User:Ruofanwu/sandbox

Motivation & applications
The performance of mobile radio communication systems is significantly affected by the radio propagation environment. Because of the blocking by the building or natural obstacles, there exists multiple paths between the transmitter and the receiver with different time variances, phases and attenuations. In the Single-Input Single-Output (SISO) system, multiple propagation paths could be a big problem for the signal optimization. However, based on the development of multiple input multiple output (MIMO) system, it is becoming an advantage on enhancing channel capacity and improving QoS. In order to evaluate effectiveness of these multiple antenna systems, a measurement of the radio environment is needed. Channel sounding is such a technique that can estimate the channel characteristics for the simulation and design of antenna array.

Problem statement & basics
In case of multipath, the wireless channel is frequency dependent, time dependent and position dependent. Therefore, the following parameters are used to describe the channel: In order to characterize the propagation path between each transmitter element and each receiver element, a broadband multi-tone test signal is sent. The transmitter continuously provides a periodic test sequence and, at the receiver end, the arriving test sequence is correlated with the original sequence. This impulse-like auto correlation function is call Channel Impulse Response (CIR).
 * Direction of departure(DOD)
 * Direction of arrival (DOA)
 * Time delay
 * Doppler shift
 * Complex polarimetric path weight matrix

MIMO Vector Channel Sounder
Based on the multiple antennas at the both transmitters and receivers, MIMO vector channel sounder can be effectively collect the propagation direction at the both end of connection and significantly improve the resolution of the multiple path parameters.

K-D model of wave propagation
A finite sum of discrete, locally planar waves is considered instead of a ray tracing model in order to reduce the computation consumption and lower the requirement of optics knowledge, which means the waves are considered to be planar between the transmitters and the receivers. The other two important assumptions are established:
 * The relative bandwidth is small enough so that the time delay can be simply transformed to a phase shift among the antennas.
 * The array aperture is small enough that there is no observable magnitude variation.

based on such assumption, the basic signal model is describe as:

$$ h(\alpha,\tau,\psi_R,\upsilon_R,\psi_T,\upsilon_T) = \sum_{p=1}^P \gamma_p\delta(\alpha-\alpha_p)\delta(\tau-\tau_p)\cdot\delta(\psi_R-\psi_{R_p})\delta(\upsilon_R-\upsilon_{R_p})\cdot\delta(\psi_T-\psi_{T_p})\delta(\upsilon_T-\upsilon_{T_p}) $$

where $$\tau_p$$ is the TDOA of the wave-front $$p$$. $$\psi_{R_p},\upsilon_{R_p}$$ are DOA at the receiver and $$\psi_{T_p},\upsilon_{T_p}$$ are DOD at the transmitter,$$\alpha_p$$ is the Doppler shift.

Real-Time Ultra-wideband MIMO Channel Sounding
Higher bandwidth for channel measurement is a goal of the future sounding devices. The new real-time UWB channel sounder is capable of measuring the channel in great bandwidth from near zero to 5GHz. The real time UWB MIMO channel sounding is greatly improving the accuracy of localization and detection purpose, which means the a precisely tracking of mobile devices.

Excitation signal
A multitoned signal is chosen as the excitation signal.

$$x(t) = \sum_{k=-N_c/2}^{N_c/2-1} \sin(2\pi(f_c+k\cdot\Delta f)\cdot t+\theta_k)$$

where $$f_c$$ is the center frequency, $$\Delta f = B/N_c$$ the tone spacing, and $$\theta_k$$ is the phase of the $$k^{th}$$ tone. we can obtain $$\theta_k$$ by

$$\theta_k = {{(\pi\cdot k)}^2 \over N_c / 2}$$

Data post-processing

 * 1) A DFT over K-1 waveforms that measured in each channel is performed.
 * 2) The frequency domain samples at the multitone frequencies are picked as every $$(K-1)^{th}$$ sample.
 * 3) An estimated channel transfer function $$\hat{H}(f)$$ is obtained by:

$$\hat{H}(f) = {X_{ref}(f)^*\cdot Y(f) \over {\left|X_{ref}(f)\right|}^2+c\cdot\hat{\sigma}_N^2(f)}$$

where $$\hat{\sigma}_N^2(f)$$ is the noise power, $$X_{ref}(f)$$ is a reference signal and $$Y(f)$$. The scaling factor c is defined as

$$c = {\bar{\sigma}_{ref}^2 \over max{(\bar{\sigma}_{Y}^2}-\bar{\sigma}_{N}^2),\bar{\sigma}_{N}^2}$$

RUSK Channel Sounder
A RUSK channel sounder excites all frequencies simultaneously so that the frequency response of all frequencies can be measured. The period of the test signal must be larger than the duration of frequency response in order to contain all possible time delays in the paths. The figure shows a typical channel impulse response (CIR) for a RUSK sounder. A secondary time variable is introduced so that the CIR is a function of the delay time $$\tau$$ and the observation time $$t$$. A delay-Doppler spectrum is obtained by the Fourier transformation.