# Massive MIMO in 5G: How Beamforming, Codebooks, and Feedback Enable Larger
Arrays

Ryan M. Dreifuerst  Robert W. Heath Jr Ryan M. Dreifuerst and Robert W. Heath
Jr. are with North Carolina State University, Raleigh, NC 27695
<EMAIL_ADDRESS>rwheathjr@ncsu.edu). This material is based upon work
supported in part by the National Science Foundation under Grant No. NSF-
ECCS-2153698, NSF-CCF-2225555, and NSF-CNS-2147955

## Abstract

Massive multiple-input multiple-output (MIMO) is an important technology in
fifth generation (5G) cellular networks and beyond. To help design the
beamforming at the base station, 5G has introduced new support in the form of
flexible feedback and configurable antenna array geometries. In this article,
we present an overview of MIMO throughout the mobile standards, highlight the
new beam-based feedback system in 5G NR, and describe how this feedback system
enables massive MIMO through beam management. Finally, we conclude with
challenges related to massive MIMO in 5G.

## Introduction

Multiple-input-multiple-output (MIMO) is a general class of technologies that
incorporates a number of transmission and reception techniques using multiple
antennas. Spatial multiplexing (SM), among the most well known MIMO methods,
involves the transmission of multiple data streams, called layers in 3GPP
specifications. In a single user (SU-)MIMO setting, spatial multiplexing
involves directing multiple streams to one user, resulting in an increase in
the spectral efficiency proportional to the number of streams. Similarly, the
concept can be applied in a multiple user (MU-)MIMO setting, where the layers
may be split among users.

MIMO usage in mobile standards has played a growing role since the inception
of SM in 3GPP Release 7. MIMO was a backbone of the evolved high speed packet
access (HSPA+) that would enable doubling the achievable data rates with two-
layer MIMO. The subsequent Release $8$ would increase the downlink MIMO
capabilities to $2\times 2$ with two layers each going to two users, although
uplink capabilities were still limited to a single user. Release $8$ would
also introduce other forms of multi-antenna techniques in the form of
transmission modes. These formats include single-antenna, transmit diversity,
open-loop SU-MIMO, closed-loop SU-MIMO, closed-loop rank-$1$ precoding
(beamforming), and MU-MIMO. Releases $9$ and $10$ would introduce larger array
sizes–up to $8$ downlink antennas–and transmission modes $8$ and $9$ which
extend the closed-loop SM to $8$ antennas or transmit diversity if feedback is
unavailable. The introduction of larger arrays also enabled multi-layer
beamforming (BF), which is different from previous SM by using multiple
antennas for each layer. Academically, this is usually referred to as
precoding, but precoding is used in 3GPP notation to describe the multiplexing
of the data streams onto the ports as shown in Figure 1.

Throughout Releases $8-12$, antenna arrays have been assumed to have the same
structure where antennas are built in columns and each column (as well as each
polarization in dual-polarized arrays) is separately controlled for SM in the
azimuth direction. Some basic degree of elevation control was further enabled
with mechanical and electrical tilting of the arrays, though it was not until
later that tilting was dynamically controlled and became standardized. Release
$13$ introduced a study item on full-dimension MIMO (FD-MIMO) that included
controllable elements in both the azimuth and elevation directions for 3D
beamforming. Additionally, the mapping of ports and physical antennas was
separated so that multiple antennas could be controlled from a single channel
state information (CSI) port (e.g. there does not need to be a one-to-one
mapping). This paradigm shift in antenna arrays allowed networks to use
larger, more directive arrays without needing to update the standards or
feedback by “grouping” antennas into subarrays that are transparent to the UE.
With the interest in larger arrays and separation of physical antennas and
logical elements, Release $13$ can be seen as a pivotal point in the evolution
towards massive MIMO (M-MIMO).

