3.1. Formation and characteristics of heterogeneous cellular network
In 1947, Bell Laboratories introduced the concept of cellular wireless communication, and completed the feasibility demonstration of related technologies in 1977, which laid a solid foundation for human society to enter the era of personal mobile communication anytime and anywhere. In the next 30 years, with the emergence and development of a new generation of large-scale integrated circuit technology, cellular network has been constantly updated and developed rapidly, and has become one of the most important parts of human life. In 1980, a truly high-capacity cellular system was born. Although 1g system has achieved unprecedented success, it still has many shortcomings, such as low frequency, low privacy, easy to be interfered, unable to provide data services and automatic roaming services.
The emergence of the idea of multi-layer cellular network can be traced back to the mid-1990s, when the goal of researchers was to provide better quality of service for voice users. The use of heterogeneous cellular network is now regarded as the key technology to meet the future 5g demand, meet the rapid growth of data rate demand, improve weak signal coverage, and improve spectrum efficiency and energy efficiency. Figure 1 shows the specific process of heterogeneous cellular network, and its types and properties are shown in Table 1.
Table 1
Types and characteristics of low power nodes in heterogeneous cellular networks
Node type | Transmitting power | Coverage | Layout environment | Deployer | Installation cost |
MBS | 46dBm | 1-10km | Outdoor layout | Operator | Expensive |
RN | 30dBm | 300m | Outdoor layout, indoor enhancement | Operator | Moderate |
PBS | 23-30dBm | < 300m | Outdoor layout/indoor layout | Operator | Moderate |
FBS | 23dBm | < 50m | Indoor layout | Operator | Moderate |
Unlike traditional macro cell-based networks, in addition to macro base stations with higher transmit power, HCN has other low-power nodes that can provide services to users, including pico base stations, femto base stations, and relay nodes. Different LPNs in HCN have their own characteristics, as shown in Table 1. It can be seen that, unlike other LPNs, FBS can be used independently by users to improve indoor signal coverage and improve business experience.
For a network composed of the same type of MBS or LPN, this can be referred to as the HCN layer. Therefore, Fig. 2 shows a multilayer HCN containing MBS, PBS, FBS and RN. Among them, the coverage of the macro cell is much larger than that of the pico base station and the femto base station, but due to the high cost of provision, their density will be much lower than the latter.
3.2. Heterogeneous cellular network algorithm
In order to simplify the analysis, it is assumed that there is only a pair of communication channels between the FU and the FBS in each femtocell in each time slot. In actual systems, this assumption can be realized through flexible scheduling. This article mainly discusses the problem of sub-channel allocation in the downlink transmission scenario (Note: Based on the above assumptions, the proposed mechanism is also applicable to the uplink transmission scenario), as shown in Fig. 3.
The increase of channel power is as formula (1):
$${g}_{n,m}^{k}=\left\{\begin{array}{c}-28-35{log}_{10}\left({d}_{n,m}\right)-\phi , n=m\\ -38.5-20{log}_{10}\left({d}_{n,m}\right)-{L}_{wall}-\phi ,n\ne m\end{array}\right.dB$$
1
The signal-to-noise ratio at the data receiving end can be expressed as formula (2):
$${\gamma }_{n}^{k}=\frac{{p}_{n}^{k}{g}_{n,n}^{k}}{{I}_{n}^{k}+{B}_{0}{N}_{0}}=\frac{{p}_{n}^{k}{g}_{n,n}^{k}}{\sum _{m=1,m\ne n }^{N}\sum _{l\in {S}_{m}\cap \left\{k\right\}}{p}_{m}^{l}{g}_{m,n}^{l}+{B}_{0}{n}_{0}}$$
2
Using Shannon’s formula, the femto base station bandwidth n (bandwidth for short) can be expressed as formula (3):
$${R}_{n}=\sum _{k\in {S}_{n}}{R}_{n}^{k}=\sum _{k\in {S}_{n}}{B}_{0}{log}_{2}\left(1+{\gamma }_{n}^{k}\right)$$
3
For each player n, its strategy space is composed of all available sub-channel sets, which can be expressed by formula (4):
$${S}_{n}=\left\{{S}_{n}\right|{S}_{n}\subset \left\{\text{1,2},\dots ,K\right\},\left|{S}_{n}\right|={K}_{n}\}$$
4
The utility function of player n can be expressed as formula (5):
$${U}_{n}\left({\left({S}_{n}\right)}_{n\in N}\right)=\sum _{k\in {S}_{n}}{B}_{0}{log}_{2}\left(1+\frac{{p}_{n}^{k}{g}_{n,n}^{k}}{{I}_{n}^{k}{(S}_{-n})+{B}_{0}{n}_{0}}\right),\forall n\in N$$
