Yes, of course it's possible. Just keep in mind that antennas are not magic. A perfectly isotropic (spherical reception pattern) cannot possibly be better than 0dBi. Any antenna with more than unity gain is doing so by having less-than-unity gain in certain directions while having greater-than-unity gain in others. You know, the gain pattern.
I like to think of antennas as something analogous to the reflector cup in a flashlight - it's not actually increasing the amount of light a flashlight's bulb is putting out, it's simply concentrating it in a cone. Antenna's are similar.
So, can you create an antenna that has ~3dBi gain for cellular frequencies? Most definitely. You could create a a PCB antenna that has in excess of 11dBi gain (by making a yagi style antenna using pcb traces) if you wanted. The pcb would be huge, and the directionality would require you have it pointed directly at the cellular tower, but it would work, sure.
As for something practical, a simple dipole/whip style antenna, but on a pcb, is easily done and should get you 2dBi easily, though at the cost of a toroidal radiation pattern. This radiation pattern is well suited to cellular network use, however, as long as the orientation is fairly constant. This is the same radiation pattern as most wifi routers and receivers have.
A 1/2 wave dipole (just google pcb dipole to get an idea of the fairly abundant geometries one can use on a pcb to implement a dipole) ought to give you 2dBi-2.1dBi gain easily. At 1800MHz, a typical GSM frequency, this would require (at the most efficient receiving geometry but also least efficient in size) about 8.3cm of inline copper trace length. In other words, your pcb would need to be, at its longest, slightly longer than 8.3cm.
The easiest way to get 3dBi gain would simply be a 2-element collinear array. These are simply two 1/2 wave dipoles in the same plane. This would require a pcb roughly 17cm long unfortunately. However, you would get double the gain vs a single dipole, which equates to about 3dBi.
So yes, it is not only possible, but fairly trivial depending on how large you're willing to go. I am sure there are more efficient geometries with similarly acceptable radiation patterns, any of which could be implemented in the form of a PCB. And at 1800MHz, dielectric loss from FR4 is small enough that it can simply be ignored on these scales.
In theory, you could simply scale up any of the readily available 2.4GHz 3dBi pcb antenna geometries to the wavelength of 1800MHz (or whatever) and get similar results.
The shape very much affects how the size will play.
For the simple case of a dipole antenna, the best performance (in terms of power transfer) will be obtained with half the wavelength of the signal to be transmitted or received. You also get local minima in the impedance for values of \$k \lambda + \frac{\lambda}{2}\$, and increasing lambda will mean more directionality on the main lobe(s) but also more side lobes. Shortly put, it can be worse and typically \$\frac{\lambda}{2}\$ is the best.
If you have a more directional antenna like the yagi, the size will be primarily influenced by the main folded dipole , and the reflectors and directors will be sized accordingly. But a larger antenna may mean more directors (usually the reflector is one) and therefore, again, more directivity.
For other antennas like the parabolic reflector, size can improve gain/directionality but the benefits will get progressively lower.
Best Answer
Real antenna gain is nearly always referred to the theoretical isotropic antenna. The isotropic antenna emits power in all directions equally therefore it projects power onto the surface of a sphere where the antenna is at the centre of the sphere.
At distance r (radius of sphere), the power from an isotropic antenna is passing thru a spherical area of \$4 \pi r^2\$ square metres.
Normal antennas (such as dipoles) do not transmit this power in all directions therefore they are said to have a gain in certain directions compared to the isotropic antenna and, indeed there is more power per sq metre at a comparable distance, but this is beginning to become "directional". Therefore the higher the directionality of an antenna, the more power it concentrates in one direction (reciprocal for receiving antennas too) and the higher the gain.
What is the likely incident power received and what is the minimum power needed by the receiver. A good figure for required power by the receiver is based on the signal data rate: -
Received power is -154dBm + 10\$log_{10}\$(data rate) - from this you can calculate the headroom, add maybe 20 dB for fade margin (could be lower if you accept a longer delay and you are moving).
I have no idea.