TABLE I: 3GPP jargon summary Term | Description
---|---
MIMO | Multiple-input-multiple-output technologies
Layers | Data streams using the same time-frequency resources
TM | Transmission mode; defines a set of supported MIMO techniques like SM, beamforming, etc.
SM | Spatial multiplexing; MIMO method of transmitting multiple data layers
FD-MIMO | A MIMO layout with beamforming in azimuth and elevation direction
Port | A non-unique subset of antenna elements controlled by an RF chain
RSRP | Reference signal received power
Feedback | A general term encompassing the information from the RX based on reference signals
CSI | Channel state information; partial or complete knowledge of the wireless channel
RI | Rank indicator; provides maximum supportable layers as feedback
CQI | Channel quality indicator; encodes the reference signal metric (i.e. RSRP, RSSI)
PMI | Precoder matrix indicator; provides feedback for closed-loop MIMO
SSB | Synchronization Signal Block; for coarse beam training, synchronization, and initial access
CSI-RS | CSI reference signal; a known pilot sequence used for beam training and channel estimation
DMRS | Demodulation reference signal; a known pilot sequence used to aid demodulation
TABLE II: Comparison of flexible configurations in LTE and 5G NR | Subcarrier Spacing | MU-MIMO Support | CSI-RS Ports | MIMO Feature
---|---|---|---|---
LTE (Rel $8$-$9$) |  $15$ kHz | $4\times 2$ | $\\{1,...16\\}$ | TM $1$-$8$
LTE-A (Rel $10$-$12$) |  $15$ kHz | $4\times 2$ | $\\{1,...16\\}$ | Codebook BF
LTE-A Pro (Rel $13$-$14$) |  $15$ kHz | $8\times 2\text{ or }4\times 4$ | $\\{1,...32\\}$ | FD-MIMO
5G FR1 [0-3GHz] (Rel 15-17) |  $\\{15,30\\}$ kHz | $8\times 2\text{ or }4\times 4$ | $\\{1,...32\\}$ |  $4$ beam SSB
5G FR1 [3-6GHz] (Rel 15-17) |  $\\{15,30,60\\}$ kHz | $8\times 2\text{ or }4\times 4$ | $\\{1,...32\\}$ |  $8$ beam SSB
5G FR2 (Rel 15-17) |  $\\{60,120,240\\}$ kHz | $8\times 2\text{ or }4\times 4$ | $\\{1,...32\\}$ |  $64$ beam SSB

Terminology in mobile broadband includes many acronyms and differences from
academic wireless research. To assist readers, Table I outlines important
terms necessary for understanding MIMO and feedback in 3GPP standards. An
important distinction in mobile networks is an additional set of terms to
differentiate the physical antennas from the logical processing chains and
further-up data layers, as shown in Figure 1. The data layers are each
associated with demodulation reference signals (DMRS) for estimating the
effective channel seen by the user equipment (UE). The layers are then
precoded over logical antenna ports, which are each mapped to individual
resource grids and then sent to the physical antennas. Furthermore,
polarization naturally applies to the system by mapping two logical ports onto
orthogonal polarized antennas. The logical ports can apply to a non-exclusive
subset of the physical antennas, so long as the same subset is used
consistently. Each logical port is equipped with its own resource grid and
mapper to take advantage of the flexible delineation between ports and
physical antennas. Further evolution of the flexibility occurs when the
physical antennas are not co-located, which enables multi-panel arrays and
cell-free massive MIMO. The coordination of disaggregated antenna panels was
introduced in LTE-A release $11$ as a centralized radio access network (C-RAN)
although the idea has been brought back up in recent years as distributed MIMO
or cell-free massive MIMO. We provide a simple visualization of these
situations in Figure 2.

Figure 1: The data processing flow from data layers to antenna outputs in a 5G
base station. First the streams (and DMRS) are multiplexed according to the
precoding matrix, which assigns the layers to the ports. Then, the result,
along with CSI-RS, is beamformed to the logical ports. The logical processes
are then mapped onto OFDM resource grids and potentially beamformed again onto
the corresponding physical antennas. 5G uses dual polarized arrays to transmit
multiple layers on orthogonal electromagnetic wave directions. Figure 2:
Visualization of MU-MIMO, massive MIMO, and coordinated multi-point or cell-
free M-MIMO. In cell-free massive MIMO, there is a centralized compute node,
multiple access points, and user equipment (UE). The compute node uses the
distributed access points like logical elements and processes the data across
the network.