5
At this stage, for each player in the game, the strategy used and the optimal answer can be expressed as formula (6):
$$\underset{{S}_{n}}{{arg}}max{U}_{n}\left({S}_{1},{S}_{2}\right)=\underset{{S}_{n}}{{arg}}max{\gamma }_{n}^{{S}_{n}}\left({S}_{1},{S}_{2}\right)$$
6
Player n in the game should define a mixed strategy that he follows at time t, as in formula (7):
$${Q}_{n}=({q}_{1},{q}_{1},\dots ,{q}_{\left|{S}_{n}\right|})\in \varDelta \left({S}_{n}\right)$$
7
The probability that participant n chooses the i-th strategy in the strategy space is expressed as formula (8):
$${q}_{i}\ge 0,{\forall }_{i}\in \left\{\text{1,2},\dots ,\left|{S}_{n}\right|\right\},\sum _{i=0}^{\left|{S}_{n}\right|}{q}_{i}=1$$
8
The specific process of calculating the mixed strategy is as formula (9):
$${Q}_{n}\left(i\left({F}_{n}\right)\right)=\frac{1}{\left|{S}_{n}\right|},\forall {F}_{n}\in {S}_{n}$$
9
Among them, there is formula (10):
$${Q}_{n}\left(i\left({F}_{n}\right)\right)=\left\{\begin{array}{c}\frac{{\epsilon }^{w}}{\left|{S}_{n}\right|-1}, \forall {F}_{n}\in {S}_{n},{F}_{n}\ne {S}_{n}(t-1) \\ 1-{\epsilon }^{w} otherwise\end{array}\right.$$
10
The Fn parameter is used to regulate the player's utility in the game, as in formula (11):
$$\widehat{U}\left(t\right)={\left(\frac{{U}_{n}\left(t\right)}{{F}_{n}}\right)}^{\beta }ϵ\left(\text{0,1}\right),{\forall }_{t}$$
11
If there is no intra-layer interference, then the player n can obtain the maximum capacity, namely formula (12):
$${R}_{n,max}^{k}=B{log}_{2}\left(1+\frac{{p}_{n}^{k}{g}_{n,n}^{k}}{{B}_{0}{N}_{0}}\right)$$
12
For Fn, the following settings can be made, such as formula (13):
$${F}_{n}=\text{m}\text{a}\text{x}\left\{\sum _{l\in {S}_{n}}{R}_{n,max}^{l}|{S}_{n}\subseteq {S}_{n}\right\}$$
13
Then the strategy counter should be updated according to the current emotional state, as in formula (14):
$${C}_{n}\left(i\left({S}_{n}\left(t\right)\right)\right)={C}_{n}\left(i\left({S}_{n}\left(t\right)\right)\right)+1$$
14
When the algorithm jumps out of the loop, each player in the game completes the learning process and chooses the final strategy according to formula (15):
$${S}_{n}^{D}=\underset{{S}_{n}}{{arg}}max{C}_{n}\left(i\left({S}_{n}\right)\right),\forall {S}_{n}\in {C}_{n},\forall n\in N$$
15
Many strategies in the strategy room can maximize the standardized utility of the players, namely formula (16):
$${\left({S}_{n}^{O}\right)}_{n\in N}=\underset{{{(S}_{n})}_{n\in N}\in {{(C}_{n})}_{n\in N}}{arg}max\widehat{U}\left({{(S}_{n})}_{n\in N}\right)$$
16
3.3. Heterogeneous cellular network simulation scenarios and parameter settings
In addition, NST is uniformly distributed in a disk-shaped area centered on SR and a radius of SR. The simulation assumes that all STs have the same ER request. In the absence of specific instructions, the values of all simulation parameters will be as shown in Table 2. In addition, the simulation result corresponding to each data point is obtained by averaging 10,000 independent simulation results.
Table 2
Parameter | Value |
Cognitive system radius | 0.2 km |
Noise power spectral density | 5x10− 16W/Hz |
PT transmission power | 0.2W |
ST's transmission power limit | 0.1W |
Reference distance | 0.1 km |
Free space gain at distance d | -31.54dB |
Path loss factor | 3.71 |
Shadow fading variance | 1dB |
In this case, the locations of the transmitter and receiver are shown in Fig. 4, where PR is located at (0,0) kilometers, and PT and SR are located at 0.5 kilometers and 0.25 kilometers north of PR.
The increase of E means the slowdown of the algorithm's convergence speed (the increase of algorithm complexity), and the decrease of Br after the execution of the algorithm means the improvement of resource utilization. Therefore, by adjusting the size of the iterative step size of the price factor, the trade-off between algorithm complexity and resource usage is realized, as shown in Table 3.
Table 3
Algorithm expected number of iterations
| E | Br(MHz) | E | Br(MHz) | E | Br(MHz) |
5 | 57 | 0.1246 | 116 | 0.0684 | 476 | 0.0187 |
8 | 118 | 0.0586 | 246 | 0.0248 | 948 | 0.0057 |
10 | 161 | 0.0478 | 356 | 0.0298 | 1248 | 0.0087 |
16 | 196 | 0.0435 | 397 | 0.0247 | 1548 | 0.0089 |
20 | 225 | 0.0485 | 446 | 0.0258 | 1887 | 0.0054 |
Figure 5 shows that as the number of STs increases, the benefits realized in the cognitive system increase, mainly because the proposed algorithm can check the benefits of multiple people in the system from the perspective of EE.