The present disclosure relates to a technology for calculating a channel capacity for a non-stationary large-scale antenna array, and belongs to the technical field of wireless communication and channel modeling.
In order to achieve the objective of faster, farther, and larger capacity information transmission, the large-scale antenna array is regarded as one of the key technologies in the fifth generation of mobile communication systems (5G), which represents the spatial dimension of communication. The large-scale antenna array is more suitable for the sixth generation of mobile communication systems (6G), however with the number of antennas increases, the antenna array will be in the near-field region, which is defined by the Fresnel region of the array, including the distance below Rayleigh distance, i.e., 2L2/λ, where λ and L denote the wavelength and maximum size of the antenna array, respectively. At this time, the spherical wavefront needs to be considered instead of the original previous plane wavefront. When the distance between antenna arrays is extremely close, the mutual coupling will be formed by the electromagnetic interaction between antenna elements, and the mutual coupling effect exhibits different performance in transmitting and receiving antenna arrays, which is basically not reflected in the previous channel model.
The Shannon channel capacity calculation formula is based on the assumption of wide-sense stationary signals, so it is not suitable for calculating the non-stationary channel capacity. The effect of non-stationary characteristics on the capacity of the multi-antenna channel model is not considered. In addition, the channel capacity is merely simulated in the previous study, with no measurement data for the real environment as support, resulting in a lack of verification. In order to calculate the capacity of the non-stationary channels more accurately, a new method for calculating the capacity needs to be proposed and the correctness of the new method can be verified.
Technical problems: the objectives of the present disclosure are to provide a method suitable for calculating the capacity of a non-stationary channel through constructing a 6G non-stationary massive multiple-input multiple-output (MIMO) channel model, solve the limitation of the Shannon channel capacity formula in the non-stationary channel, and find the influence of the non-stationarity on the channel capacity.
Technical solutions: The complete technical means and methods of the present disclosure.
In order to realize the above objectives, the present disclosure provides a method for calculating the capacity of the non-stationary 6G massive MIMO channel. The method comprises the following specific steps.
In Step 1, a non-stationary channel model for a large-scale antenna array with the mutual coupling effect is constructed.
In Step 2, a channel measurement system for a large-scale antenna array is built to obtain measurement data.
In Step 3, simulation parameters for a channel with the large-scale antenna array are optimized, and the spatial cross-correlation function is simulated.
In Step 4, according to the spatial cross-correlation function, a spatial stationary interval is proposed and calculated.
In Step 5, according to the stationary interval, a channel capacity within the interval and a total channel capacity are calculated.
In Step 6, simulation results are compared with measurement results, to verify the correctness of the capacity calculation of the non-stationary channel.
The steps of Step 1 are specifically as follows.
In Step 101, the channel matrix
for a non-stationary massive MIMO channel model is constructed, where PL denotes the path loss (PL), SH denotes the shadowing (SH) that follows a lognormal distribution, BL denotes the blockage loss (BL), and OL denotes the oxygen loss (OL). HS=[hqp(t, τ)]M
where KR denotes a rice factor, the NLOS components hqp(t, τ) are calculated by the following formula:
where {·}T denotes the transposition operator, the carrier frequency is represented as fc, Pqp,m
In Step 102, the spherical wavefront is modeled. According to the geometry relationship as illustrated in
where dm
A relationship in spherical coordinate systems is as follows:
where ϕE,m
where ϑT denotes the angle between the transmitting antenna array and the m-th ray, and ωpT denotes the angle between the scatterer Sm
for the receiving terminal, the dp,m
In Step 103, an evolution on an array axis is modeled. Generations and disappearances of clusters are characterized by utilizing the birth-death process in the present disclosure, and for the transmitting terminal, the survival probability of the cluster on the array axis is calculated by the following equation:
where λR denotes the disappearance rate of the cluster, DcA denotes a scenario-dependent coefficient in the spatial domain. Similarly, the survival probability at the receiving terminal is:
where δq denotes the distance from the first antenna to the q-th antenna at the receiving terminal. Therefore, the number of newly generated clusters generated by the spatial evolution is represented as:
where λG denotes the generation rate of the clusters.
In Step 104, the mutual coupling effect between antennas is modeled. The antenna radiation pattern is affected by the mutual coupling because the distance between antennas in the massive MIMO channel is extremely short. The impedance matrix is utilized in the present disclosure to describe the mutual coupling between antennas, and the complete communication system is referred to
where u1, i1 denote port voltages and port currents at the transmitting terminal, respectively and u2, i2 denote port voltages and port currents at the receiving terminal, respectively, Z11, Z22 denote a transmitting impedance matrix and a receiving impedance matrix respectively, and Z12, Z21 denote mutual impedance matrixes.
