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Abstract
In order to break through the inherent limitation of channel capacity, we employ a correlated multiple input multiple output (MIMO) framework over non-line-of-sight (NLOS) ultraviolet (UV) turbulent channels. Subsequently, a method of segmented correlation is proposed to define the spatial correlation of UV MIMO structures. Furthermore, the correlation and channel capacity are studied with varying elevation angle, turbulence intensity, signal-to-noise ratio (SNR) and number of transceiver in pairs (NTPs). The results show that this correlated MIMO framework can obtain higher channel capacity by reducing the elevation angle of the transceivers or increasing turbulence intensity or NTPs. Moreover, channel capacity increases with the SNR. But at low SNR, a larger gain of channel capacity can be provided. Therefore, this paper develops the capacity of UV turbulent channels and provides a guide for optimal parameter configuration of correlated UV MIMO.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Ultraviolet communication(UVC), new type of wireless optical communication technology, has been widely studied for its important potential value in the future military and commercial fields [1,2]. As a major mode of UVC, non-line-of-sight (NLOS) is generally exploited because it can bypass obstacles and transmit information through scattering in the atmosphere [3–6]. Based on this feature, compared with conventional radio frequency (RF) communication, the NLOS UVC has many advantages, such as good security, strong anti-interference ability, easy to deployment, and all-weather service [7]. But, the ultraviolet NLOS channel has the flaw in channel capacity. Specifically, it is difficult to achieve high data rate, only a few megabits per second (Mbps) [8], due to the following two aspects of channel characteristics. a) Channel fading and pulse broadening caused by atmospheric scattering limit the effective bandwidth [9,10]. b) Channel turbulence caused by atmospheric disturbance reduces the reliable data rate of UVC system [11,12].
To solve the above problems and improve the communication throughput, some researchers have studied NLOS UVC from the perspective of channel coding [13–15]. Nevertheless, because these techniques of channel coding cannot overcome the inherent bandwidth limitations of the channel and offset turbulence effects, higher spectral efficiency and reliability are still needed for turbulent UVC. According to modern digital communication theory, MIMO technology, which is widely used in 5G communication, provides a new direction to solve this bottleneck [16]. Unfortunately, ultraviolet MIMO communication technology is still in its infancy. To date, the published literature mainly focuses on the study of receiving diversity system in ultraviolet SIMO communication [17–19]. There are few researches on UV MIMO architecture due to the following two constraints. a) For RF MIMO systems, it can improve the data rate while maintaining high power efficiency. But in ultraviolet MIMO, the receiving power of every branch is easily affected by the directivity of the communication link. It generally requires additional power demand, resulting in a loss of power efficiency. b) The spatial correlation of multi-channels directly affects the comprehensive performance of MIMO communication system [20]. However, current research on UV MIMO only considered the influence of a single condition. For example, Ref. [21] proposed a UV MIMO model (without additional power) and analyzed the bit error rate (BER) of MIMO system. But the influence of channel correlation is not considered. In [22], a UV MIMO based on linear array of transceivers was proposed to verify that the correlation decreases with the increase of transmitters interval. But the total power loss follows, and it did not take into account turbulence, nor did it accurately define spatial correlations. Although these issues are considered in Ref. [23]. Based on the ultraviolet turbulence channel, a single-scatter SIMO model is proposed, and the spatial correlation of this model located at the transmitter. Nevertheless, it could not be extended to the MIMO system architecture with receiver correlation.
Therefore, in this paper, a correlated UV MIMO turbulent channel model is established to improve the channel capacity without reducing energy efficiency. Based on this architecture, the influence of various parameter on spatial correlation and channel capacity is further analyzed under the assumption of small beam angle. In general, the major contributions of this paper can be summarized as follows:
- (1) We extend the definition of spatial correlation to the UV MIMO architecture by considering both the path overlap of receiver and transmitter, and propose a channel description method based on segmented correlation. By this method, a channel matrix with complex correlation is generated to evaluate the channel capacity.
- (2) We comprehensively evaluate the effectiveness of the correlated MIMO architecture from the effect of elevation angle, turbulence coefficients and transmission distance. Numerical simulation results show that the correlated MIMO is feasible to achieve higher average channel capacity (ACC), although the spatial correlation cannot be ignored under this framework.
