# Performance Analysis of MIMO System with Single RF Link Based on Switched Parasitic Antenna
## 2 Theory of MIMO System
### Single Link MIMO System  
The basic structure of the single RF link of 2 \(\times\) 2 MIMO system based on the switched parasitic antenna is shown in Figure 1. From the view of the function, the single RF link MIMO system can be divided into two parts, the transmitter and the receiver. The original binary code was radiated through the switch parasitic antenna after a series of transformation to the RF signal. The receiver is the inverse process, which will convert the RF signal to the binary code. From the view of the signal, the whole system can be divided into baseband digital processing and analog RF processing. In the baseband, the signal will complete the generation and recovery process, and the RF part mainly involves signal transmission and reception. The baseband and RF processing are realized by a digital-to-analog converter (DAC) or analog-to-digital converter (ADC). The single RF link is concentrated in the transmitter, and receivers adopt the conventional uniform array antenna. The core idea of a single RF link MIMO system based on switched parasitic antenna is to map multiple signals at the transmitter to a set of far field radiation patterns orthogonal to each other in free space. One channel of input is feed to the antenna after the modulation, frequency conversion and filtering process. The other input symbols are directly connected with the parasitic elements to control the state of varactor diodes loaded in parasitic elements, which will change the far field radiation pattern subsequently. The number of parasitic elements depends on the size of the MIMO system. As for 2 \(\times\) 2 MIMO system, two far-field radiation patterns can be achieved by two elements. On the basis of this, for the N \(\times\) N MIMO system, every increase in N will correspond to two more parasitic elements. It is worth mentioning that the varactor diode is introduced to achieve smooth transform of impedance and the performance have significantly improved compared with other diodes, such as Positive Intrinsic-Negative (PIN) diodes, but the external DC bias network is complex. The load reactance value of the parasitic unit loaded on the antenna is directly controlled by the exclusive operation (XOR) of two input signal \(b_{1}\) and \(b_{2}\). It will change the current direction of the antenna structure and form multiple directional patterns. The transmitted signal of the transmitting antenna arrives at the receiving end of the system after mixing the Rayleigh channel with additive white Gauss noise. The task of the receiver is to recover two digital signals as quickly and accurately as possible. In the two branches of the antenna, the RF module is the same as the demodulation module, but the signal recovery module will process the two signals differently. The performance of the receiver will be measured by the accuracy of the recovered binary signal. The method is to measure the bit error rate by comparing the recovered bits with the input symbols at the transmitter. Figure 1: Diagram of single radio frequency (RF) link Multiple-Input Multiple-Output (MIMO) system. The two mirror-symmetry directional functions are represented by \(\mathcal{G}_{1}(\theta,\varphi)\) and \(\mathcal{G}_{2}(\theta,\varphi)\), which satisfies the condition \(\mathcal{G}_{2}(\theta,\varphi)=\mathcal{G}_{1}(\theta,\pi-\varphi)\). The correlation can be expressed as:  
\[\rho_{12}=\frac{1}{\sqrt{P_{1}P_{2}}}\iint\mathcal{G}_{1}(\theta,\varphi) \mathcal{G}_{2}^{*}(\theta,\varphi)\sin(\theta)d\theta\;d\varphi \tag{1}\]  
\[P_{1}=\frac{1}{4\pi}\iint\left|\mathcal{G}_{1}(\theta,\varphi)\right|^{2}\sin (\theta)d\theta\;d\varphi \tag{2}\]  
\[P_{2}=\frac{1}{4\pi}\iint\left|\mathcal{G}_{2}(\theta,\varphi)\right|^{2}\sin (\theta)d\theta\;d\varphi \tag{3}\]  
\(P_{1}\) and \(P_{2}\) represent the radiation power at the direction of \(\mathcal{G}_{1}(\theta,\varphi)\) and \(\mathcal{G}_{2}(\theta,\varphi)\), respectively.