1. Plug this antenna into a spectrum analyzer and get an idea of the dBm it receives under the environment field you're in.
2. Since youve got the antenna area you can use the formula Area_effective = eff*Area_physical = Directivity*(lambda^2/4pi) to get an idea of the received power. If you have an estimate of the power RF density on your environment [W/m2] you multiply it by the area_effective and get the received power.
3. You can model you antenna inside CST Microwave Studio and terminate your antenna with 50 Ohms. Illuminate it by a plane wave and monitor the current/voltage developed at the antenna load.
Since youve got a router 1 meter away by Friis you get a first order estimate of the power density on your antenna.
Roughly speaking you need an antenna with larger area. Maybe a Patch array, or a broadband antenna which is able to collect signals from other rf bands (mobile phone).
I had done a project near to your idea, the single element antenna cannot charge the battery. but you can enhance the received power to charge the phone by 2 ways;
1. Make array of antennas and connect them in parallel (then the internal resistance will be smaller which will effect the power and increased it).
OR
2. Design a single antenna, then connect it to a voltage multiplier, try to enhance your design to get output voltage =4 V and that is possibly can be. the limitation here that the output current value will be very small, this will make the charging process of phone very slow.
1.Is a 4*4 array sufficient to charge a 1500 mah??
2.If we use a voltage multiplier ,with the low ouput current value is it practically feasible to charge the phone battery considering the losses from the recteanna circuit involved.
Make a target to get 4-5 V from your antenna, try first to design the antenna and connect it to a simple voltage multiplier, the function of voltage multiplier is to convert the AC signal which captured from the antenna into output DC voltage and increase the value of output voltage by increasing its stages. after get the output try to enhance it by make array of antenna or increase the stages of the rectifier.
You can follow these articles and design the same but change the value of the frequency to 2.45 Ghz because I am working on 900 MHz frequency