2Probability Theory

The reason why many wireless communication books start from probability theory is that wireless communications deal with uncertainty. If there are no channel impairments by nature, we can receive the transmitted messages without any distortion and don’t need to care about probability theory. However, nature distorts and interferes when electromagnetic waves propagate. In wireless communication systems, the received messages over a wireless channel include many channel impairments such as thermal noises, interferences, frequency and timing offsets, fading, and shadowing. Thus, wireless communication systems should overcome these impairments.

2.1 Random Signals

Wireless communication systems are designed to deliver a message over a wireless channel. It is assumed that the transmitted messages include a random source and the received messages cannot be predicted with certainty. In addition, wireless channel impairments including thermal noises are expressed as random factors. Therefore, we need to know mathematical expression and characteristics of random signals.

We can divide signals into deterministic signals and non-deterministic signals. The deterministic signals are predictable for arbitrary time. It is possible to reproduce identical signals. The deterministic signals can be expressed by a simple mathematical equation and each value of the deterministic signal can be fixed as shown in Figure 2.1. We know each value with certainty at any time through ...

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