ESPRIT based DoA Estimation

This module implements a method for estimating the delays using Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) method.

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Code example

# Ntx, Nty, dtx, dty will be taken from antenna arrays propoerties
# Hk is estimated at the receiver.
# However, for perfect CSI, it can be directly taken from channel.OFDM.
Lpath      = 5 # Returns DoAs for 5 strongest paths
espritDoa  = ESPRIT_DoA(Ntx, Nty, Hk.shape[1]) # Create a ESPRIT DoA Object
xoA_est    = espritDoa(Hk, Lpath, dtx, dty)    # Return 2 x 5 DoA matrix
# row-0 is azimuth angles for each path
# row-1 is elevation angles for each path

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class toolkit5G.Positioning.ESPRIT_DoA(Nr_x, Nr_y, Nobservation)

This module provides an API to estimate the 2D $($ azimuth ($\theta$) and elevation ($\varphi$) $)$ direction of Arrival using ESPRIT(Estimation of signal parameters via rotational invariant techniques). The module expects OFDM channel estimates (${\text{H}}_{\text{k}}$) as an input and exploits the structure in this channel using number of antennas placed in columns (${\text{N}}_{\text{r,x}}$), number of antennas placed in rows (${\text{N}}_{\text{r,y}}$), spacing between antennas placed in columns (${\text{d}}_{\text{r,x}}$) and spacing between antennas placed in rows (${\text{d}}_{\text{r,y}}$) to estimate the 2D ($\{({\theta }_l,{\varphi }_l){\}}_{l=0}^{L-1}$) angle of arrival traced by multi-paths ($L$) while propagating over the wireless channel.

Tip

• ${\text{N}}_{\text{r,x}}$ and ${\text{N}}_{\text{r,y}}$ are inputted using Nr_x and Nr_y to __init__ method.

• ${\text{d}}_{\text{r,x}}$ and ${\text{d}}_{\text{r,y}}$ are inputted using d_spcgx_Rx and d_spcgy_Rx to __call__ method.

• $L$ is inputted as numPaths.

• $\{({\theta }_l,{\varphi }_l){\}}_{l=0}^{L-1}$ is $2\times L$ vector returned by the class.

Parameters:

• Nr_x – int Defines the Number of Antenna in the receiver side along the x-axis.Should be a positive integer greater than 2.

• Nr_y – int Defines the Number of Antenna in the receiver side along the y-axis.Should be a positive integer greater than 2.

• Nobservation – int Defines the number of time samples. They may be fft size or fft size*numSymbols etc. Should be a positive non-zero integer.

Important

Nr_x and Nr_x must be even integers to estimate 2D direction of arrivals.

Input:

• Hk (np.ndarray) – Defines the channel matrix. It should have a size (Nr_x*Nr_y, Nobservation).

• numPaths (int) – Defines the number of propagation paths.

• d_spcgx_Rx (number) – Defines the spacing between antennas along x-axis. It should be >0.

• d_spcgy_Rx (number) – Defines the spacing between antenna along y-axis. It should be >0.

Output:

(2, numPaths), float – 2D angles of arrival of numPaths strongest multi-paths in the channel. Row-0 is azimuth angles for each path and row-1 is elevation angles for each path.

Raises:

• ValueError – [Error-ESPRIT_DoA]: ‘Hk’ should be a 2D NumPy array!

• ValueError – [Error-ESPRIT_DoA]: Input Dimensions mismatch!n Hk.shape[0] should equal Nr_x*Nr_y and Hk.shape[1] should equal Nobservation.

• ValueError – [ESPRIT-DoA]: ‘Nr_x’ must be positive even integer, greater than or equal to 2

• ValueError – [ESPRIT-DoA]: ‘Nr_y’ must be positive even integer, greater than or equal to 2

• ValueError – [ESPRIT-DoA]: ‘Nobservation’ must be a positive integer

• ValueError – [ESPRIT-DoA]: ‘d_spcgx_Rx’ must be a positive number > 0!

• ValueError – [ESPRIT-DoA]: ‘d_spcgy_Rx’ must be a positive number > 0!