  We explore the degrees of freedom (DoF) of three classes of finite state
compound wireless networks in this paper. First, we study the multiple-input
single-output (MISO) finite state compound broadcast channel (BC) with
arbitrary number of users and antennas at the transmitter. In prior work,
Weingarten et. al. have found inner and outer bounds on the DoF with 2 users.
The bounds have a different character. While the inner bound collapses to unity
as the number of states increases, the outer bound does not diminish with the
increasing number of states beyond a threshold value. It has been conjectured
that the outer bound is loose and the inner bound represents the actual DoF. In
the complex setting (all signals, noise, and channel coefficients are complex
variables) we solve a few cases to find that the outer bound -and not the inner
bound- of Weingarten et. al. is tight. For the real setting (all signals, noise
and channel coefficients are real variables) we completely characterize the
DoF, once again proving that the outer bound of Weingarten et. al. is tight. We
also extend the results to arbitrary number of users. Second, we characterize
the DoF of finite state scalar (single antenna nodes) compound X networks with
arbitrary number of users in the real setting. Third, we characterize the DoF
of finite state scalar compound interference networks with arbitrary number of
users in both the real and complex setting. The key finding is that scalar
interference networks and (real) X networks do not lose any DoF due to channel
uncertainty at the transmitter in the finite state compound setting. The finite
state compound MISO BC does lose DoF relative to the perfect CSIT scenario.
However, what is lost is only the DoF benefit of joint processing at transmit
antennas, without which the MISO BC reduces to an X network.
