This post was last edited by chenjingjing on 2023-12-11 13:07
1 Introduction
In industrial applications, low-rate, large-scale and long-distance wireless self-organizing networks have not been widely deployed. The fundamental reason is that their stability, reliability and real-time performance have not been well guaranteed. In such self-organizing networks, the jump relationship between nodes is mostly determined by their relative position and signal strength; due to differences in installation location, deployment density, startup time, etc., the network topology often has obvious differences. In some branches of the network, the number of hops may be shallow, such as 1-2 hops, while some branches are deeper, such as 6-8 hops. In these areas with shallow network hops, the packet loss rate is relatively small, the communication delay is relatively small, and the reliability and real-time performance are also relatively good; while in those areas with deep network hops, the packet loss rate is also relatively high, the communication delay is relatively large, and the reliability and real-time performance are naturally poor.
2. Industry issues
As an upper-layer application system, when users set the data transmission frequency (how many application layer data packets are sent to the target node per second, not the wireless communication rate of the network itself), they often do not care much about the network topology; in fact, there is no way to care about this, because it is not fixed in itself, so when setting the retransmission time threshold, the communication delay and packet loss rate caused by different network hops are often not fully considered. Once the setting is unreasonable, serious response timeout and communication failure will occur; even if the correct time parameters are set, the network topology may still change because the open wireless channel is often disturbed by the outside world, not to mention the topology change caused by the user's later addition of equipment or temporary secondary power-on of some equipment.
From the basic working principle of self-organizing networks, we can see that the depth of network hops is determined by the deployment environment and some other factors, and there is a great deal of randomness and uncertainty. In some physical branches of the network, the number of network hops must be deeper than other areas, and the packet loss rate and communication delay in this area must be greater than other areas, and the reliability and real-time performance brought about are naturally worse. This can be explained through mathematical probability theory.
3. Probability Analysis
In a specific electromagnetic environment, each wireless communication system with each configuration parameter has a roughly determined bit error rate BER (Bit Error Rate) and packet error rate PER (Packet Error Rate), and the relationship between the two is as follows:
PER=1 - ( 1 – BER ) n
Where n is the length of the packet, that is, the total number of bits.
Considering that wireless ad hoc network systems are based on data packets as the basic transceiver unit, this paper selects PER as the basis for analysis. For the convenience of description, we assume that the packet loss rate PER is p, then the probability of successful communication P1, that is, the probability of no packet loss is 100% - p, that is, 1-p; for a two-hop wireless network, in order to achieve end-to-end successful transmission, then the two consecutive hops must be transmitted successfully. According to the knowledge of probability theory, the probability of success P2 should be equal to the product of the success probabilities of the two hops, that is,
P 2 = P 1 * P 1 = P 1 2 = ( 1 – p ) 2
Similarly, for a multi-hop wireless link consisting of n+1 nodes and n hops, if the final destination node wants to correctly receive the data sent by the source node, it is required that each intermediate node from node 2 to node n+1 must correctly receive the data sent by the previous hop. As long as one link fails, the final destination node will not be able to correctly receive the data sent by the source node. Therefore, the total communication success rate Pn should have the following relationship according to the knowledge of probability theory:
P n = ( P 1 * P 1 …. * P 1 ) = P 1 n = ( 1 – p ) n
In order to more intuitively illustrate the actual communication effect, we take the electromagnetic environment with a packet error rate PER of 10%, that is, p=0.1, as an example, and calculate the link communication success rate under different network hops, as shown in the following table:
From the table above, we can see that as the number of network hops increases, the communication success rate decreases significantly. When it comes to the fifth hop n=5, that is, the sixth link node, the success rate is already below the psychological "passing line" of 60%. Many people have already determined that the link is unstable in this situation. In fact, many engineer friends have discovered this phenomenon when debugging ZigBee networks on site, but few people think about the mathematical principles behind it.
4. Summary
Through the above analysis, we can see that in an outdoor long-distance wireless self-organizing network, due to the large link loss between nodes, its link budget is relatively insufficient, so its packet error rate PER will increase accordingly, that is, the packet loss probability p will be relatively large; and in a large-scale network, the communication links of some branch nodes will be relatively deep, that is, the number of network hops n is relatively large. In this case, its communication success rate Pn will naturally drop significantly, and people will feel that this link is not very stable.
At this point, some readers may be thinking, this is easy, just use the TCP algorithm! Add an end-to-end data retransmission mechanism, and the problem will be solved immediately? Is it really so? Please read the subsequent article for details!
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