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Degrees of Freedom of Interference Channels with CoMP Transmission and Reception

We study the Degrees of Freedom (DoF) of the K-user interference channel with coordinated multi-point (CoMP) transmission and reception. Each message is jointly transmitted by M_t successive transmitters, and is jointly received by M_r successive receivers. We refer to this channel as the CoMP channel with a transmit cooperation order of M_t and receive cooperation order of M_r. Since the channel has a total of K transmit antennas and K receive antennas, the maximum possible DoF is equal to K. We show that the CoMP channel has K DoF if and only if M_t + M_r is greater than or equal to K+1. For the general case, we derive an outer bound that states that the DoF is bounded above by the ceiling of (K+M_t+M_r-2)/2. For the special case with only CoMP transmission, i.e, M_r = 1, we propose a scheme that can achieve (K+M_t-1)/2 DoF for all K < 10, and conjecture that the result holds true for all K . The achievability proofs are based on the notion of algebraic independence from algebraic geometry.