This document summarizes a project to design an analog filter bank circuit to calculate Fourier series coefficients for a time reversal division multiple access (TRDMA) wireless network-on-chip system. The filter bank contains high-Q bandpass filters and is simulated using Cadence software. Preliminary results show the first 7 coefficients can be accurately calculated but accuracy decreases for higher coefficients. Future work includes adding self-calibration of sampling switches and accounting for delays in the high frequency circuits. The calculated coefficients will be used to generate a time-reversed waveform for transmission in the TRDMA system.

1. A
Filter
Bank
of
High-­‐Q
Bandpass
Filters
to
Find
Fourier
Series
Coefficients
for
TRDMA
system
Jinyanzi
Luo,
Dr.Benjamin
Belzer
School
of
Electrical
Engineering
and
Computer
Science
Washington
State
University,
Pullman,
WA
99164
Motivation
● Previously proposed TRDMA systems utilized digital sampling,
which is not practical for WiNoCs due to extremely short-
duration on-chip impulse response, so analog TRDMA system is
need to be designed.
● TRDMA offers a power and area efficient method by creating
spatial channels between each Tx/Rx pair in WiNoC.
Time Reversal Division Multiple Access
(TRDMA)
● A wirelessly transmitted signal will take multiple paths to a
receiving antenna, a phenomenon known as the multipath
effect. TRDMA takes advantage of this multipath effect via
channel reciprocity to spatially and temporally focus all of a
signal’s energy on a desired receiver. Utilizing TRDMA for
wireless network-on-chip (WiNoC) application can:
1. Reduce the power needed to transmit information
between processors that are far apart.
2. Enable multiple omni-directional antennas to transmit
information to multiple receivers simultaneously using
spatial multiplexing, while avoiding temporal inter-
symbol interference(ISI).
● An impulse at a receiving node using TRDMA can be achieved
by sending a time-reversed impulse response from a
transmitting antenna. In order to accomplish this:
1. The impulse response from Rx to Tx must first be
obtained by Tx during a recording phase.
2. The impulse response must then be time-reversed and
sent by the Tx during the transmitting phase.
● At WiNoC data rates (ten of Gb/s) it is currently not possible to
digitally record the impulse response, so the impulse response
must be learned via an analog circuit
● On-chip antennas that employ Wireless Network-on-chip
(WiNoc) systems allow wireless communication between cores
across long distances.
Introduction
I
would
like
to
specially
thank
:
● Dr.Benjamin
Belzer,
Joe
Balyon,
and
Jorge
Pires
for
their
help
on
this
project.
● Noel
Wang
and
Kevin
Johnson
for
providing
a
foundaWon
for
this
research.
● WSU
EECS
faculty
and
staff
for
making
this
research
possible.
This
work
was
supported
by
the
NaWonal
Science
FoundaWon’s
REU
program
under
grant
number
CNS
1359461
Acknowledgement
Results
Method
● A commercial circuit simulation software package called Cadence is
used to construct the filter bank.
● The input signal of the bank is the impulse response from a Finite
Difference Time Domain simulation of on-chip wireless transmission.
Conclusion
Future Work
Fourier Series
● Fourier discovered that a periodic function can be represented
by an infinite sum of sine or cosine functions that are
harmonically related.
● Signals can be approximated by Fourier Series via the following
the expression:
● A time-reversed version of the waveform is computed by
inverting the signs in front of the bn coefficients.
● Self-calibration circuit for the coefficient sampling times is
needed.
● Summing all the coefficients to generate the time-reversed
waveform of the incoming impulse.
● These antennas suffer from high power dissipation and timing delays
due to their token-passing wireless access control protocols.
● The Fourier Series (FS) coefficients are needed to recreate or to store
the impulse waveform that is sent from Rx to Tx during the recording
phase.
● To demonstrate the feasibility of analog TRDMA with FS
approximations, a filter bank of high-Q bandpass filters are designed
in order to calculate the FS coefficients
Introduction Cont.
Fig 3. Filter Bank Circuitry: contains integrator, voltage followers/buffer, voltage gains,
switches, capacitors, resistors and bandpass filters.
Fig 2. Two GHz High-Q bandpass filter circuitry, which is derived from inductor-less
Antoniou circuit
Fig 1. Block diagram for computing the first 10 FS coefficients with bandpass filters
Fig 3. a0 waveforms: switch opens at T
= 2𝝅/⍵0, where ⍵0 is fundamental
frequency we set it to 1GHz, so T=1ns
Fig 5. A square wave going through the second filter for finding the second pair
of FS coefficients
Fig 4. Found delays through the filters,
which did not happen in LTSpice
simulation
● Switches in the bank are calibrated to open at correct peak
and zero-crossing time for cosine and sine input waveforms.
● The coefficients became less accurate after the 7th filter, no
solution has found yet to what caused this phenomenon.
● At the high frequencies simulated by Cadence, the delays
through the circuits must be taken into account when
sampling the an and bn coefficients.
Fig 6. Four methods of computing Fourier Series Coefficients are compared with
the ideal coefficients given in mathematical formulas.