- (3) The optimal configuration of various parameters for increasing channel capacity is discussed. Specifically, in the case of strong turbulence or low SNR, the small elevation angle of transceiver is beneficial to the improvement of ACC. It provides effective theoretical guidance for the configuration and implementation of NLOS UVC MIMO.
2. System model and spatial correlation
In this section, we describe the ultraviolet NLOS MIMO channel with single scattering in detail, and interpret the geometric parameters between transceivers. Then the spatial correlation of turbulent channels is defined and the theoretical expression is derived. In addition, a subsection correlation scheme is proposed, the coefficient matrix of the correlated random channel is obtained.
2.1 MIMO system model
Figure 1(a) illustrates a single scattering channel model of NLOS ultraviolet MIMO based on the elevation angle of different transceivers, and describes the geometric configuration with m transmitters and n receivers in three dimensions. The total transmitting power is fixed as ${{P}_{{T}}}$, so under the assumption of equal power, the transmitting power of each transmitter is PT/m. This MIMO structure ensures that every receiver can fully capture optical signals and obtain high energy efficiency. In addition, the transceiver separation distance is d. The center of common volume is represented by Pij, the distance from transmitter Ti to receiver Pij is ${{d}_{{ij}}}$, and the distance from Pij to Rj is ${d}_{{ij}}^{{\prime}}$. Meanwhile, a detailed illustration of transmission links is provided in the projected view of Fig. 1(b). ${{T}_{{i}}}$ emits a beam with divergence ${{\theta }_{{Ti}}}$ and elevation angle ${{\beta }_{{Ti}}}$. ${{R}_{{j}}}$ receive the photon with field of view (FOV) of ${{\theta }_{{Ri}}}$ and elevation angle of ${{\beta }_{{Rj}}}$. Correspondingly, the scattering angle is expressed as ${{\theta }_{{ij}}} = {{\beta }_{{Ti}}} + {{\beta }_{{Rj}}}$, and we can get ${{d}_{{ij}}} = {dsin}{{\beta }_{{Rj}}}/{sin}{{\theta }_{{ij}}}$ and ${d}_{{ij}}^{{\; {\prime}}} = {dsin}{{\beta }_{{Ti}}}/{sin}{{\theta }_{{ij}}}$, geometrically.
Fig. 1. (a) NLOS MIMO UV system under consideration. (b) Detailed illustration of the links between the transmitters and the receivers.
2.2 Definition and coefficient matrix of spatial correlation
According to [23], the spatial correlation of turbulent ultraviolet channels is expressed as the degree of channel path overlap. In the $m \times n$ MIMO system, the transmitters and receivers are $({{{T}_{1}},{{T}_{2}}, \ldots {{T}_{m}}} )$ and $({{{R}_{1}},{{R}_{2}}, \ldots {{R}_n}} )$ respectively. For any two channels, the combination of transceivers in pair is expressed as $[{({{{T}_{{i1}}},{{T}_{{i2}}}} ),({{{R}_{{j1}}},{{R}_{{j2}}}} )} ]$. Therefore, the correlation scenarios of any two channels can be simplified into the two cases as shown in Fig. 2(a). In the case 1(dotted red ellipse), there is no path overlap between the two links, and the channel correlation is 0. But, as shown in the case 2 (dotted blue ellipse), when the two links have the same transmitter (or receiver), partial path overlap will lead to the spatial correlation of the channel.
Fig. 2. (a)Two correlation cases of different transceiver combinations. (b)The channel correlation of the same transmitter in detail.
Taking the scenario of the same transmitter as an example, the spatial correlation is obtained by mathematical analyzing. As shown in Fig. 2(b), the system composed of transmitter ${{T}_{{i}}}$, receivers ${{R}_{{j1}}}$, ${{R}_{{j2}}}$, and I is the link gain of signal amplitude (energy). Because the NLOS turbulent channel can be equivalent to the superposition of two independent LOS turbulent processes [24], the link gain from ${{T}_{{i}}}$ transmitter to receiver ${{R}_{{j}}}$ can be expressed as follows:
For the UV MIMO channel model, the correlation in the scenario of Fig. 2(b) can be given byComparing the two situations in case2, the same receiver and the same transmitter are very similar, except for the position of path overlap (the red line segment). Comprehensively, considering these two scenarios, the spatial correlation formula can be obtained
However, the complex correlation between multi-channel coefficients cannot be directly obtained according to Eq. (5). How to accurately represent the complex correlation is a key problem that should be solved. A subsection correlation scheme is proposed because the NLOS turbulence channel can be equivalent to two independent LOS channels. Taking 2×2 MIMO as an example, the complex correlation of the channel matrix H is represented by subsection correlation in Fig. 3. The channel coefficient ${h_{ij}}$ is decomposed into two independent random distributions ${h_{ij\_1}}$ and ${h_{ij\_2}}$. The integrated correlation of channel coefficients can be expressed by inter-segment correlation, via the following two processes.
