  [Abridged] Sub-mm observations of the William Herschel Deep Field using
LABOCA revealed possible counterparts for 2 X-ray absorbed QSOs. The aim here
is to exploit EVLA imaging at 8.4 GHz to establish the QSOs as radio/sub-mm
sources. The challenge in reducing the EVLA data was the presence of a strong
4C source in the field. A new calibration algorithm was applied to the data to
subtract it. The resulting thermal noise limited radio map covers the 16'x16'
Extended WHDF. It contains 41 sources above a 4-sigma limit, 17 of which have
primary beam corrected flux. The radio observations show that the absorbed AGN
with LABOCA detections are coincident with radio sources, confirming the
tendency for X-ray absorbed AGN to be sub-mm bright. These sources show strong
ultraviolet excess (UVX) suggesting the nuclear sightline is gas- but not
dust-absorbed. Of the 3 remaining LABOCA sources within the ~5' half-power beam
width, 1 is identified with a faint nuclear X-ray/radio source in a nearby
galaxy, 1 with a faint radio source and 1 is unidentified in any other band.
  More generally, differential radio source counts are in good agreement with
previous observations, showing at S<50 micro-Jy a significant excess over a
pure AGN model. In the full area, of 10 sources fainter than this limit, 6 have
optical counterparts of which 3 are UVX (i.e. likely QSOs) including the 2
absorbed quasar LABOCA sources. The other faint radio counterparts are not UVX
but are only slightly less blue and likely to be star-forming/merging galaxies,
predominantly at lower luminosities and redshifts. The 4 faint, optically
unidentified radio sources may be either dust obscured QSOs or galaxies. These
high-z obscured AGN and lower-z star-forming populations are thus the main
candidates to explain the observed excess in faint source counts and hence the
excess radio background found previously by the ARCADE2 experiment.
