Sounds like you're trying to re-invent something that already exists to some degree in the marketplace:
http://www.interceptinvestigations.com/CounterSurv...

What you'll need to do is to find one that can detect cellphones that are turned off, which requires a combination active/passive detector.

TTFN

You will probably have troubles with reflections and resultant hot spots. Jails are usually made from materials that will reflect RF. I can't see good DF-ing conditions inside a jail.

Have you considered just jamming the cell phones - I've read that cell phone jammers are more-or-less commercially available (not sure if they're totally legal). Seems like an easier approach.

Cell phones jamming:
  http://cellantenna.com/CJAM/cjam.htm

Not as much 'fun' as tracking them down and catching them in the act, but certainly a ~lot~ less work.

I'd say it's a tricky antenna direction finding problem, although if you're walking along, you could tell which cell it's in easily when you pass by the cell.

Patch antennas won't cover that frequency bandwidth, much too wide. You need something else, bicone or notch type antenna.

Narrow beamwidth, if 50 degrees x 50 degrees is an antenna 12" square, if you want 25x25 degrees, it's 24" square. So do you really need narrow beamwidth? You probably want to hide it under clothing if the answer is yes and you can't make it flat for low cost.

You could make a very low cost system, simple antenna and a low cost wide open detector to find a cell phone, about $20 in parts if you plan to walk by the cells to detect it.

Jamming is a good idea, and very simple. Europeans use cell jammers but they're illegal in the US.

If you just need a simple antenna, I made one that covers that range, wide beamwidth though. A simple notch antenna, piece of metal with a slot in it, and a cable across the slot, size is 4"x6"x 0.03" in size, weighs about 5 ounces.

kch

While I cannot give you the name of the product, I have seen a handheld detector designed to detect cellphones switched on in a passengar aircraft.  It detects the emissions from a phone that is switched on, measures the field strength and estimates range.  It is effective over 20-30 ft or so.  DF-ing in a confined space will prove very unreliable due to reflections.

I think that DF-ing inside a building comes always with reflections. The antenna will be used when the the policemen are on their control-walks along the corridors (I suppose most times during the night). The problem with normal antennas with wide beamwidth was that the policemen were not able to investigate whether the cellphone was activated in the cell behind this or that door or one floor up or below this level.
The frequency range should take care of the next inventions on the cellphone market like UMTS.
Jamming is impossible. This jail is inside a big (well known) city, not ouside in the countryside.
Just by the way, I suppose that reflections might be not so very much misleading. The door of each cell is made from wood! So each cell is like a big cavity.

Another way to make a narrower beamwidth antenna is to enclose your antenna in foam microwave absorber. Having the antenna embedded in an absorber piece (with a hollowed out center area so that gain is not reduced too far) would reduce back and sidelobes to help the antenna be more directional. I did this for 6-18 ghz notch antennas and the antenna patterns became perfectly smooth, and it reduced the back and sidelobes(@90 degrees off boresight). If you have money to purchase antennas, there are 1-2.5 ghz ridged waveguide gain standard horn antennas from AEL (now BAE), their H-5001 has gain from 11-17 dBi over the frequency band. It's fairly large and heavy, aperture is 12 x 16 inch aperture and about 20 inches long, weighs about 15 lbs, but that shows you what size is common for your frequency range in higher gain antennas.

kch