Abstract
Data Acquisition
Results
This project is focused on implementing source location algorithms to
find the direction of arrival of transmitted radio frequency signals on an
array of receivers. The MuSIC (multiple signal classification) algorithm
is used, as well as a variant, smooth-MuSIC, which mitigates the effects
of multipath interference. Beamforming techniques, which combine
temporal and spatial filtering, are also used to find the direction of
arrival. These strategies minimize the transmission power needed to
send a signal. Further work building on this research can implement
directional transmission and receiving with beamforming, which yields
many advantages including minimized signal interception. The results
from this research can be used to make adaptive arrays of receivers
that minimize noise or interfering signals, as well as address universal
communications issues on a cost-effective platform.
• The data acquisition process imposed a different arbitrary phase
difference of the received data from each receiver. A training
sequence was devised to synchronize the signals with the time they
actually arrived.
Overview
• A 20kHz tone was generated and modulated with a 2.4GHz carrier
wave.
When a signal is intercepted by receivers that are not equidistant from
the transmitter, each receiver perceives the signal in a different phase. If
the signals do not show too much noise or multipath interference, one
can find the angle of arrival from the correlation of the signals. However,
with noisy signals or signals with interference, one must utilize more
complex algorithms to estimate the direction of arrival. Additionally, if
there are multiple signals being transmitted, one cannot use the
correlation to find the angle of arrival. However, techniques such as
beamforming or the MuSIC algorithm allow for the determination of
multiple signals arriving at the array of receivers at the same time.
• Receivers are within half a wavelength (~6cm) of each other to
prevent spatial aliasing.
• The incoming waveforms were processed with either beamforming or
the Multiple Signal Classification algorithm (MuSIC), as well as with a
correlation.
• Both actual and simulated data (with added noise) where analyzed.
• Simulated data was generated in Labview, and all data was analyzed
in Labview and a Matlab node within.
In simulations, a signals with a magnitude of 0.015 could be
resolved with MuSIC with added Gaussian white noise of standard
deviation 0.5, which far overshadowed the signal. The MuSIC
spectrum was not always consistent at this very noisy level, but one
could average a few snapshots to find a consistent direction of
arrival. The direction of arrival could also be determined with
beamforming, but it was not as sharp at this level of noise. The
correlation result was extremely inconsistent.
• Data was bottlenecked at the 1Gb switch on its way to the computer,
which caused frequent overflow.
• Transmission from the far field to prevent any near field complications.
• A plane wave approximation was used.
Simulated data at angle of 45 degrees, with signal magnitude 0.015 and noise standard
deviation of 0.5
Experimental Setup
Goal: To implement source location algorithms that use data
from an array of receivers to discern the location of the source.
When actual data was gathered, both algorithms worked well. Noise
and interference were low enough that the algorithms and the
correlation technique agreed, though the correlation results were not
as consistent as those of beamforming and MuSIC
Tx
2.4G
Signals on an array of 3 receivers, with transmitter at 30 degrees.
Mathematic Foundation
Beamforming is a process that applies different weights and time delays
to each signal in a phased array to maximize certain qualities. It is a
versatile tool that can be used for directional transmission or receiving,
as well as improving the signal-to-noise ratio of the receiver inputs.
With beamforming, direction of arrival is ascertained by maximizing
the output power of the following, where d is the steering vector and R is
the estimated covariance matrix.
1
X is a NxM matrix of reciever input,
where N is the number of receivers
1Gb
Switch
φ
λ/2
λ/2
Rx
Rx
Rx
2.4G
2.4G
2.4G
Measured data at angle of 60 degrees at a distance of 1.5 meters.
GPS Disciplined
Oscillator
10MHz Reference
Clock Signal
2
All transceivers are connected to a reference signal and a clock
source, and the carrier frequency is 2.4GHz.
3
In the MuSIC algorithm, the following is maximized, where Qn is the
eigenvectors of R corresponding to the noise:
𝑃𝑚𝑢𝑠𝑖𝑐 𝜑 =
1
𝑠𝐻
𝐻
𝜑 𝑸𝒏 𝑸𝒏 𝑠 𝜑
After implementing these two algorithms, there remain many
possibilities for exploring the advantages of each, as well as the
implement of more methods for detection of direction of arrival.
Noise was added in a simulation, but the effects of multipath
interference and noise on an actual signal need to be tested.
Additionally, the characteristics of a beamforming signal that is not
a pure tone are yet to be determined. In the future, adaptive
algorithms that rely on communication between the receivers and
the transmitters may improve direction detection as well as yield a
clearer signal.
References and Acknowledgments
1.Nehorai, A. Lecture slides from CSSIP Lab.
2,3.Professor Raviraj Adve’s notes: http://www.comm.utoronto.ca/~rsadve
Thanks to Ed Richter for spending countless hours on this project, Jichuan Li for assisting
with the theoretical background and Professor Nehorai for making this possible.