving base station, and α is the path loss factor during signal transmission.

[0020] Further, The first moment of is calculated as:

[0021]

[0022] In the formula, 2F1(a, b; c; d) is the Gaussian hypergeometric function, f Z (z) is the probability density function of the distance between the user at the origin and its serving base station, expressed as f Z (z) = 2πλz exp(-πλz 2 ).

[0023] Further, The second moment of is calculated as:

[0024]

[0025] Where W = [z, +∞) is an integral interval, H ij The expression of (W) is:

[0026]

[0027] Further, The expression is:

[0028]

[0029] In the formula, is the normalized incomplete Beta function.

[0030] The beneficial effects of the present invention are:

[0031] The present invention obtains an approximate expression of the complementary cumulative distribution function of the probability of successful transmission under network conditions by using the first-order moment and the second-order moment of the upper bound of the probability of successful transmission under network conditions and using the Beta function approximation. Based on the approximate expression, the percentage of users in the network that can achieve the required link performance can be obtained, thereby realizing the link-level performance analysis of multi-antenna wireless networks, and providing more effective information for multi-antenna wireless network performance analysis and network base station deployment. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 4 is a relationship diagram between the successful transmission probability threshold and CCDF under different SIR thresholds in an embodiment of the present invention. DETAILED DESCRIPTION

[0033] The present invention is further described below in conjunction with the accompanying drawings. The following specific implementations are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0034] A multi-antenna wireless network performance analysis method is proposed. The method considers that a base station equipped with M antennas is deployed in the network, and the spatial position distribution of the base station is modeled by a homogeneous Poisson point process Φ with a parameter λ. Without loss of generality, a specific user located at the origin of the coordinate is taken as the object for analysis. Based on the stationarity of the Poisson point process, the performance of this user can characterize the performance of any position in the network. First, in a multi-antenna wireless network, the upper bound of the network conditional successful transmission probability is calculated when the base station position distribution is given; secondly, the first-order moment and the second-order moment of the upper bound are calculated; finally, based on the first-order moment and the second-order moment, and using the Beta function approximation, the complementary cumulative distribution function approximate expression of the conditional successful transmission probability is obtained, and the percentage of users in the network that can achieve the required link performance can be obtained by using this expression, thereby realizing fine-grained analysis of the performance of multi-antenna wireless networks.

[0035] In the network considered in this embodiment, each base station uses M antennas to provide services to the single-antenna user closest to it. Considering the base station downlink transmission, the signal-to-interference ratio expression received by a specific user is:

[0036]

[0037] Where h0~Γ(M,1) is the equivalent channel gain between the base station and the user, which follows the gamma distribution; α is the path loss factor during signal transmission; Z is the distance between a specific user and its serving base station; h x ~Γ(1,1)=Exp(1) is the interference channel gain between the interfering base station and the specific user, which obeys the exponential distribution; Φ b The set of all interfering base stations for a specific user.

[0038] When the base station location distribution Φ is given, the conditional successful transmission probability CSP of the network is defined as:

[0039]

[0040] In the formula, SIR is the signal-to-interference ratio received by a specific user, τ is a given receiving SIR threshold, It represents the probability that variable X is greater than x.

[0041] Since h0~Γ(M,1) obeys the gamma distribution, its complementary cumulative distribution function CCDF is Consider the normalized incomplete gamma function A lower bound of β=(M!) -1 / M , we can get an upper bound of the conditional transmission success probability CSP of the network Its specific expression is:

[0042]

[0043] For the upper bound Find its first moment The expression is:

[0044]

[0045] In the formula, 2F1(a, b; c; d) is the Gaussian hypergeometric function, f Z (z) = 2πλzexp(-πλz 2 ) is the probability density function of the distance between a specific user and its serving base station.

[0046] Furthermore, for the upper bound Find its second moment The expression is:

[0047]

[0048] In the formula, It is the conditional successful transmission probability CSP further conditioned on Z=z.

[0049] The expectations The specific expression is:

[0050]

[0051] In the formula, Ω=[z,+∞) is an integration interval, H ij The expression of (Ω) is:

[0052]

[0053] Furthermore, the conditional successful transmission probability (CSP) P of the network s The complementary cumulative distribution function CCDF You can use the upper bound The complementary cumulative distribution function CCDF Approximately, Then it can be approximated by Beta approximation as Its specific expression is:

[0054]

[0055] In the formula, and is the normalized incomplete Beta function.

[0056] The method specifically comprises the following steps:

[0057] (1) Calculate the conditional successful transmission probability (CSP) P of the network when a given realization of Φ is given s The upper bound of Conditional successful transmission probability P s The definition is It represents the probability that the signal-to-interference ratio (SIR) received by the user is greater than the given threshold τ when a realization of Φ is given. When a realization of Φ is given, the users in the network are served by the base station closest to them. The upper bound of CSP is The specific expression is:

[0058]

[0059] Where, β = (M!) -1 / M , Φ b is the set of all interfering base stations of a specific user located at the origin, Z is the distance between the specific user and its serving base station, and α is the path loss factor during signal transmission.

[0060] (2) Calculation The first moment of in, It refers to the expectation of the random variable X; the specific expression is:

[0061]

[0062] In the formula, 2F1(a, b; c; d) is the Gaussian hypergeometric function, f Z (z) is the probability density function of the distance between a specific user and its serving base station.

