One of the solution is that we can change the Baud Rate by giving AT command,
AT+CIOBAUD= Required Baud Rate
We can change the baud rate to 9600 by just writing AT+CIOBAUD=9600. And our problem is solved. But what I found is that, in my module this command was not at all working. I don't know the reason but it may be because of older firmware may not have this command defined in it.
So first go for this step. If Your Baud Rate get changed, than no need to read this blog further. The response after entering this command will be something like this.
But If you face the similar problem which I have faced i.e. The command is not at all working on your module, than you need to go for firmware upgrading of your wifi module.
Firmware upgrading is not at all difficult. Just 2-3 steps and 2-3 minutes and you are done with it. First of all you need to download these necessary files before proceeding further.
After that, Open esp8266_flasher in that folder. And than select the bin file i.e. the firmware version you want to update, and also provide the COM port. It will be same port on which your Arduino is connected. Than click the download button.
It will take a minute while flashing your module. And after it complete its work, than you are ready to play with this module at 9600 Baud rate using Software Serial. And the good news is that, in this firmware, you can change the baud rate by the command AT+CIOBAUD to you required baud rate.
You can definitely watch my video in which I'm flashing my own module. I have made it in two Languages,
Files for upgrading ESP8266 firmware click here.