Nowadays there are a lot of various places in the country where cell phones do not work, even with amplifiers. You could not be able to do anything about this except purchase quite expensive satellite phone. A lot of other areas have marginal coverage. There could be a signal in the air, however your mobile phone is able to opt for it due to different reasons.
Modern cell phones have quite low power output (a third of one watt if not less) as well as quite puny little antenna that decreases that one third of a watt to less. However with a proper sized external antenna you are able to enhance mobile phone signal many times.
Apart from this, to that antenna a cell phone repeater that boosts your cell phone puny wattage up to the maximum wattage that is allowed by the FCC (3 watts) could be easily added.Previously, the majority of cell phones were made with a small antenna jack on the back side of the mobile phone, under the rubber plug that could be easily connected to a rooftop magnetic mount antenna. However the modern problem is that a lot of new high tech mobile phones do not have these external antenna ports.In such case your only option is to use a stick in passive adapter which conducts the signal from the internal antenna of your cell phone into the wire leading to the external antenna.These are quite lossy and do not conduct much of the cell phone signal into the outside antenna. The other alternative is to use a wireless repeater type of the cell phone booster.