Ideally, we expect to see only two tones at 2.451GHz and 2.449GHz
as shown on the left side of Fig. 1. However in the transmitted sig-
nal, whose spectrum is plotted on the right side of Fig. 1, we can
easily see that there are several other distortions present in addition
to the two main tones that were transmitted. These distortions can be
classified into two major categories:
1. Linear Components: This corresponds to the two main tones them-
selves which are attenuated and could consist of reflections from the
environment. These are linear components because the received dis-
tortion can be written as a linear combination of different delayed
copies of the original two tones.
2. Non-Linear Components: These components are created because
radio circuits can take in an input signal x and create outputs that
contain non-linear cubic and higher order terms such as x
3
, x
5
.
These higher order signal terms have significant frequency content
at frequencies close to the transmitted frequencies, which directly
correspond to all the other harmonics we see on the right side of
Fig. 1. Harmonics, as the name suggests, are signal distortions
which occur at equally spaced frequency intervals from the trans-
mitted frequencies. As the right side of Fig. 1 shows, we see spikes
at frequencies 2.447GHz and 2.453GHz, that are spaced 2MHz
apart from the two transmitted tones 2.451GHz and 2.449GHz, on
either side.
3. Transmitter Noise: The general increase we see in the base signal
level which we can clearly see on the sides of the two main tones is
noise from the radio transmitter. A radio will of course always have
noise, which works out to a noise power level of -90dBm [15]). But
as we can see, the power at the side-bands is significantly higher, on
the level of −50dBm, or 40dB higher than the thermal noise floor.
This extra noise is being generated from high power components in
the radio transmitter such as power amplifiers. In the radio literature
this is referred to as broadband noise [12]. Further radios have phase
noise generated by local oscillator (LO), which is typically of level
of −40dBm, or 50dB above (not seen in the Fig. 1).
2.1 Requirements for Full Duplex Designs
The above analysis suggests that any in-band full duplex system
has to be able to cancel all the above distortions in addition to the
main signal component itself, since all of these are within the fre-
quency band we are transmitting and receiving on and act as strong
self-interference to the received signal itself. In this section, we dis-
cuss how strong each of these components are for typical transceivers,
and what are the requirements for full duplex. We will state all self-
interference power levels relative to the receiver noise floor. The
reason is that to implement full duplex, we need to cancel any self-
interference enough so that its power is reduced to the same level as
the receiver noise floor. There is no point in canceling beyond that
since we won’t see any benefits — the received signal’s SNR will
then be dictated anyway by the receiver noise floor which cannot be
canceled or reduced, just as it is today in half duplex radios.
We use similar experiments for OFDM-wideband signals to quan-
tify the power levels of the different distortions, shown in the left
side of Fig. 2. In a typical WiFi radio using 80MHz bandwidth,
the receiver has a noise floor of −90dBm (1 picowatt). First, since
the main signal component is being transmitted at 20dBm (100mW),
self-interference from the linear main component is 20 − (−90) =
110dB above the receiver noise floor. Second, we observed exper-
imentally that the non-linear harmonics are at −10dBm, or 80dB
above the receiver noise floor. Finally, the transmitter noise is at
−40dBm, or 50dB above the receiver noise floor. Note that these
numbers are consistent with other RF measurement studies reported
in the literature [21] for standard WiFi radios.
There are four takeaways from the above analysis:
• Any full duplex system needs to provide 110dB of linear self-
interference cancellation to reduce self-interference to the receiver
noise floor. This will ensure that the strongest component (the main
signal) which is 110dB above the noise floor will be eliminated.
• A full duplex system has to reduce non-linear harmonic components
that are 80dB above the noise floor, so any full duplex technique has
to provide at least 80dB of non-linear self-interference cancella-
tion.
• Transmitter noise is by definition noise and is random. In other
words, we cannot infer it by any algorithm. Hence the only way to
cancel transmitter noise is to get a copy of it where it is generated,
i.e. in the analog domain and cancel it there. This implies any
full duplex system has to have an analog cancellation component
that provides at least 50dB of analog noise cancellation so that
transmitter noise is reduced to below the receiver noise floor.
• A final constraint is that RX chains in radios get saturated if the
input signal is beyond a particular level that is determined by their
ADC resolution. Assuming a 12 bit ADC resolution typically found
in commodity WiFi radios, we have a theoretical 72dB of dynamic
range, which implies that the strongest signal level that can be input
to the radio relative to the receiver noise floor is −90dBm+72 =
−18dBm. However, in practice it is necessary to leave 2 bits worth
of margin, i.e a 12 bit ADC should be used as if it is a 10 bit ADC to
reduce quantization noise. So the maximum input signal level can
be −90dBm+60 = −30dBm. Since in WiFi, the transmitted self-
interference can be as high as 20dBm, a full duplex system needs
to have an analog cancellation stage that provides 60dB of self-
interference reduction (we keep a further 10dB margin for OFDM
PAPR where instantaneously an OFDM signal’s power level can
rise 10dB above the average power).
To sum up, any full duplex design needs to provide 110dB of linear
cancellation, 80dB of non-linear cancellation, and 60dB of analog
cancellation.
Transmitted Signal
60 dB of
Analog
Cancellation
Receiver
80 dB
Harmonics
50 dB
Transmitter
noise
110 dB
Main
Signal
50 dB of
Digital
Cancellation
20
-90
-40
-10
Power in dBm
-90 dBm Receiver Noise floor
10 dB PAPR
Receiver
Saturation
-30
Figure 2: On the left hand side we see transmitted signal with sub-
components. On the right hand side we see how this impacts the requirements
of analog and digital cancellation.
2.2 Do Prior Full Duplex Techniques Satisfy these
Requirements?
There are two state-of-the-art designs: ones which use an extra
transmit chain to generate a cancellation signal in analog [6] and
ones which tap the transmitted signal in analog for cancellation [11,
3]; both use a combination of analog and digital cancellation. Note
that all these designs use at least two antennas for transmit and re-
ceive instead of the normal single antenna, and the antenna geometry
ones use more than two.
Designs which use an extra transmitter chain report an overall to-
tal of 80dB of self-interference cancellation (we have been able to
reproduce their results experimentally). Of this, around 50dB is ob-
tained in the analog domain by antenna separation and isolation be-
tween the TX and RX antennas of around 40cm (the designs also