In the past, I have advocated both Direct Representation, a form of proportional representation, and the institutional protection of federalism by having state governments at least partially elect the national government, as was the case in the U.S. before the 17th Amendment. How these two institutional features might fit together is not immediately obvious, but the solution is relatively simple:

At the state level, each population elects it’s representatives (parties) in the normal Directly Representative way. At the national level, Direct Representation elections are also held normally except the votes are cast by all the individual state parties using the votes they have been delegated instead of by voters in each of the states. In this way, both the state and national legislatures remain Directly Representative, and the national legislature remains representative of the state governments.