IEEE Circuits and Systems Magazine - Q2 2019 - 39

In FH architecture, the digital precoder B FH has dimension M FH # U. The analog precoder matrix R FH has
dimension N FH # M FH and its m th column rFH,m represents the phase shifting from N FH phase shifters connected to the m th RF-chain, i.e.,
R HF = 6rHF, 1 rHF, 2 g rHF,MFH@.

(3)

each element in R FH has unit magnitude.
We make the following assumptions. Firstly, the channel
information H u is known to both transmitter and receivers. A practical way of channel estimation can be found
in [18]. Secondly, each UE receiver is equipped with a
phased array with only one RF-chain. As a consequence,
BS assigns one data stream to each UE receiver. Thirdly,
all receivers have the same pre-beamforming SNR and
BS assigns equal power among data streams. Fourthly,
the combining vector of each receiver w u is chosen as
the primary left eigenvector of channel matrix H u after
magnitude normalization in each element.
The SINR at the u th receiver array is denoted as
SINR u =

gu
v 2n, rx

+

2

v n2 , tx

(4)

+ v 2int

where the sig na l power ga in g u is g iven by g u =
2
arg min g E y u - gs u . All signal, noise, and interference
powers are relative powers, referenced to 46 dBm transmit power based on Table II. As a consequence, receiver
2
thermal noise power E w Hu z r = v 2n, rx is treated as constant in each use case. The multiuser interference is
2
v 2int = E y u - g u s u .
In the remaining of the sections, we discuss how to
design array parameters for each architecture to reach
targeted SINR for three use cases.
B. Array Size and Transmit Power Gain
In principle, increased transmit power P (out) and array size
N both improve signal power gain g u in (4). Effectively,
they provide higher equivalent isometric radiation
power (EIRP) and help achieve target SINR from Table II.
In DA and FH, output power of each PA P (out) /N is split
into U parts due to multiplexing and even power allocation. Thus each stream in each PA has output power
P (out) / (NU ). The coherent summation of N-elements via
beamforming provides N2 times increased power. In SA,
however, PAs are partitioned into groups to amplify different streams. For each stream, each PA element out(out)
puts P SA /N SA, while the beamforming gain is N 2SA /U 2 .
As a consequence, maximum output signal power after
beamforming in each architectures is
(out)

G DA =

(out)

(out)

P
N SA
P DA N DA
P
N FH
, G SA = SA 2 , G FH = FH
.
U
U
U

secoND QuArter 2019

(5)

It is clear that SA is in an disadvantage in terms of signal power gain. SA requires to use more array elements,
output power, or both for the comparable output power
to DA and FH architectures.
C. Precoder Design
Given maximum signal output power G, the the precoder
determines the actual signal power g u and multiuser
interference v 2int in (4). In this subsection, we discuss
precoding techniques for three architectures.
In DA architecture, maximum ratio transmission
(MRT) and zero-forcing (ZF) are two commonly used
linear precoding approaches. The former maximizes
the signal strength at destination and approaches maximum gain discussed in Section II-A, while the latter
eliminates multiuser interference. It is commonly believed that because mmW signals suffer from severe
propagation loss, the interference is generally less
troublesome than sub-6 GHz systems. However, the interference from transmitted sidelobes, if not properly
handled, can still affect the achievable rate at receivers.
In this work, we propose to use regularized zero-forcing
beamforming [53], where the introduced regularization coefficient a DA facilitates controlling both signal
strength and interference at the receiver.
B DA = l DA G HDA (G DA G HDA + a DA I ) -1,

(6)

In the above equation, G DA is the post-combining multiuser channel with the u th row as {G DA} u = w Hu H u . The
regularization coefficient a DA controls the behavior of
the precoder, i.e., MRT when it approaches positive infinity and ZF when it approaches zero. One can expect
SINR maximization when a DA is selected to be the largest with constraint that v 2int % v 2n, rx . Power scaling parameter l DA is used to guarantee total transmit power
2
(out)
constraint B SA = P DA .
Precoding approaches with SA and FH architectures
are currently actively investigated by researchers and
are mostly for systems where analog beamformer has
phase-only tuning capability. The optimal hybrid precoding is a mixed integer programming problem and
its optimal solution must be solved via potentially exhaustive search. Many sub-optimal methods have been
proposed for near optimal performance, e.g., works in
[54] for FH architecture. In [54], the analog precoder is
selected to point beams towards directions of intended
receivers. The digital precoder is then used to handle
associated interference among beams synthesized by
phase shifters. In the following paragraphs regarding
precoding algorithm for SA and FH, we adopt assumption of phase-only analog precoder.
ieee circuits AND sYstems mAGAziNe

39



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