Fig. 3. Schematic diagram of the subsection correlation and the complex correlation of the channel matrix in 2 × 2 UV MIMO.
Firstly, the random channel coefficients are expressed by piecewise superposition, and $\lg {h_{ij\_1}} \sim N({1,{\sigma_{{d_{ij}}}}^2} )$, $\lg {h_{ij\_2}} \sim N({1,{\sigma_{{{d^{\prime}_{ij}}}}}^2} )$, the normalized random coefficient of channel can be written as
Secondly, the random sequence of channel coefficients is required owing to subsequent performance simulation. the sequence of channel coefficients satisfying correlation can be generated through the following four steps:- Step 1: generate mutually independent random sequences ${h_{11\_1}}(n )$ and ${h_{12\_1}}(n )$. Where $n = 1,2 \ldots N$ and $N$ is the sequence lengths.
- Step 2: Carry out sequence correlation processing, and get the sequence ${\hat{h}_{{12\_1}}}(n )$ from the two previous independent sequences.$${\hat{h}_{{12\_1}}}(n ) = {\rho \mathord{\left/ {\vphantom {\rho {\sqrt c }}} \right.} {\sqrt c }}{h_{11\_1}}(n )+ \sqrt {1 - {\rho ^2}} {h_{12\_1}}(n )$$where $\rho = {{\sigma _{i{j_{1}}}^2} \mathord{\left/ {\vphantom {{\sigma_{i{j_{1}}}^2} {{\sigma_{i{j_1}}}{\sigma_{i{j_2}}}}}} \right.} {{\sigma _{i{j_1}}}{\sigma _{i{j_2}}}}},c = {{\sigma _{i{j_{1}}}^2} \mathord{\left/ {\vphantom {{\sigma_{i{j_{1}}}^2} {\sigma_{i{j_2}}^2}}} \right.} {\sigma _{i{j_2}}^2}}$.
- Step 3: generate independent random sequences ${h_{{11\_2}}}(n )$ and ${h_{{12\_2}}}(n )$, then we can get the two random channel coefficients as follows
- Step 4 : Repeat the above steps to generate the remaining channel coefficients ${h_{21}}(n )$ and ${h_{22}}(n )$ according to the generated coefficients ${h_{{1}1}}(n ),{h_{{1}2}}(n )$.
3. Parameter configuration and simulation analysis
This section first verifies the correctness of the correlated channel coefficient by comparing with the results in Ref. [24]. Then, taking 2×2 MIMO as an example, the influence of elevation angle, transceiver distance, and turbulence intensity on spatial correlation and average channel capacity is analyzed. Finally, the MIMO architecture is extended to 3×3, and the influence of SNR on channel capacity is simulated. The default parameter settings are shown in Table 1.
Table 1. The default parameter settings
3.1 Validation of correlation channel matrix
To verify the reasonableness of the correlation method given in section 2, we take the 2×2 MIMO as an example in Fig. 3, and set the parameters as follows: the transmission distance d = 100m, elevation angles of the transmitters ${\beta _{{T_1}}} = 3{{0}^{\circ} },{\beta _{{T_2}}} = 3{{5}^{\circ} }$, elevation angles of the receivers are $\beta _{R_1} = 30^{\circ} , \ \beta _{R_1} = 60^{\circ}$ respectively, and set $C_n^2 = {10^{ - 14}}$.