[0063] (3) Calculation The second moment of The specific expression is:

[0064]

[0065] In the formula, Ω=[z,+∞) is an integration interval, H ij The expression of (Ω) is:

[0066]

[0067] Probability density function f Z The specific expression of (z) is f Z (z) = 2πλzexp(-πλz 2 ).

[0068] (4) Based on The first and second order moments of CSP are approximated by Beta function to obtain the approximate expression of the complementary cumulative distribution function (CCDF) of CSP. in express The probability that the value of is greater than the given successful transmission probability threshold x∈[0,1];

[0069] (5) Using the approximate expression of the obtained CCDF Analyze the distribution performance of the network's conditional successful transmission probability; It can be approximated by Beta approximation, and its expression is:

[0070]

[0071] In the formula, and is the normalized incomplete Beta function.

[0072] The specific analysis method is:

[0073] S51, with the successful transmission probability threshold x∈[0,1] as the horizontal coordinate, Draw the simulation curve for the ordinate;

[0074] S52, based on the simulation curve, take the point (x, y) on the curve, and obtain the proportion y of the number of users whose successful transmission probability can reach x in the network, thereby realizing network performance analysis.

[0075] Figure 1 The relationship between the CCDF approximation result and the successful transmission probability threshold of the embodiment in a multi-antenna network is given, wherein the number of antennas equipped in each base station in the network is M = 8. As can be seen from the figure, under different values ​​of the received signal-to-interference ratio SIR threshold τ, the CCDF approximation expression proposed in the present invention can well match the Monte Carlo simulation results, thereby verifying the effectiveness of the CCDF approximation expression proposed in the present invention.

[0076] Furthermore, based on the CCDF approximate expression proposed in the present invention, Figure 1 The following information can also be obtained: when the received signal-to-interference ratio SIR threshold τ is 0dB, 5dB, 10dB, 15dB, 20dB, and 25dB, the number of users in the network whose successful transmission probability can reach 0.8 accounts for 99%, 83%, 50%, 28%, 16%, and 9%, respectively. It can be seen that by using the analysis method proposed in the present invention, more information about the distribution of user link performance in the network can be obtained, thereby providing more useful information for network deployment and realizing fine-grained analysis of multi-antenna wireless network performance.

[0077] In summary, the present invention can realize fine-grained analysis of multi-antenna wireless network link performance distribution, thereby providing more detailed network performance information and more effective information for multi-antenna wireless network performance analysis and network base station deployment.

[0078] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made in form and details without departing from the scope defined by the present invention.

Claims

1. A multi-antenna wireless network performance analysis method, characterized in that: There are multiple base stations deployed in the network, each base station is equipped with M antennas, and the spatial position of the base station is represented by a two-dimensional random point process F. The method includes the following steps: S1, calculate the conditional successful transmission probability P of the network given a realization of F s The upper bound of S2, calculation The first moment of in, It refers to the expectation of the random variable X; S3, calculation The second moment of S4, based on The first-order moment and the second-order moment of are approximated by the Beta function to obtain the approximate expression of the complementary cumulative distribution function of the conditional successful transmission probability. in express The probability that the value of is greater than the given successful transmission probability threshold x∈[0,1]; S5, using the approximate expression of the complementary cumulative distribution function Analyze the distribution performance of the network's conditional successful transmission probability: S51, with the successful transmission probability threshold x∈[0,1] as the horizontal coordinate, Draw the simulation curve for the ordinate; S52, based on the simulation curve, take the point (x, y) on the curve, and obtain the proportion y of the number of users whose successful transmission probability can reach x in the network, thereby realizing network performance analysis.

2. A multi-antenna wireless network performance analysis method according to claim 1, characterized in that: The two-dimensional random point process F is a homogeneous Poisson point process with a parameter λ, where λ is the density of base stations.

3. A multi-antenna wireless network performance analysis method according to claim 2, characterized in that: The conditional successful transmission probability P s It represents the probability that the signal-to-interference ratio (SIR) received by the user is greater than the threshold t when a given realization of F is given.

4. A multi-antenna wireless network performance analysis method according to claim 3, characterized in that: Given a realization of F, users in the network are served by the base station that is closest to them.

5. A multi-antenna wireless network performance analysis method according to claim 4, characterized in that: The calculation method is: Where, β = (M!) -1 / M , F b is the set of all interfering base stations of the user at the origin, Z is the distance between the user at the origin and its serving base station, and α is the path loss factor during signal transmission.

6. A multi-antenna wireless network performance analysis method according to claim 5, characterized in that: The first moment of is calculated as: In the formula, 2F1(a, b; c; d) is the Gaussian hypergeometric function, f Z (z) is the probability density function of the distance between the user at the origin and its serving base station, expressed as f Z (z) = 2plzexp(-plz 2 ).

7. A multi-antenna wireless network performance analysis method according to claim 6, characterized in that: The second moment of is calculated as: In the formula, Ω=[z,+∞) is an integration interval, H ij The expression of (Ω) is:

8. The method for analyzing performance of a multi-antenna wireless network according to claim 7, characterized in that: The expression is: In the formula, is the normalized incomplete Beta function.

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