Eliminating Channel Feedback in
Next-Generation Cellular Networks
The MIT Faculty has made this article openly available. Please share
how this access benefits you. Your story matters.
Citation Vasisht, Deepak, et al. "Eliminating Channel Feedback in Next-
Generation Cellular Networks." Proceedings of the 2016 ACM
SIGCOMM Conference, 22-26 August, 2016, Florianopolis, Brazil,
ACM Press, 2016, pp. 398–411.
As Published http://dx.doi.org/10.1145/2934872.2934895
Publisher Association for Computing Machinery
Version Author's final manuscript
Citable link http://hdl.handle.net/1721.1/115348
Terms of Use Creative Commons Attribution-Noncommercial-Share Alike
Detailed Terms http://creativecommons.org/licenses/by-nc-sa/4.0/
Eliminating Channel Feedback in Next-Generation
Cellular Networks
Deepak Vasisht
†
, Swarun Kumar
‡
, Hariharan Rahul
†
, Dina Katabi
†
†
MIT CSAIL,
‡
CMU
deepakv@mit.edu, swarun@cmu.edu, rahul@csail.mit.edu, dk@mit.edu
ABSTRACT
This paper focuses on a simple, yet fundamental question:
“Can a node infer the wireless channels on one frequency
band by observing the channels on a different frequency
band?” This question arises in cellular networks, where the
uplink and the downlink operate on different frequencies.
Addressing this question is critical for the deployment of key
5G solutions such as massive MIMO, multi-user MIMO, and
distributed MIMO, which require channel state information.
We introduce R2-F2, a system that enables LTE base sta-
tions to infer the downlink channels to a client by observing
the uplink channels from that client. By doing so, R2-F2 ex-
tends the concept of reciprocity to LTE cellular networks,
where downlink and uplink transmissions occur on different
frequency bands. It also removes a major hurdle for the de-
ployment of 5G MIMO solutions. We have implemented R2-
F2 in software radios and integrated it within the LTE OFDM
physical layer. Our results show that the channels computed
by R2-F2 deliver accurate MIMO beamforming (to within
0.7 dB of beamforming gains with ground truth channels)
while eliminating channel feedback overhead.
1. INTRODUCTION
The high cost of cellular spectrum has motivated net-
work providers to seek advanced MIMO techniques to im-
prove spectral efficiency [22, 3, 54]. Yet, only point-to-point
MIMO multiplexing can be performed efficiently in current
networks [24]. More advanced MIMO solutions such as mas-
sive MIMO [31], coordinated multi-point [32], distributed
MIMO [39], and multi-user MIMO [5], all require the base
station to know the downlink channels prior to transmission.
In the absence of this information, the base station cannot
beamform its signal to its users. Today, the only way to learn
the downlink channels is to have the user perform the mea-
Permission to make digital or hard copies of all or part of this work for personal
or classroom use is granted without fee provided that copies are not made or
distributed for profit or commercial advantage and that copies bear this notice
and the full citation on the first page. Copyrights for components of this work
owned by others than the author(s) must be honored. Abstracting with credit is
permitted. To copy otherwise, or republish, to post on servers or to redistribute to
lists, requires prior specific permission and/or a fee. Request permissions from
permissions@acm.org.
SIGCOMM ’16, August 22 - 26, 2016, Florianopolis , Brazil
c
2016 Copyright held by the owner/author(s). Publication rights licensed to
ACM. ISBN 978-1-4503-4193-6/16/08. .. $15.00
DOI: http://dx.doi.org/10.1145/2934872.2934895
Channel at Band 1 Channel at Band 2
Paths along which signal is
received
Figure 1: R2-F2’s Approach: R2-F2 extracts the paths of
the signal from channels on band-1 to reconstruct the corre-
sponding channels on band-2.
surements and send the channels back to the basestation.
Measuring the channels on the one thousand LTE subcar-
riers for every antenna on the base station, and feeding those
measurements back to the base station generates much over-
head [9, 54, 52, 44]. This feedback overhead is excessive
even in today’s networks which have a limited number of
antennas on the base station – about 4.6 Mb/s of signaling
per user in a 20 MHz 4×2 network [22, 3]. The problem
escalates in future 5G networks which rely on large MIMO
systems with many antennas (massive MIMO, CoMP, etc.).