As shown on the left of Fig. 4, the distribution histogram of channel coefficient sequence ${h(n)}$ is consistent with the PDF curve of NLOS turbulence channel coefficient h obtained from Ref. [24]. Moreover, the PDF illustration of the different channel coefficients (${{h}_{{11}}},{{h}_{{12}}},{{h}_{{21}}},{{h}_{{22}}}$) is shown on the right of Fig. 4. The PDF of the turbulence channel varies with the elevation angle of the transceivers, which indicates that elevation angle is a key parameter to be considered. Furthermore, the correlation of 2×2 MIMO channels is shown in Table 2. The numerical simulation results close to the theoretical value of Eq. (5), and error range is $\Delta {\rho } \le {0.0024}$. it means the correlation can be meet by these coefficient sequence. Therefore, combining the above two conclusions, the correlated channel matrix can be obtained accurately. Accordingly, the subsection correlation scheme is feasible for the subsequent analysis of MIMO channel capacity.
Fig. 4. The distribution histogram of the sequences h(n) and the PDF of different channel coefficient h of 2×2 MIMO
Table 2. The correlation of 2×2 MIMO channel
3.2 Influence of elevation angle on spatial correlation
In this section, the influence of elevation angle on spatial correlation of channels is analyzed. If other parameters remain unchanged (the details are listed in Table 1.), transceiver separation distance d = 500m, and the elevation angles of the transceiver are configured as follows: ${10^ \circ } \le {\beta _{{T_1}}} \le {70^ \circ },\ {\beta _{{T_2}}} = {\beta _{{T_1}}} + {{3}^\circ },\ {15^ \circ } \le {\beta _{{R_1}}} \le {45^ \circ },{\beta _{{R_2}}} = {\beta _{{R_1}}} + {15^ \circ }$.
The trend of the spatial correlation between channel coefficient ${h_{11}},\ {h_{12}},\ {h_{21}}$ and ${h_{22}}$ is shown in Fig. 5. Accordingly, three conclusions can be drawn from the three-dimensional diagram. a) If the transmitter is the same, the trend of spatial correlation (such as, ${\rho _1}$ and ${\rho _3}$)is the same. The spatial correlation decreases with ${{\beta }_{{T1}}}$ and increases with ${{\beta }_{{R1}}}$ in the case 1. b) If the receiver is the same, the trend of spatial correlation (such as, ${\rho _2}$ and ${\rho _4}$)is the same. In the case 2, the spatial correlation increases with ${{\beta }_{{T1}}}$ and decreases with ${{\beta }_{{R1}}}$. c) Comparing the above two situations, it should also be noted that spatial correlation(such as, ${\rho _1}$, ${\rho _2}$ or ${\rho _3}$, ${\rho _4}$) shows a negative trend due to differences in transceivers in the case 3.
3.3 Influence of average correlation on channel capacity
According to Eq. (11), the channel coefficients with complex correlations are obtained, and the random coefficient matrix of the ${i} \times {j}$ MIMO system can be expressed as
According to Eq. (13), the cumulative distribution function (CDF) of instantaneous channel capacity was considered in Fig. 6. The default parameter configuration is the same as the environment in section 3.2, and then we changed the parameters such as ${{\beta }_{{T}}}$, ${C_n}$, NTPs and correlated or independent (COD) to obtain different CDF. Obviously, CDF is not convenient to directly describe the overall channel capacity of the system, so we need to consider a new effective indicator. According to the Refs. [23],the outage probability probability may be considered, and a reasonable channel capacity threshold ${C_{th}}$ should be set in advance. However, it is difficult to set an applicable threshold in this paper, for the following two main reasons: a) When the parameters affect the range of channel capacity roughly (e.g. ${{\beta }_{{T}}}$, such as case1), the threshold can be set to effectively compare the difference in outage probability.But, when the parameters have a great influence on the channel capacity (${C_n}$, NTPs and COD, such as case 2), a fixed threshold will make the outage probability not accurate enough. b) Different parameters need to set different thresholds, which is not conducive to comparing the influence of different parameters on channel capacity as a global index. Therefore, ACC was designed as the global indicator (because the CDF curve is smooth and changed similarly), it can be expressed as
Fig. 6. The CDF of channel capacity under different parameters (${{\beta }_{\textrm{T}}}$, ${C_n}$, NTPs and COD).
In order to evaluate the influence of spatial correlation on channel capacity, the numerical simulation of average channel capacity is carried out according to Eq. (14). But the relationship between spatial correlation and channel capacity cannot be described uniformly due to the inconsistent trend of different channel coefficients. Hence, the average correlation is introduced to synthetically analyze the spatial correlation in the channel matrix ${{H}_{{2 \times 2}}}$, which is denoted by ${\rho _{av}} = {{({{\rho_1} + {\rho_2} + {\rho_3} + {\rho_4}} )} \mathord{\left/ {\vphantom {{({{\rho_1} + {\rho_2} + {\rho_3} + {\rho_4}} )} 4}} \right.} 4}$. In addition, assume the SNR is 10 dB, and keep the parameters setting as in the previous section.