One of the cornerstones of 5G is a focus on flexibility. To that end, 5G NR
incorporates a flexible numerology, configurable bandwidth parts, and numerous
feedback formats. This flexibility is especially important for the two
frequency ranges (FR1: $0$-$6$GHz, FR2: $\geq 6$GHz) which correspond to
different subcarrier spacings, bandwidths, and feedback regularity. We
summarize some of the possible configurations in Table II. Of the changes in
5G, the new format beam management based on synchronization signal blocks
(SSB) and channel state information reference signals (CSI-RS) is distinctly
different from the CSI feedback process in LTE. The primary reasons for the
new processes are: 1) Beamforming is enabled at every step including initial
access to improve the SNR during synchronization and channel estimation. 2)
Beam management integrates analog beam training with CSI feedback for new
antenna array configurations like hybrid architectures. 3) The new feedback
format (type-II) provides high resolution CSI feedback to improve MU-MIMO
performance.

In the next section, we will describe the reference signals, which include
known pilot sequences and configuration information, used in the downlink for
5G networks. There are additional reference signals for uplink-based beam
management, but most of the focus will be on the downlink herein. In the
following sections, we will describe the feedback associated with beam
management and address how the integration of beam training improves the
initial access performance and enables new, massive architectures.

## Reference signals

Reference signals (both SSB and CSI-RS) serve important tasks like
synchronization, channel estimation, and handover in 5G networks. Within the
reference signals, there are known pilot sequences with mathematical
properties that aid tasks like synchronization, as well as configuration
information like the base station capabilities and logical geometry. 5G NR
uses synchronization signal (SS) blocks, as a reference signal for
synchronizing user equipment (UE) and obtaining basic feedback during initial
access. SSBs are transmitted periodically by the base station once every
$\\{5,10,20,40,80,160\\}$ ms. The base station transmits a specific primary
and secondary synchronization sequence as well as embedded DMRS. In total, the
SSB waveform spans $240$ subcarriers and $4$ OFDM symbols for each block. The
entire process includes at least one but as many as $\\{4,8,64\\}$ SS Blocks
in an SS-Burst, depending on the frequency range, each of which is transmitted
time-sequentially according to [1, Section 4.1]. Note that both frequency and
time offsets can be set to prevent SSB collisions with nearby stations. By
using multiple SSBs, the base station can beamform each one differently so
that the UE can listen to the entire burst and provide the BS with the best
beamformer index within the measurement report, thereby selecting a potential
beam for downlink transmission or angular direction for requesting additional
feedback.

In contrast to SSB reference signals, CSI-RS can be configured with reference
symbols transmitted across a wider bandwidth and can occur periodically or
aperiodically. CSI-RS also enable feedback for massive hybrid arrays by
training the analog beamforming with precise CSI-RS beamformers without the UE
needing knowledge of the physical antenna geometry. The CSI-RS index defines
the UE-recommended analog beamformer and is always fed back in every feedback
packet. If PMI is configured, the UE must also provide precoding information
using knowledge of the logical port geometry provided by the BS. The drawback
to CSI-RS, especially for large arrays, is an excess of overhead and
potentially out-of-date information. In particular, UEs are not required to
update the CSI-RS index for a CSI-RS resource if the process has been updated
within the last $5$ subframes, or if the number of CSI processes exceeds the
limitations defined in Table 7.2.1 of [1]. This means that channel information
may become stale for large arrays which leads to misaligned beamforming and
suboptimal performance. Furthermore, CSI-RS are expensive to allocate because
only one CSI-RS is utilized over a set of resources to prevent interference.

## Feedback

The base station can configure CSI reports, which are packets containing
feedback, either periodically or aperiodically, with reference signals
multiplexed between the ports. A report generally includes the channel quality
indicator (CQI) and a reference signal indicator (SSBRI/CRI). Additionally, a
rank indicator for multi-stream communication and a precoding matrix indicator
(PMI) can be included in the CSI report. Furthermore, some quantities such as
CQI and PMI can include both wideband (average across the bandwidth) and
subband components to increase the feedback and precoder responsiveness in
frequency selective channels. The CQI provides a measure of the strength of
the channel and is used to determine the modulation order and code rate for
the downlink transmission. The reference signal indicator is used to report
the strongest received reference signal index of the beamformed reference
signals for beam training. The PMI field has different characteristics
depending on the feedback format but it carries the primary CSI information
for the base station.