In fact, the LTE standardization body that is investigating
high-order MIMO systems with up to 64 antennas (Release
13), has declared this problem as a major challenge for future
LTE networks [24]
1
.
The goal of this paper is to enable cellular base stations to
estimate the downlink channels without any user feedback. A
natural approach that can help us achieve this goal is channel
reciprocity [26]. Reciprocity implies that uplink and down-
link channels are the same,
2
so long as both the base station
and the clients transmit on the same frequency band. Indeed,
reciprocity has been proposed to minimize channel feedback
in WiFi networks [33, 15], where both the access point and
its clients transmit on the same frequency. Unfortunately, the
vast majority of today’s cellular connections (including ev-
ery LTE network in the U.S. [41]) employ Frequency Di-
vision Duplexing (FDD) [21], i.e., they transmit data from
the phone and base station at different dedicated frequency
bands. Thus, extending reciprocity to LTE networks requires
answering the following fundamental question: How do we
infer the wireless channels on one frequency band by observ-
ing those channels on a different band?
1
For example, with 64-antenna base stations, the need to
learn the downlink channels consumes 48% of the traffic
generated by the base station, simply to send per-antenna ref-
erence signals [24].
2
Modulo a constant factor.
0 50 100 150
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Angle (in degrees)
Rel. Power
Power Profile
Figure 2: Power Profile: The power profile represents the
relative power of the signal coming along different spatial
directions.
We introduce R2-F2, a system that does exactly that – i.e.,
it can infer the RF channels on one band by observing them
on a different band. Before we dive into R2-F2, let’s explain
why wireless channels vary across frequency bands in the
first place. RF signals are waves whose phase changes with
time and frequency. The wireless channels are the result of
those waves traversing multiple paths, reflecting off walls
and obstacles, then combining at the receiver. Due to their
frequency-dependent phases, RF waves that combine to re-
inforce each other on one frequency may cancel each other
on another frequency. As a result, wireless channels could
look quite different at different frequencies.
R2-F2 infers wireless channels across frequencies by
leveraging a simple observation: while the channels change
with frequencies, the underlying physical paths traversed by
the signal stay the same. Hence, R2-F2 operates by identify-
ing a transform that allows it to map the observed channels
to the underlying paths, then map them back to the channels
at a different frequency, as shown in Fig. 1.
But how do we identify a frequency-invariant transform
for mapping channels to paths? It is natural to look into
past work on RF-based localization systems since, like us,
they need to relate RF channels to the underlying paths. Lo-
calization systems [53, 27, 4, 29, 28] exploit the MIMO
antennas on a base station to create a power profile that
shows the spatial directions of the incoming signal, as il-
lustrated in Fig. 2. Each peak in the profile is, then, asso-
ciated with the direction of an underlying path. Unfortu-
nately, these localization power profiles are unsuitable for
our purpose. While they reveal information about the direc-
tion of the signal, they lack information about the exact dis-
tance travelled by the signal and whether the path is direct
or reflected off a wall. Such missing parameters introduce
frequency-dependent phase variations in RF waves travelling
along different spatial paths, and hence, change the channel
values. Furthermore, in §4, we show that, due to window-
ing and superposition effects, the power profiles change with
frequency and deviate from the spatial directions of the un-
derlying paths. Our empirical results in §8 demonstrate that
using the localization power profiles for recovering the un-
derlying channels eliminates 60% of MIMO SNR gains.
R2-F2 builds on the insights learned from RF-localization,
but it is the first to enable LTE base stations to infer the
downlink channels without any feedback, and at an accu-
racy suitable for MIMO techniques. In §5, we explain how
we design a channel-to-path transform that incorporates the
information needed to predict channels across frequencies.
We further embed this transform in a full system that over-
comes additional practical challenges, including accounting
for: (1) frequency offset between the user and the base sta-
tion; (2) hardware differences in transmit and receive chains;
and (3) packet detection delay — all of which affect wireless
channels differently at different frequency bands.