When a uniform linear array of isotropic antennas is considered, the mutual coupling effect considering an input and a load impedance is represented as:
where ZG denotes an input impedance of an element in a free space, and ZL is a matched load impedance. The current vector is represented as I and the matrix Z can be extended to:
therefore, the channel matrix after adding the mutual coupling effect can be represented as:
where cpR and cpT denote coupling matrixes of the receiving terminal and transmitting terminal, respectively.
The massive MIMO channel measurement system constructed in Step 2 can be referred to
The steps of Step 4 are specifically as follows.
In Step 401, for the channel capacity studied in the present disclosure, a circumstance when channel state information (CSI) is unknown at the transmitting terminal, the CSI is completely known at the receiving terminal and the channel matrix is random can be adopted:
where ρ denotes the signal-to-noise ratio (SNR), and H denotes the channel matrix.
In Step 402, the spatial stationary interval is defined and calculated according to the spatial cross-correlation function.
The estimated period can be measured by the stationary interval, during which the channel amplitude response can be considered to be wide-sense stationary. The definition of time-domain stationary interval can be analogized, which is the maximum time length when the autocorrelation function of the delay power spectral density exceeds 80% of a threshold, where 80% of the threshold is an empirical value that can be adjusted as needed. After analogy, the definition of spatial stationary interval is proposed, which is the maximum number of antennas when the spatial cross-correlation function of angular power spectral density exceeds 80% of the threshold. Therefore, an improvement of a stationary interval I(r) in space s is defined as:
where inf{·} denotes an infimum of the function, Δr denotes a number of antennas in the spatial stationary interval, and RΛ(r, Δr) denotes a normalized spatial cross-correlation function of the angular power spectral density:
where
The steps of Step 5 are specifically: firstly, according to the stationary interval obtained in the Step 4, the channel is divided into n segments, and according to a stationary interval Δri at an i-th segment, the channel capacity of the i-th segment is calculated as follows:
where Gi denotes the general channel matrix at the i-th segment.
Eventually, a total channel capacity in an entire observation interval R is obtained as follows:
The specific contents of Step 6 are to compare the simulation model in Step 1 with the measurement data obtained in Step 2 to eventually verify the correctness of the proposed channel capacity calculation formula.
Beneficial effects: the benefits and targets achieved by the present disclosure are as follows.
The non-stationary characteristics and mutual coupling effects of massive MIMO are introduced on the basis of traditional wireless channel modeling in the present disclosure, and a novel method for calculating the non-stationary channel capacity is proposed. Since the unique massive MIMO channel measurement system, the verification on the accuracy of the model and the calculation method can be supported in the present disclosure, and the problem that the Shannon channel capacity formula is not applicable in the non-stationary channel can be solved. In addition, compared with other channel models, the channel model proposed by the present disclosure is more consistent with the real communication scenario, the accuracy of the channel model can be verified by the channel measurement system, and the channel capacity calculation formula proposed by the present disclosure has the characteristics of low complexity.
The following is a detailed description of the present disclosure in conjunction with the drawings and specific embodiments. This embodiment 1 is implemented on the premise of the technical solutions in the present disclosure, and provides a detailed implementation and a specific operation process, but the protection scope of the present disclosure is not limited to the following embodiments.
The examples are given according to the contents included in the claims.
As illustrated in
In Step 1, a non-stationary channel model for a large-scale antenna array with the mutual coupling effect is constructed.
In Step 2, a channel measurement system for a large-scale antenna array is built to obtain measurement data.
In Step 3, simulation parameters for a channel of the large-scale antenna array are optimized, and the spatial cross-correlation function is simulated.
In Step 4, according to the spatial cross-correlation function, a spatial stationary interval is proposed and calculated.
In Step 5, according to the stationary interval, a channel capacity within the interval and a total channel are calculated.
In Step 6, simulation results are compared with measurement results, to verify the correctness of the capacity calculation of the non-stationary channel.
The steps of Step 1 are specifically as follows.