Figure 7(a) describes the three-dimensional view of average correlation with the change of elevation angle of the transceiver, and marks several typical regions (e.g. A, B, C and D) with ellipses. It can be observed directly that the correlation of region A is the lowest, namely the best configuration region. Combined with the Table 3, we can generalize two main conclusions as follows. a) The average correlation varies from 0.3964 to 0.4617, indicating that the spatial correlation of the MIMO framework cannot be negligible. b) Although spatial correlation cannot be eliminated, small elevation angles can reduce the average correlation. Specifically, in position A, not only is the average correlation of the MIMO system lower, but also the path loss of the link is smaller.
Table 3. Performance comparison of different elevation angles configuration
Fig. 7. (a) Influence of average correlation on elevation angles of transceivers (b) Influence of average correlation on channel capacity of ultraviolet 2 × 2 MIMO.
Furthermore, Fig. 7(b) analyzes the influence of average correlation on the channel capacity of 2×2 UV MIMO system. With the increase of average correlation, the channel capacity drops from 4.64 bit/Hz/s to 4.28 bit/Hz/s. Meanwhile, the average capacity of independent channel and SISO channel is 3.46 bit/Hz/s and 5.56 bit/Hz/s respectively. Comparing the three curves, the channel capacity of correlated MIMO is smaller than that of independent channels, but the correlated MIMO framework can also effectively improve the channel capacity of the system.
Therefore, we can employ the 2×2 MIMO structure based on different elevation angles to improve the channel capacity of turbulent NLOS UVC system, and a small elevation angle of is appropriate.
3.4 Influence of distance and turbulence coefficient on channel capacity
From Eq. (14), it can be known that the variance (turbulence intensity) of the received energy PDF affected by changing the distance and turbulence coefficient. Because of the change of variance in the channel random coefficient matrix, channel capacity varies with communication distance and turbulence coefficient. In order to quantitatively analyze the influence of atmospheric turbulence intensity on the average channel capacity, we employ a fixed elevation angles of transceiver to set, ${\beta _{{T_1}}} = 3{{0}^\circ },{\beta _{{T_2}}} = 3{{1}^\circ }$ and ${\beta _{{R_1}}} = 3{{0}^\circ },{\beta _{{R_2}}} = {60^ \circ }$. Assuming SNR is 10dB, and transceiver separation distance d from 50 to 100 m, the turbulence coefficient is ${C_n}$ from ${10^{ - 16}}$ to ${10^{ - 13}}$.
As shown in Fig. 8(a), for varying turbulence coefficients, channel capacity of SISO system is a constant, 3.46bit/Hz/s. But the channel capacity of correlated MIMO can reach to more than 4.40bit/Hz/s, which is always smaller than the capacity of independent MIMO. Furthermore, for small turbulence coefficients, the channel capacities are almost the same. Nevertheless, with the increase of turbulence coefficient, the loss of channel capacity becomes more obvious. Specifically, the loss reached 0.69 bit/Hz/s when ${C_n}$ is ${10^{ - 13}}$ (Strong turbulence).
Fig. 8. (a) Influence of channel turbulence on capacity of 2×2 MIMO correlation channel (b) Influence of distance on capacity of 2×2 MIMO correlation channel
In the Fig. 8(b), the effect of communication distance on channel capacity is similar to the abovementioned case. With the increase of distance, the average channel capacity of MIMO system increases gradually. Specifically, average capacity of correlated MIMO and the independent is 4.50 bit/Hz/s and 4.81 bit/Hz/s respectively, when the distance is 200 m. Therefore, from the above results, two major conclusions are outlined below.
- (a) Under the influence of atmospheric turbulence, this UV MIMO framework can obtain higher channel capacity, and the effect is more obvious when the turbulence intensity is larger.
- (b) For different turbulence intensities, the influence of channel correlation is always negative, reducing the channel capacity of 2×2 UV MIMO system.
