  In recent release of the new cellular standard known as 5G New Radio (5G-NR),
the physical downlink control channel (PDCCH) has adopted polar codes for error
protection. Similar to 4G-LTE, each active user equipment (UE) must blindly
detect its own PDCCH in the downlink search space. This work investigates new
ways to improve the accuracy of PDCCH blind detection in 5G-NR. We develop a
novel design of joint detection and decoding receiver for 5G multiple-input
multiple-output (MIMO) transceivers. We aim to achieve robustness against
practical obstacles including channel state information (CSI) errors, noise,
co-channel interferences, and pilot contamination. To optimize the overall
receiver performance in PDCCH blind detection, we incorporate the polar code
information during the signal detection stage by relaxing and transforming the
Galois field code constraints into the complex signal field. Specifically, we
develop a novel joint linear programming (LP) formulation that takes into
consideration the transformed polar code constraints. Our proposed joint LP
formulation can also be integrated with polar decoders to deliver superior
receiver performance at low cost. We further introduce a metric that can be
used to eliminate most of wrong PDCCH candidates to improve the computational
efficiency of PDCCH blind detection for 5G-NR.
