Page 125 - ITU Journal Future and evolving technologies – Volume 2 (2021), Issue 2

ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 2

and ℂ represent the real and complex number sets, re‑ the channel matrix for inter‑node interference (i.e ., be‑

spectively, {⋅} is the expectation operator, and | ⋅ | de‑ tween nodes and ) , and n ∈ ℂ ×1 represents the

notes the amplitude of a complex number. Additive White Gaussian Noise (AWGN) vector at node
2
with covariance matrix I .

2. SYSTEM AND SIGNAL MODELS Upon signal reception at the FD MIMO node , analog SI
cancellation is irst applied to the signals received at its
We consider a wireless communication system compris‑ RX antenna elements before these signals enter the RX

ing of an FD MIMO node that wishes to communicate

concurrently with a multi‑antenna node in the down‑ RF chains, as shown in Fig. 1. Notice that the output of
the analog canceler is added to the received signals be‑

link and a multi‑antenna node in the uplink, as shown
fore their input to the RX RF chains. We utilize the nota‑

in Fig. 1. We focus on investigating ef icient FD operation

tion C ∈ ℂ × to represent the signal processing re‑
at a single node, as such, we henceforth assume without
alized by the analog canceler. Depending on the deployed
loss of generality that nodes and operate in half du‑
plex mode. hardware components, the analog canceler can have as in‑

puts analog or digital signals. In Section 3, we will detail
Suppose that the FD MIMO node in Fig. 1 is equipped
the hardware characteristics of our two analog canceler

with TX antenna elements and RX antenna ele‑

ments. Each antenna element is attached to a dedicated architectures. We will also show that for both architec‑
tures, the baseband representation for the output signal
TX RF chain, and similarly holds for the RX antenna ele‑
of the analog canceler at the FD node , which we label
ments and their respective RF chains. A TX RF chain con‑ ×1
̃

sists of a Digital to Analog Converter (DAC), a mixer which as y ∈ ℂ , is given by:

upconverts the signal from the baseband to the RF, and a ̃ y ≜ C V s . (2)

Power Ampli ier (PA). An RX RF chain consists of a Low
Noise Ampli ier (LNA), a mixer which downconverts the By assuming that the digitally converted and downsam‑
signal from the RF to the baseband, and an Analog to Dig‑ pled output signals of the RX RF chains at node are lin‑
ital Converter (ADC). At the TX side, upsample and pulse early processed in the baseband by the combining matrix

shape processing are used to prepare the baseband signal U ∈ ℂ × , the estimated symbol vector s ∈ ℂ ×1
̂

for DAC sampling and RF transmission. At the RX side, a for s is derived as:

corresponding matched ilter and downsampling is per‑
̂ s ≜ U (y + y + ̃ y + n ) , (3)
formed. The half duplex multi‑antenna nodes and are
assumed to have and antennas, respectively, with where the complex‑valued ‑element vectors y and y

each antenna connected to a respective RF chain. are the baseband representations of the received signal of

For presentation clarity purposes, we assume narrow‑ interest and received SI signal, respectively, at node . In

band lat fading channels for our signal model. The ex‑ ×1

addition, n ∈ ℂ denotes the received AWGN vector

tensions for wideband frequency selective channels is the 2
at node with covariance matrix I . The vector y in

focus of ongoing works (e.g., [23]). All nodes are con‑

(3) is given by:

sidered capable of performing digital BF; for simplicity,
V s ,
y ≜ H , (4)

we assume hereinafter that digital TX and RX BF at the

focused FD MIMO node is realized with linear ilters. where H , ∈ ℂ × is the uplink channel matrix

In particular, we assume that node makes use of the (i.e ., between nodes and ) , while y is obtained as:

precoding matrix V ∈ ℂ × for processing its unit y ≜ H V s , (5)

power symbol vector s ∈ ℂ ×1 (chosen from a dis‑ ,

crete modulation set) before transmission. The dimen‑ with H ∈ ℂ × denoting the SI channel seen at the

,

sion of s satis ies ≤ min{ , }, which complies RX antennas of node due to its own downlink transmis‑

with the available spatial DoF for the downlink × sion.

MIMO channel. Similarly, node processes its unit For cases where the residual SI signal in (3) (i.e., after

power symbol vector s ∈ ℂ ×1 (chosen again from a performing analog cancellation and TX/RX digital BF) is
discrete modulation set) with a precoding matrix V ∈ above the noise loor, further digital SI mitigation [24, 25]

ℂ × , where ≤ min{ , }. Both the down‑ can be applied on the signal ̂ s to bring the residual in‑

link and uplink transmissions are power‑limited accord‑ terference below that loor. In this paper, we focus on

2 2

ing to {‖V s ‖ } ≤ P and {‖V s ‖ } ≤ P , respec‑ analyzing the combined effect of analog cancellation and

tively. Following the above de initions, the baseband re‑ TX/RX digital BF, hence, we do not model a digital SI can‑
ceived signal y ∈ ℂ ×1 at the half duplex node can be cellation stage.

mathematically expressed as:
3. ANALOG CANCELER ARCHITECTURES
V s + n ,
y ≜ H , , (1)
V s + H

In this section, we present in detail the hardware compo‑
where H , ∈ ℂ × is the downlink channel matrix nents of our two analog SI canceler architectures intro‑
(i.e., between nodes and ), H , ∈ ℂ × denotes duced in [17, 18, 19]. The irst architecture is based on
© International Telecommunication Union, 2021 111