I am using GSM MODEM provided by sim300 and i have no clue regarding the antenna specifications of the antenna used in this modem.
In the pdf file it is just mentioned that the module has 50db antenna connector.I do not know anything about this antenna connector and in what way it is related to the GSM modem antenna.?
It means that you have to connect an antenna (or antenna with cable) to the modem that is designed for a 50 Ohms impedance. In other words, you rmodem likes to see a more ore less 50 Ohms load to be happy. 50 Ohms is almost the standard reference impedance in RF telecom and measurement. By the way, video and cable distribution uses 75 Ohms.
The documentation should tell you what type of connector (socket) is used, as you need this to get the right plug to make the connection. there may also be solder pads close to the socket that can be used for direct cable connection (that means you have to solder).
To give you useful feedback: can you give us info w.r.t. external or internal antenna, plastic/metal case, size of case, available space for antenna, other (metallic) structures very close to the modem, external antenna via certain length of cable, etc.
If you have metallic case, an external quarter wave antenne can do the job when the ground of the antenna is directly connected to the case.
Antenna of the modem is connected via a brown colour wire which is ended in a connector of MMCX then for this connector,antenna is connected and is enclosed in samll black colour conical shaped plastic casing so what type of antenna is this?