Are there any other explanations for the cosmic background radiation?

Not any that make much sense, or that don't raise more questions than they solve.

The three big problems posed by the 'CBR' is that

1) it is to very high accuracy a prefect black body;

2) it is astonishingly smooth everywhere in the sky once the 'dipole' from the local motion of the Earth-Sun-Milky Way is removed, and

3) it has its peak in the microwave part of the electromagnetic spectrum.

Some time ago, the proponents of the 'Steady State' theory, and cosmologists trying to create a plausible non-Big Bang origin for this radiation, considered that the distant, early universe was populated by a dense haze of dust grains. Starlight from distant galaxies would scatter off of these dust grains and have their energy 'thermalized' to produce a 2.7 K spectrum. This had nothing to do with a primordial fireball of radiation, because you could plausibly postulate these dust grains to be present in any universe that was sufficiently old to have produced enough interstellar dust during normal stellar evolution. The main problem with this idea was that it could not reproduce the extreme uniformity of the CBR on all the different angular scales that it had been detected and measured. Dust grains produced by stellar evolution, would have to follow a distribution in space that was similar to the galaxies we see, and these are not uniformly spread out in space at all scales. There are local clusters, super clusters and other kinds of structures at least to scales as large as 300 million parsecs ( over 1 billion light years).

This theory is still considered physically interesting, and it has not gone away completely. The NICMOS infrared camera used on the Hubble Space Telescope has begun the search for infant galaxies, and it seems that even by 1 billion years after the big bang, there is plenty of infrared emission. This means that there must be dust grains forming within the first few 100 million years after the big bang. Some astronomers speculate that the first billion years in the life of the universe was spent with intense episodes of star forming, and galaxy-building activity occurring under the cloak of dark, dusty clouds. Observations by NASA's WMAP satellite in 2002, and the Next Generation Space Telescope to be launched in 2011, will take us a long way towards understanding the role of dust in the early universe, and whether it could account for some of the cosmic background we see. Although it will not likely help us to understand the 'microwave' CBR, it will probably account for most of the infrared and far-infrared cosmic background radiation which was produced long after the microwave CBR, and is not related to the big bang fireball itself.