We built R2-F2 in USRP radios and integrated it with LTE
OFDM. Our testbed emulates a small cell setting with a 5-
antenna LTE base station. We deploy our base station within
a few meters from one of the LTE base stations on our cam-
pus. Since we cannot transmit in the cellular spectrum, we
operate our testbed on the 640-690 MHz white space fre-
quency band, which is in the vicinity of the Verizon LTE
band (only 30 MHz away). Our results reveal the following:
• For an uplink-downlink frequency separation equal to that
in AT&T and Verizon networks, the channels computed
by R2-F2 deliver accurate MIMO beamforming within
0.7 dB of the beamforming obtained with the ground-
truth channels. The resulting SNR increase has improved
the average data rates in our testbed by 1.7×. This result
shows that R2-F2 can be used by MIMO solutions to de-
liver LTE throughput gain while eliminating channel feed-
back overhead.
• R2-F2 can also be used to eliminate interference at cell
edges and improve spatial reuse. In our testbed, R2-F2 re-
duced the SNR of the interfering signal from 9 dB to only
0.9 dB.
• The quality of R2-F2’s inferred channels remains high
across frequencies separated by up to 40 MHz, which is
larger than the LTE uplink-downlink separation in most
US LTE deployments. Further, the degradation of SNR
with uplink-downlink separation is less than 0.2 dB per
10MHz.
To our knowledge, R2-F2 is the first system that demon-
strates the practicality of inferring LTE downlink channels
from uplink channels using reciprocity and without channel
feedback. This result contributes a better understanding of
reciprocity in FDD systems, and a solution to one of the im-
portant challenges facing future 5G MIMO networks.
2. RELATED WORK
Related work falls under two broad categories.
(a) Channel Estimation in Cellular Networks: Much
prior work has reported the excessive overhead associ-
ated with channel estimation and feedback in cellular net-
works [9, 54, 22, 52, 44]. Even in today’s networks, which
have a relatively small number of antennas, the feedback
overhead can be prohibitive – as much as 4.6 Mb/s of sig-
nalling traffic per user in a 4×2 system [22, 3]. All recent
LTE releases recognize this challenge [3, 2, 1]. To miti-
gate the problem, the standard allows for either sending full
channel information, or compressing the information using
a codebook of limited values. Unfortunately, neither option
is satisfactory since the former causes excessive overhead,
whereas the latter leads to poor channel resolution that im-
pedes the gains of MIMO techniques [34, 14, 25]. As a re-
sult, only point-to-point MIMO is common in today’s LTE
networks (in the US), and more advanced techniques, such
as MU-MIMO have yet to gain deployment traction [13].
This problem is increasingly critical with the advent of 5G
networks which rely on large MIMO systems (e.g., massive
MIMO) to increase spectral efficiency [30, 45].
Past work on addressing this problem has focused on vari-
ous techniques for compressing channel feedback [9, 54, 40,
45]. R2-F2 is motivated by the same desire of learning down-
link channels with minimal overhead, but it aims to eliminate
channel feedback altogether, and replace it with passive in-
ference of channel values.
A few papers study reciprocity in the context of FDD sys-
tems. In particular, Hugl et. al [19] observe that the chan-
nels at two cellular FDD bands are correlated and hence
postulate that one can infer downlink channels from uplink
channels. Some papers [18, 20, 36, 37] propose theoretical
models that use large antenna arrays to infer channels on the
downlink from those on the uplink. Their models are either
based on long-term channel statistics and do not account for
fast variations, or are based on the angle of arrival power
profile (used in RF localization), which we show in §8 to
yield poor performance in practice. Further, they do not ac-
count for practical challenges in system design such as the
limited LTE bandwidth (typically 10MHz), carrier frequency
offset (CFO) and detection delay. In contrast, R2-F2 does not
need long-term statistics and is empirically demonstrated in
a testbed deployment. R2-F2 achieves this through a new de-
sign that relates the channels to frequency-invariant param-
eters (e.g., path lengths), compensates for frequency depen-
dent parameters (e.g., path phases), and accounts for distor-
tion factors (e.g., window effect).