There are two formats for PMI: predefined (type-I) or constructed (type-II).
In LTE, the PMI format is always predefined, meaning the UE would select the
PMI from an established table of precoder combinations according to a metric,
e.g. maximizing signal-to-interference-noise ratio (SINR). The benefit of
type-I PMI is that it requires low overhead and is computationally simpler for
the UE to calculate. In contrast, type-II PMI is more flexible and precise but
it comes at the cost of higher computational complexity and larger overhead.
Constructed PMI is built up as a sum of $L_{\text{CSI}}$ multipath components,
which are represented by oversampled 2D DFT beamforming vectors, with
quantized amplitude and phase components. An iterative process is used in
combination with a metric like SINR to determine the beamforming vectors and
complex weights, although, the oversample DFT is reduced to an orthogonal
basis after the first multipath component is selected so that the
$L_{\text{CSI}}-1$ beams are only chosen from the remaining orthogonal DFT
vectors. While type-II feedback is able to more accurately quantize the CSI,
it is still limited by the channel estimation accuracy and the number of
multipath components supported in the specification. Release $16$ is currently
restricted to at most $L_{\text{CSI}}=4$ in type-II feedback and
$L_{\text{CSI}}=6$ in type-II enhanced feedback. This is a strict limitation
in rich scattering environments such as macro-cell FR1 deployments, as seen in
Figure 3. Channel estimation, however, can be improved through better
estimators or by increasing the RSRP through beamformed pilot signals.

Figure 3: A comparison from our work [2] of the effective sum spectral
efficiency (SE) achieved in a simulated FR1 deployment using CSI type-II
feedback with $L_{\text{CSI}}$ multi-path feedback quantization. It can be
seen that sub-6GHz environments have very rich scattering that cannot be
captured effectively with the current 5G feedback limitations of
$L_{\text{CSI}}\leq 6$ for large MIMO arrays.

## Beam Management and Massive MIMO

Beam management is designed to unify the reference signals, channel state
information, and feedback into one process [3]. At the heart of the process
are three steps: initial access, beam reporting, and beam refinement. In some
cases, the process is expanded to include beam tracking for mobile UEs or with
separate refinement stages for the base station and UE. Ultimately, beam
management is built around the flexibility of the feedback system in 5G NR.

The initial access period includes the transmission of beamformed SSBs that
provide the UEs with a basic synchronization signal and demodulation reference
signals. This allows for UEs to save power by going inactive and rejoining the
network at a later initial access period. At the physical layer, the UE will
receive the SSBs from a single antenna or using one or more spatial filters,
such as a multi-panel handset used to overcome hand blockage. The UE will use
the received SSB for synchronization and determining the control information.
The beam reporting stage includes one or more possible SSB CSI reports which
are transmitted in the random access channel. The report includes information
for the strongest serving cell and may include a set of the next strongest
cells within the same band to assist with load balancing. The number of
reported additional cells depends on the carrier frequency, the previous state
of the UE in the network, and the bands being monitored. In a newly-active
state, the UE reports the top $6$-$16$ additional cells across each active
frequency range [1]. This reporting helps to manage handover and mitigate
cell-edge interference. In the final steps, the UE has connected to a serving
cell and is ready to start receiving data. Further beam refinement and channel
estimation can occur by transmitting reference signals with more precise
beams. Although not specified in the standard, a typical CSI-RS would cover
smaller portions of the reported SSBs’ directions or combine coherently across
a multipath channel. Using more directional or precise beams can increase the
SNR–thereby improving the channel estimates and beam alignment. Beam
refinement can also be used to adjust the beamforming slightly to track highly
mobile UEs.

One of the key limitations of the beam management framework is the finite
resources available for sweeping, refinement, and tracking. For example, the
SSB sweeping process is limited to $\\{4,8,64\\}$ SSB beams, which are
broadcast to all users, and each beam is restricted to just $240$ subcarriers
and $4$ symbols. This corresponds to $5\%$ or less of the resources available
for downlink data transmission. In contrast, CSI-RS can cover an entire
bandwidth part, typically assigned as user-specific, and up to $32$ ports can
be configured for CSI-RS. The port limitation is an important one because it
defines the maximum dimension that the UE will support for channel estimation
and PMI selection. In order to support larger arrays, Base stations are
deployed with a combination of directly-connected antennas and hybrid arrays
with phase shifters connecting the $32$ CSI-RS ports to a set of antennas. The
analog portion of the hybrid array can be trained with the SSB and CSI-RS
beams, while the PMI can be used to determine the digital precoder. The
integrated beam training and CSI acquisition in 5G enables a new level of
support for arbitrary, massive arrays.

