  In this paper, we present the error performance analysis of a multiple-input
multiple-output (MIMO) physical-layer network coding (PNC) system with two
different user-antenna selection (AS) schemes in asymmetric channel conditions.
For the first antenna selection scheme (AS1), where the user-antenna is
selected in order to maximize the overall channel gain between the user and the
relay, we give an explicit analytical proof that for binary modulations, the
system achieves full diversity order of $min(N_A , N_B ) \times N_R$ in the
multiple-access (MA) phase, where $N_A$, $N_B$ and $N_R$ denote the number of
antennas at user $A$, user $B$ and relay $R$ respectively. We present a
detailed investigation of the diversity order for the MIMO-PNC system with AS1
in the MA phase for any modulation order. A tight closed-form upper bound on
the average SER is also derived for the special case when $N_R = 1$, which is
valid for any modulation order. We show that in this case the system fails to
achieve transmit diversity in the MA phase, as the system diversity order drops
to $1$ irrespective of the number of transmit antennas at the user nodes.
Additionally, we propose a Euclidean distance (ED) based user-antenna selection
scheme (AS2) which outperforms the first scheme in terms of error performance.
Moreover, by deriving upper and lower bounds on the diversity order for the
MIMO-PNC system with AS2, we show that this system enjoys both transmit and
receive diversity, achieving full diversity order of $\min(N_A, N_B) \times
N_R$ in the MA phase for any modulation order. Monte Carlo simulations are
provided which confirm the correctness of the derived analytical results.