(b) Related Work Outside Cellular Networks: R2-F2 is
related to the problem of channel quality estimation. Some
applications aim to infer channel quality on a particular fre-
quency band, but do not need the exact channel values. For
example, two WiFi nodes may want to select the best quality
WiFi channel for their connection without actively running
measurements on all WiFi channels [10, 42]. The same ap-
plies to cognitive radios in the White Spaces [38]. These sys-
tems observe the channel on one or more bands and use that
information to infer the SNR of the channel on a different
band –i.e., the channel quality. In contrast, R2-F2 needs to
infer the full channel values–i.e., it needs both the phase and
the magnitude of the channel for every OFDM sub-carrier
and every antenna.
R2-F2 is also related to past work that focuses on esti-
mating the channels across a large band of spectrum by sub-
sampling the frequencies in that band. For example, the work
in [6] subsamples the spectrum and uses compressive sens-
ing to recover the channel values at the missed bands. This
approach does not apply to LTE networks since the observed
uplink channels do not satisfy the sampling requirements of
compressive sensing (i.e. the uplink channel is only available
on one contiguous band).
There is also a large body of work that aims to predict
wireless channels in the future based on their values in the
past [51, 8, 12]. This work does not predict channels across
frequency bands. R2-F2 is complementary to this work in
that it estimates wireless channels at different values of fre-
quency as opposed to different points in time.
Finally, we note that R2-F2 is related to a wide range
of systems for the TV whitespaces that aim to predict oc-
cupancy [7, 43] or interference [55] by hopping between a
minimal number of frequency bands. R2-F2 complements
these systems by estimating the wireless channel at any tar-
get frequency band based on sampling the channel at one
other band.
3. BACKGROUND
In this section, we list a few known results in modeling
wireless channels, which are important for the rest of the
exposition. Note that the mathematical expressions refer to
the transmission frequency by the corresponding wavelength
λ.
Wireless channels describe how the signal changes as it
propagates from transmitter to receiver. They are a direct
function of the paths along which the signal propagates as
well as the transmission frequency. In particular, the chan-
nel of a narrowband signal traversing a single path is given
by [47]:
h = ae
−j2π
d
λ
+jφ
(1)
where λ is the wavelength, a is the path attenuation, d is the
distance the path traverses, and φ is a frequency-independent
phase that captures whether the path is direct or reflected.
Since the signal travels along multiple paths, say N, the
channel at a receive antenna can be written as:
h =
N
X
n
a
n
e
−j2π
d
n
λ
+jφ
n
, (2)
which is the sum of the channel components over all paths
that the signal takes between transmitter and receiver.
Finally, we note that base-stations have multiple antennas,
so they obtain one channel per antenna. For a K antenna base
station, the set of channels, h
i
on antenna i is:
h
i
=
N
X
n
a
n
e
−j2π
d
n
λ
+jφ
n
e
−j2π
ilcosθ
n
λ
, (3)
where θ
n
is the angle-of-arrival of the signal along path n, d
n
is the distance travelled by the signal along path n to the first
antenna and l is the pairwise separation between antennas on
the base station. Note that the above equation depends both
on frequency and all underlying signal propagation paths.
4. INTUITION UNDERLYING R2-F2
R2-F2’s primary objective is to infer wireless channels on
a target frequency band, given the wireless channels on a
different frequency band. In order to achieve this objective,
R2-F2 relies on the observation that the channels are the di-
rect result of the signal paths. While the channels change
−1 −0.5 0 0.5 1
0
0.2
0.4
0.6
0.8
1
cos θ
Amplitude
−1 −0.5 0 0.5 1
0
0.2
0.4
0.6
0.8
1
cos θ
Amplitude
−1 −0.5 0 0.5 1
0
0.2
0.4
0.6
0.8
1
cos θ
Amplitude
−1 −0.5 0 0.5 1
0
0.2
0.4
0.6
0.8
1
cos θ
Amplitude
−1 −0.5 0 0.5 1
0
0.2
0.4
0.6
0.8
1
cos θ
Amplitude
𝑎
"
𝑒
$%
&'(
)
*
)
+,
)
𝑎
&
𝑒
$%
&'(
-
*
)
+,
-
−1 −0.5 0 0.5 1
0
0.2
0.4
0.6
0.8
1
cos θ
Amplitude
𝑎
"
𝑒
$%
&'(
)
*
-
+,
)
𝑎
&
𝑒
$%
&'(
-
*
-
+,
-
User
Base'Station
ℎ
"
ℎ
&
(a)
(b’)
(c’)
(d’)
(e’)
(b)
(c)
(d) (e)
𝜃
F
F
Figure 3: Transforming Signal Paths to Channels on Two Frequency Bands: (a) Consider two signal paths emerging
from 80
◦
and 105
◦
as shown. Their corresponding attenuations are: a
1
, a
2
, distances traversed are d
1
, d
2
, and phase offsets
due to reflectors (or lack there-of) φ
1
, φ
2
. (b)-(b’) Depicts the signal components of individual paths across angle-of-arrival.