## FR1 and FR2

The key differentiator between FR1 and FR2 i.e. sub-6GHz compared to
mmWave–for a set of antenna arrays of equal aperture–is the propagation
environment, bandwidth available, and reliance on beam-based architectures. At
sub-6 GHz, the propagation environment tends to be more reflective. This
results in multipath propagation that is beneficial for traditional spatial
multiplexing. In FR1, users are not expected to beamform, so beam training is
only necessary on the BS side. Furthermore, because BS arrays have a limited
physical size and therefore a relatively small number of FR1 antennas, the
beam-based system is used in a limited format [4]. For example, the UE may
only employ a single antenna during SSB reception and uplink transmission and
the BS may reduce the number of active SSB beams because precise beamforming
is unnecessary in low-band environments.

In FR2, the full beam-based system is employed with BS beam training,
repetition, and UE beam training all occurring. During the refinement period,
the BS can sweep over a subset of the CSI-RS codebook, and feedback is
gathered via one or more CSI-RS measurement reports. When increasing the
carrier frequency to millimeter-wave bands, the paths tend to have a strong
line of sight component, but very weak reflected components that restrict
multi-layer communication. In fact, MU-MIMO does not appear to be active in
any FR2 developments, and even $4\times 2$ MU-MIMO in FR1 has only recently
been recorded in commercial networks [5]. While FR1 deployments are often able
to support more spatial multiplexing layers, the bandwidth of a mmWave channel
in FR2 is much larger, allowing for as much as four times larger data rates.

## Challenges

There are a series of challenges associated with massive MIMO compared to
traditional architectures. Questions of power consumption, feedback, hardware
cost, computational/algorithmic complexity, and robustness are all exacerbated
with massive arrays. Furthermore, these challenges are also impacted by the
specifications and beam management framework in particular. Here we outline
$3$ challenges specific to M-MIMO arrays in the 5G beam management framework.

First, prior to any deployment, a group of codebooks must be designed. The
design of codebooks is critical due to varying RF environments and user
mobility patterns. In particular, a BS must have codebooks for: 1) initial
access (SSB) coverage, 2) refinement (CSI-RS), and 3) feedback and mobility.
For case 1, the codebook is generally small due to the limited number of SS
blocks defined by $N_{\text{SSB}}$ in Table II, which is never more than $64$.
Furthermore, the SSB process has a short repetition period with a default of
$20$ms. In contrast, the CSI-RS codebook used for refinement is often much
larger to maximize the signal quality and alignment of the beam with a user.
For example, the CSI-RS codebook might contain as many as $4-16$x more beams
than the number of BS RF chains. The BS would make use of these beams at a
slower timescale than the SSB process, typically $80$ms with additional
aperiodic usage as needed. While both of these codebooks can be specific for a
given BS, the third codebook that is used for feedback and mobility must be
known by the entire network. The feedback codebook enables quantizing the
multipath information at the UE side and providing the quantized
representation in the PMI for the BS. In the case of reciprocity (e.g. in
time-division duplexing), the PMI may be reduced or neglected, although the
feedback is often still helpful due to the wireless link being asymmetric [6,
4]. Therefore, the UE and the BS must both use the same codebook for feedback
to correctly share the PMI information. The design of codebooks for SSB and
CSI-RS is an active area of research due to the significant gains that can be
achieved over generic strategies like DFT codebooks [7]. Additionally,
although enhanced type-II feedback codebooks have already been implemented in
3GPP release $16$, MU-MIMO performance is still severely limited and new
codebooks that can efficiently support massive MIMO arrays are needed to
reduce the performance loss.

Once the codebooks are determined, an intelligent process for beam selection
and sweeping is necessary. The process of sweeping and beam selection has
generally received the most focus in beam management tasks [8, 9, 10],
although it is still largely unclear how system performance is impacted by new
sweeping algorithms. In particular, characterizing when the improved alignment
outweighs the cost of additional overhead and interference in realistic,
large-scale settings is still an active area of research. The greatest
reduction of overhead could be seen by minimizing the CSI-RS usage because a
typical CSI-RS codebook can include hundreds or thousands of beamforming
vectors in modern 5G codebooks. At the same time, CSI-RS beam selection is
heavily dependent on the SSB beam selection. Some of the simplest sweeping
algorithms are based on hierarchical or tiered search [9, 11], where all of
the CSI-RS beams within an SSB beam are used for each user. In an M-MIMO array
the angular resolution is very fine, though, so there are many possible CSI-RS
beamformers within an SSB beam and the difference in SNR between the beams
could be significant depending on the environment. Other algorithms have been
proposed based on machine learning, compressive sensing, and channel
statistics [8] and references therein. 3GPP has also introduced a study item
on machine learning with an explicit focus on improving beam management and
feedback through artificial intelligence. These works present new potential
directions, but significant research still remains in evaluating such
algorithms in realistic scenarios.