3.5 Influence of SNR and on average channel capacity
In this section, to further summarize and analyze the channel capacity of the proposed UV MIMO framework, we extend the 2×2 transceivers array to the 3×3 case (Since the number of transmitters is limited by the total energy, the number of receivers is limited by FOV, and the large NTPs may lead to additional correlation between receivers, 3×3 is employed as the typical representative). According to Eq. (14), SNR is also a key parameter for channel capacity. In order to study the influence of SNR on average channel capacity over strong turbulence, we set the SNR from 0 dB to 20 dB, which is different from the fixed SNR in the above. Moreover, other parameters remain unchanged, the elevation angles are configured as follows, ${\beta _{{T_1}}} = 3{{0}^ \circ }$, ${\beta _{{T_2}}} = 3{{1}^ \circ }$, ${\beta _{{T_3}}} = 3{{2}^ \circ }$ and ${\beta _{{R_1}}} = 2{{0}^ \circ }$, ${\beta _{{R_2}}} = 4{{0}^ \circ }$, ${\beta _{{R_3}}} = 6{{0}^ \circ }$.
As shown in Fig. 9, when the SNR is 0 dB, the channel capacity of SISO system is 1 bit/Hz/s, the channel capacity of correlated and independent 2×2 MIMO is 1.65 bit/Hz/s and 1.79 bit/Hz/s respectively. Meanwhile, the channel capacity of correlated and independent 3×3 MIMO channel is 2.18 bit/Hz/s and 2.45 bit/Hz/s, respectively. When the SNR gradually rises to 20dB, the channel capacity of SISO system is 6.66 bit/Hz/s, the channel capacity of correlated and independent 2×2 MIMO is 8.54 bit/Hz/s and 10.19 bit/Hz/s, respectively. and the channel capacity of correlated and independent 3×3 MIMO is 11.14 bit/Hz/s and 14.18 bit/Hz/s, respectively.
Fig. 9. The influence of SNR on the average capacity of UV MIMO channels with different number of transceiver in pairs.
Further analysis is shown in Fig. 10, We standardized the channel capacity of the SISO to be 100%, when the SNR is 0dB and 20dB. Numerical results demonstrate that the capacity gains of two correlated MIMO increase by 65% and 118% respectively in low SNR condition (0dB). Meanwhile, the capacity gains of two independent MIMO increase by 79% and 145% respectively. In contrast, at high SNR (20dB), the capacity gains of two correlated MIMO channels increase by 65% and 118%, and the independent increase by 53% and 122%.
Consequently, the following three conclusions can be outlined: a) Comparing with SISO, 2×2 MIMO and 3×3 MIMO, the channel capacity increases obviously with the increase of the number of transceiver in pairs. b) Although the channel capacity of correlated MIMO is smaller than that of theoretical independent case, this MIMO framework does increase the channel capacity. c) With the increase of SNR, the channel capacity of MIMO system increases gradually, but the gain of channel capacity decreases.
4. Conclusion
In this study, a model of NLOS UV MIMO turbulent scattering channel with correlation is constructed, and the influence of elevation angle on the correlation between channels is studied. In addition, according to the characteristics of turbulent NLOS channel, a channel description method based on segmented correlation is proposed to generate a random channel matrix with complex correlation. Specifically, we simulated and analyzed the influence of key parameters such as transmission distance, turbulence coefficient, average correlation and number of transceivers in pairs on the average channel capacity of UV MIMO system. The important conclusions such as innovative work and parameter optimization configuration are shown below.
- (1) The channel coefficients obtained by subsection correlation method can satisfy both the constraints of turbulent UV channel PDF and complex correlation matrix, which proves the feasibility of subsection correlation scheme.
- (2) When the elevation angles of the transceivers increase, the average correlation varies from 0.3964 to 0.4617, and ACC drops from 4.64 bit/Hz/s to 4.28 bit/Hz/s, reducing elevation angle can obtain larger channel capacity.
- (3) The channel capacity increases with distance or turbulence coefficient, and this UV MIMO framework is more effective under strong turbulence conditions. Thus, this structure can be used to combat turbulence effects.
- (4) Comparing 3×3 UV MIMO with 2×2, increasing the pairs of transceiver antennas can significantly improve the average channel capacity of the system.
- (5) When the SNR increases from 0dB to 20dB, the UV MIMO channel capacity gradually increases and can reach more than 8.54 bit/Hz/s. But, larger channel capacity gain can be obtained under the low SNR.
Funding
National Natural Science Foundation of China (61571067).
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