We observe two spikes at 80
◦
and 105
◦
as expected scaled by the respective path amplitudes. The peaks differ only in phase.
(c)-(c’) Incorporates the windowing effect that causes the peaks to be convolved with sinc functions. The red and blue sinc
correspond to the red and blue path. Further, the width of the sincs changes with frequency. (d)-(d’) Depicts the superposition
of the sinc functions in both frequency bands. The two plots look very different – both due to the difference in shape of the sincs
as well as the difference in their phases. (e)-(e’) Denotes the wireless channels obtained after applying the Fourier Transform
on the two bands – two different sets of values.
across frequencies, the underlying paths stay the same. Thus,
if one could obtain a frequency-invariant representation of
signal paths from wireless channels on any given frequency,
one can recreate an estimate of the channels at any other fre-
quency of interest.
But what is a frequency-independent representation of sig-
nal paths that can be mapped to (and from) wireless chan-
nels? The answer to this question lies in Eqn. 3, which
defines wireless channels based on underlying propagation
paths. Specifically, wireless channels h
i
depend on four dis-
tinct attributes of signal paths: (1) Their attenuation a
n
; (2)
Their frequency-independent phase φ
n
, that distinguishes the
direct path from reflected paths; (3) Their angle of arrival θ
n
;
(4) The distance they traverse d
n
. These four quantities, when
listed for each path, fully define the wireless channels on any
given frequency. More importantly, none of these parameters
depend on the frequency at which the channel is obtained.
In other words set of four-tuples of the form (a
n
, φ
n
, θ
n
, d
n
)
is a natural representation of signal paths that is frequency-
invariant.
Now that we have a representation of signal paths, we
need to understand how to extract it given wireless chan-
nels on any frequency. To do so, observe that wireless chan-
nels in Eqn. 3 take the form of the familiar discrete Fourier
transform (parameterized by spatial angle-of-arrival cos θ).
In particular, this Fourier transform takes as input quantities
that depend directly on our signal path four-tuples. Since the
discrete Fourier transform is invertible, one might wonder if
we can simply apply the inverse Fourier transform to retrieve
the signal paths given wireless channels. Unfortunately, our
task is not this simple. This is because, upon inverting the
Fourier transform, we get quantities that depend not just on
our signal path four-tuples, but also the frequency. As a re-
sult, teasing apart signal four-tuples from wireless channels
requires removing this dependency on frequency.
To understand how to achieve this, it is instructive to study
how the same signal 4-tuples manifest as different wire-
less channels on two different frequencies, say 600MHz and
650MHz. We do so in the context of a specific example. Con-
sider Fig. 3(a) which depicts signals from the phone to the
base station traversing two paths. Let the corresponding sig-
nal path 4-tuples be: (a
1
, φ
1
, θ
1
= 80
o
, d
1
= 19.5m) and
(a
2
, φ
2
, θ
2
= 105
o
, d
2
= 23m). These undergo four distinct
transformations, inclusive of the Fourier transform, before
they become the overall wireless channels on the two fre-
quencies (from Fig. 3(a) to (e)-(e’)) as described below:
• Phase Variation (Fig. 3(a) to (b)-(b’)): We first be-
gin by mapping the signal path 4-tuples to inputs of the
Fourier tranform. Recall from Eqn. 3 that these inputs are
simply the wireless channel components along individual
paths at the two frequencies. Fig. 3(b)-(b’) visualizes the
amplitude and phase of the signal components from the
two paths across angle-of-arrival. As expected, both these
plots have two spikes that correspond to the two paths,
scaled by their respective attenuations. In fact, the two