Читать книгу Spatial Multidimensional Cooperative Transmission Theories And Key Technologies - Lin Bai - Страница 25
2.1.1Spatial signal combination
ОглавлениеIn 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 is the channel gain vector and is the noise vector. The channel gain h which describes the channel transmission characteristics is one of the key parameters in the combination of received signals.
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 in Eq. (2.1) will be quite different. In other words, the signal-to-noise ratio of these received signals is different. If the received signals are represented by the respective corresponding vectors in the vector space, then according to mathematical derivation, the total signal strength will increase as the vector space dimension increases, although the signal strength may become weak in a certain dimension.
In the actual production process, the channel gain between the transmitter and the receiver is affected by many factors such as transmission distance and multipath propagation. The transmission distance determines the average gain of the channel, while multipath propagation and the motion of the transmitter and receiver affect the instantaneous channel gain. In addition, moving the obstacles between the transmitter and the receiver can also result in time-varying channel gains. Due to the influence of various factors, the channel in wireless communication system is often a fading channel. In the fading channel environment, the signal-to-noise ratio (SNR) can be regarded as a time-varying random variable. However, when the SNR is below a certain threshold, the receiver cannot detect the signal. Therefore, we should try to reduce the probability that the SNR is lower than the threshold, namely reducing the probability of interruption. To solve this problem, we can use multi-receiving antenna diversity technology to reduce the probability of interruption, so as to obtain better signal detection performance. The gain obtained from this diversity is called the spatial diversity gain.
We call the vector space of the received signal as Space Domain, and the channel gain generated by the multidimensional signal (or multiple copies of the same signal) is known as the spatial diversity gain. In what follows, we will focus on several ways of combining signals in a wireless communication system.