  Conventional beamforming with fixed-position antenna (FPA) arrays has a
fundamental trade-off between maximizing the signal power (array gain) over a
desired direction and simultaneously minimizing the interference power over
undesired directions. To overcome this limitation, this letter investigates the
movable antenna (MA) array enhanced beamforming by exploiting the new degree of
freedom (DoF) via antenna position optimization, in addition to the design of
antenna weights. We show that by jointly optimizing the antenna positions
vector (APV) and antenna weights vector (AWV) of a linear MA array, the full
array gain can be achieved over the desired direction while null steering can
be realized over all undesired directions, under certain numbers of MAs and
null-steering directions. The optimal solutions for AWV and APV are derived in
closed form, which reveal that the optimal AWV for MA arrays requires only the
signal phase adjustment with a fixed amplitude. Numerical results validate our
analytical solutions for MA array beamforming and show their superior
performance to the conventional beamforming techniques with FPA arrays.
