I have read in a paper that a variable 'x' is the rotation angle of the user's antenna array with respect to moving direction. I am wondering how can we calculate this variable x?
Following information may not be useful but just in case it is necessary. Let us assume that BS has M ULA and user has N ULA.
I don't think anyone can answer your question because you have not given any of the information that is needed. Did you mean to include a file?
Malcolm White , I read a paper (given below). In the channel model, they mentioned that '\eta' is rotation angle of the user antenna array w.r.t. moving direction. Let us assume that we have one base station (BS) and one user (moving), both are equipped with uniform linear array (ULA). How can we calculate rotation angle of user's antenna array in such a scenario?
Paper: "Angular-Domain Selective Channel Tracking and Doppler Compensation for High-Mobility mmWave Massive MIMO"
For reference, you can read 3-4 lines below equation (1) of the above paper.
You are referring to eqn 1 of the paper "Angular-Domain Selective Channel Tracking and Doppler Compensation for High-Mobility mmWave Massive MIMO". This is an equation which describes a wireless channel consisting of plane waves. The terms of interest are f_d,t which is the maximum Doppler frequency offset, \theta_t,q and \eta_t.
As f_d,t is a frequency, it must be multiplied by time somehow as it is in the argument of exp(). I cannot see any time in the formula but it might be that DFO is normalised per symbol time so that the factor 2 \pi f_d,t i produces the increasing phase offset with symbol index as required.
The index q is over all possible propagation paths. These arrive at the antenna in the plane of travel of the antenna from multiple different angles. Hence there are generally many such paths and hence values of q. The total number is L_t where t counts the times frames. \theta_t,q and L_t change from frame to frame. \eta_t is the orientation of the antenna with respect to the direction of motion. This changes with time because the user is rotating the antenna during motion.
The term cos(\theta_t,q + \eta_t) is what is confusing you.
THE IMPORTANT THING TO NOTE IS THAT DOPPLER SHIFT IS:
1. ZERO FOR RAYS ARRIVING AT PERPENDICULAR INCIDENCE TO THE DIRECTION OF MOTION
2. MAXIMUM FOR THOSE ARRIVING FROM THE DIRECTION OF MOTION and
3. MINIMUM FOR THOSE ARRIVING OPPOSITE TO THE DIRECTION OF MOTION
This is handled by the cosine. You will need to consult a Physics text for this.
In order to compute the total angular effect of the Doppler you must add \theta_t,q and \eta_t.
The rotation angle 'x' of the user's antenna array with respect to the moving direction can be calculated using the direction of arrival (DOA) of the signal.
Assuming that the user is moving in a straight line towards or away from the base station, the DOA of the signal can be estimated by analyzing the phase differences between the signals received by the antennas in the user's antenna array. The phase differences can be used to estimate the angle of arrival of the signal, which can then be used to calculate the rotation angle 'x'.
To be more specific, let's consider the case where the base station has an M-element uniform linear array (ULA) and the user has an N-element ULA. Let 'd' be the spacing between adjacent elements of the user's array and 'λ' be the wavelength of the signal. Let 'θ' be the DOA of the signal and 'φ' be the rotation angle of the user's antenna array with respect to the moving direction.
Then, the phase difference between the signals received by the i-th and (i+1)-th elements of the user's array can be expressed as:
Δφ_i = 2πd/λ * (sin(φ + θ) - sin(θ))
where 'i' is an integer from 1 to N-1.
Assuming that the spacing between adjacent elements is small compared to the wavelength of the signal (i.e., d
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