In Step 101, the channel matrix
for a non-stationary massive MIMO channel is constructed, where PL denotes the path loss, SH denotes the shadowing that follows a lognormal distribution, BL denotes the blockage loss, and OL denotes the oxygen loss. HS=[hqp(t, τ)]M
where KR denotes a rice factor, the NLOS components hqp(t, τ) are calculated by the following formula:
where {·}T denotes the transposition operator, the carrier frequency is represented as fc, Pqp,m
In Step 102, the spherical wavefront is modeled. According to the geometry relationship as illustrated in
where dm
A relationship in spherical coordinate systems is as follows:
where ϕE,m
where ϑT denotes the angle between the transmitting antenna array and the m-th ray, and ωpT denotes the angle between the scatterer Sm
for the receiving terminal, the dp,m
In Step 103, an evolution on an array axis is modeled. Generations and disappearances of clusters are characterized by utilizing the birth-death process in the present disclosure, and for the transmitting terminal, the survival probability of the cluster on the array axis is calculated by the following equation:
where λR denotes the disappearance rate of the cluster, DA denotes a scenario-dependent coefficient in the spatial domain. Similarly, the survival probability at the receiving terminal is:
where δq denotes the distance from the first antenna to the q-th antenna at the receiving terminal. Therefore, the number of newly generated clusters generated by the spatial evolution is represented as:
where λG denotes the generation rate of the clusters.
In Step 104, the mutual coupling effect between antennas is modeled. The antenna radiation pattern is affected by the mutual coupling because the distance between antennas in the massive MIMO channel is extremely short. The impedance matrix is utilized in the present disclosure to describe the mutual coupling between antennas, and the complete communication system is referred to
When a uniform linear array of isotropic antennas is considered, the mutual coupling effect considering an input and a load impedance is represented as:
where ZG denotes an input impedance of an element in a free space, and ZL is a matched load impedance. The current vector is represented as I and the matrix Z can be extended to:
therefore, the channel matrix after adding the mutual coupling effect can be represented as:
where cpR and cpT denote coupling matrixes of the receiving terminal and transmitting terminal, respectively. Eventually, the channel matrix with mutual coupling effect is obtained.
The massive MIMO channel measurement system constructed in Step 2 can be referred to
As illustrated in
The steps of Step 4 are specifically as follows.
In Step 401, for the channel capacity studied in the present disclosure, a circumstance when CSI is unknown at the transmitting terminal, the CSI is completely known at the receiving terminal and the channel matrix is random can be adopted:
where ρ denotes the signal-to-noise ratio (SNR), and H denotes the channel matrix.
In Step 402, the spatial domain stationary interval is defined and calculated according to the spatial cross-correlation function.
The estimated period can be measured by the stationary interval, during which the channel amplitude response can be considered to be wide-sense stationary. The definition of time-domain stationary interval can be analogized, which is the maximum time length when the autocorrelation function of the delay power spectral density exceeds 80% of a threshold, where 80% of the threshold is an empirical value that can be adjusted as needed. After analogy, the definition of spatial stationary interval is proposed, which is the maximum number of antennas when spatial cross-correlation function of angular power spectral density exceeds 80% of the threshold. Therefore, an improvement of a stationary interval I(r) in space s is defined as:
where inf{·} denotes an infimum of the function, Δr denotes a number of antennas in the spatial stationary interval, and RΛ(r, Δr) denotes a normalized spatial cross-correlation function of the angular power spectral density:
where
The steps of Step 5 are specifically: Firstly, according to the stationary interval obtained in Step 4, the channel is divided into n segments, and according to a stationary interval Δri at an i-th segment, the channel capacity of the i-th segment is calculated as follows:
Eventually, a total channel capacity in an entire observation interval R is obtained as follows:
The schematic diagram of the capacity comparison between the stationary channel and the non-stationary channel eventually obtained is as illustrated in
The specific contents of Step 6 are to compare the simulation model in Step 1 with the measurement data obtained in Step 2 to eventually verify the correctness of the proposed channel capacity calculation formula.
Provided in the present disclosure is a method for calculating the channel capacity for the non-stationary large-scale antenna array. Compared with the existing channel capacity calculation method, the non-stationarity of the channel and the mutual coupling effect of the antenna are considered in the method of the present disclosure, and the calculation result is compared with the channel measurement result, solving the problems that the previous channel capacity calculation is not applicable in the non-stationary channel. The method for calculating the capacity of the non-stationary channel provided in the present disclosure passes the measurement fitting, provides CIRs of the whole communication channel, and analyzes the spatial cross-correlation function and channel capacity of the system accordingly.
It should be understood that the present disclosure is described by some embodiments, it is known for those skilled in the art that the features and embodiments may be modified or equivalently replaced without deviating from the spirit and scope of the present disclosure. In addition, under the instructions of the present disclosure, these features and embodiments may be modified to adapt to specific situations and materials without deviating from the spirit and scope of the present disclosure. Therefore, the present disclosure is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of the present application fall within the scope protected by the present disclosure.
Number | Date | Country | Kind |
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202210208323.4 | Mar 2022 | CN | national |
Filing Document | Filing Date | Country | Kind |
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PCT/CN2023/087941 | 4/12/2023 | WO |