Finally, a critical issue in beam management is the challenge of mobility
robustness. Even with sufficient feedback at one time instance, the BS needs
to update the information at least as fast as the channel coherence time to
accurately direct the beams. The coherence time, though, depends on the
carrier frequency and mobility [12, section 3.4.3]. Furthermore, with highly
directive beamforming, mobility can result in misaligned beams that reduce
performance or even cause radio link failure [10]. Mobility is especially
challenging for vehicular UEs in FR2 bands, which have mobility patterns and
extremely directive beams that must adjust frequently. While mobility is
challenging for the base station, it is often more difficult for a UE. The UE
needs to update the combining weights to match the beamformed channel
coherence time, which is on the order of milliseconds. To assist with this,
multi-panel arrays [13] have been standardized in Release 16 to reduce link
failure and improve robustness. Multi-panel and geometry-aware research is
expected to become an active area of interest as a result of the recent
standardization. Research efforts have also attempted to improve mobility
management with methods such as multi-modal data [10] and machine learning
[14]. These methods tend to consider single-beam or single-layer data in
mmWave settings, but spatial multiplexing will further challenge mobile
communications due to the precise precoding and combining required to achieve
coherent processing.

## Conclusion

In this article, we have brought together the ideas of feedback and massive
MIMO in light of the recent releases of 5G NR. The first focus has been on the
integration of beam management, reference signals, and feedback that are
enabling MU-MIMO in network deployments. Still, both FR1 and FR2 deployments
have yet to reach the potential for massive MIMO due to challenges like
codebook design and mobility robustness. We expect massive MIMO will be an
active area of research and industrial growth throughout the continued
development of 5G and future wireless generations.

## References

  * [1] 3GPP, “TS 38.213 – Physical layer procedures,” 2021.
  * [2] R. M. Dreifuerst and R. W. Heath, “Initial access codebook design and CSI type-II feedback for sub-6GHz 5G NR,” _in submission to IEEE Trans. Wirel. Commun._ , 2023.
  * [3] M. Giordani _et al._ , “A tutorial on beam management for 3GPP NR at mmWave frequencies,” _IEEE Commun. Surv. Tutorials_ , vol. 21, no. 1, pp. 173–196, Jan. 2019.
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|  Ryan Dreifuerst is a PhD student at North Carolina State University. He
obtained his B.S. in Electrical Engineering from Milwaukee School of
Engineering with minors in Mathematics and Physics. He also received his B.S.
in Electrical and Communications Engineering from Technische Hochschule
Lübeck. He received his M.S. in Electrical Engineering at The University of
Texas at Austin (UT Austin). Ryan has spent the previous summers working with
Meta, Qualcomm, and Samsung Research America on 5G and 6G wireless systems.
His research lies at the intersection of machine learning and signal
processing. Specifically, he has focused on augmenting machine learning with
domain knowledge for physical layer processing and beam-based MIMO algorithms.
---|---
|  Robert W. Heath Jr. is the Lampe Distinguished Professor in the Department
of ECE at North Carolina State University. He is the recipient or co-recipient
of several awards including the 2019 IEEE Kiyo Tomiyasu Award, the 2020 IEEE
Signal Processing Society Donald G. Fink Overview Paper Award, the 2020 North
Carolina State University Innovator of the Year Award, and the 2021 IEEE
Vehicular Technology Society James Evans Avant Garde Award. He authored
"Introduction to Wireless Digital Communication” (Prentice Hall in 2017) and
"Digital Wireless Communication: Physical Layer Exploration Lab Using the NI
USRP” (National Technology and Science Press in 2012). He co-authored
“Millimeter Wave Wireless Communications” (Prentice Hall in 2014) and
"Foundations of MIMO Communications" (Cambridge 2019). He is a licensed
Amateur Radio Operator, a registered Professional Engineer in Texas, a Private
Pilot, a Fellow of the National Academy of Inventors, and a Fellow of the
IEEE.
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