Sub-millimetre source identifications and the micro-Jansky source population at 8.4 GHz in the William Herschel Deep Field

[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.