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Chapter 2
The Overview of Multi-Antenna Signal and System
Wireless communication faces many challenges such as limited available wireless spectrum resources and complex space–time variation in the wireless communication environment. How to effectively utilize the optimal spatial signal combination method to improve the performance and spectrum efficiency of wireless communication systems is a very important and difficult technology for the next generation of wireless communication. This chapter will first introduce the basic theories of multi-antenna spatial signal combination and detection and then introduce the basic knowledge of array antenna from the perspective of signal space propagation. The pattern synthesis technology in the array antenna will be the focus of discussion. Finally, another wide application of multi-antenna technology will be introduced, namely the basic principle and signal detection method of multi-input and multi-output (MIMO) systems.
2.1Spatial Signal Combination and Detection Basis
The received signal combination is a technology for combining multiple received signal values, and it is particularly significant in attenuating signal fading in the processing of wireless communication matrix signals. By providing multiple receiving antennas at the receiving end of the wireless communication system, better signal receiving performance can be obtained. This section assumes that multiple antennas at the receiving end can be equivalently replaced, and each receiving antenna can be regarded as a receiving device corresponding to a specific wireless channel. Since multiple receiving antennas can obtain multiple received signals, in order to obtain a larger signal gain, we need to properly combine the multiple received signals. In this section, we will consider the statistical characteristics of background noise on the basis of the statistics and certainty of the signals, and then combine the received signals.
Among the various signal combination technologies currently in existence, the technology that is easiest to implement is the linear signal combination technology, which is also the focus of our research.
2.1.1Spatial signal combination
In a wireless communication system, it is assumed that there are N receiving antennas at the receiving end. In general, the source signal received by the receiving end must contain signal attenuation or distortion due to channel noise interference when transmitting in a specific channel. Since multiple receiving antennas can obtain observations of multiple received signals, the received signal can be represented by a signal vector in the signal vector space. As N increases, the number of dimensions in the signal vector space increases accordingly. Therefore, a subvector space of a signal vector with a high signal gain must be produced.
If s is used to denote the transmitted signal, then the signal received by the n pairs of receiving antennas at the receiving end can be expressed as
where hk represents the channel gain corresponding to the kth received signal and nk represents the noise of the kth received signal. It can be represented by a vector as follows:
Fig. 2.1. Schematic diagram of the system model for receiving signals from multiple antennas.
where
Figure 2.1 is the schematic diagram of a system model for receiving signals from the N pairs of antennas at the receiving end. Since multiple receiving antennas can receive multiple observations for the same signal at the same time, a more accurate signal estimation can be obtained by properly combining these different observations.
Using a linear combination of a vector y, the estimated value of s can be obtained as follows:
where w = [w1 w2 · · · wN]T represents a linear combination vector.
Of the various signal combination technologies currently available, the technology that can be easily implemented is through the linear signal combination technology, and the mathematical analysis is also relatively simple. Therefore, we will focus on the linear signal combination technology.
In a wireless communication system, utilizing a certain technology to obtain multiple copies of the same source signal at the receiving end can effectively improve the reliability of signal transmission, such as the multi-antenna receiving technology mentioned above, or repeatedly transmitting the same signal several times at the transmitting end. If each signal passes through different channels during transmission and arrives at the receiving end with different receiving states, then the received signal strength of each signal which is expressed
