Multiple-Antenna Placement Delivery Array for Cache-Aided MISO Systems

We consider the cache-aided multiple-input single-output (MISO) broadcast channel, which consists of a server with
$L$
antennas and
$K$
single-antenna users, where the server contains
$N$
files of equal length and each user is equipped with a local cache of size
$M$
files. Each user requests an arbitrary file from library. The objective is to design a coded caching scheme based on uncoded placement and one-shot linear delivery, to achieve the maximum sum Degree-of-Freedom (sum-DoF) with low subpacketization. It was shown in the literature that under the constraint of uncoded placement and one-shot linear delivery, the maximum sum-DoF is
$\min \left\{{L+\frac {KM}{N},K}\right\}$
. However, previously proposed schemes for this setting incurred either an exponential subpacketization order in
$K$
, or required specific conditions in the system parameters
$L$
,
$K$
,
$M$
and
$N$
. In this paper, we propose a new combinatorial structure called multiple-antenna placement delivery array (MAPDA). Based on MAPDA and Latin square, the first proposed scheme achieves the maximum sum-DoF
$\min \left\{{L+\frac {KM}{N},K}\right\}$
with the subpacketization of
$K$
when
$\frac {KM}{N}+L=K$
. Subsequently, for the general case we propose a transformation approach to construct an MAPDA from any
$g$
-regular PDA (a class of placement delivery arrays for the shared link caching problem where each integer in the array occurs
$g$
times). When
$g$
-regular PDA corresponds to the Maddah-Ali and Niesen scheme, the resulting MAPDA yields the maximum sum-DoF
$\min \left\{{L+\frac {KM}{N},K}\right\}$
with reduced subpacketization compared to the existing schemes. The general scheme can be extended to the multiple independent single-antenna transmitters (servers) corresponding to the cache-aided interference channel proposed by Naderializadeh et al. and the scenario of transmitters equipped with multiple antennas.