Sound Similar iusse to my old phone xperia tx,that is my first time use Sony phone,when I switch to 2g network my xperia tx has no signal,I try flash different brand can't sovle problem.only stay in 3g network then phone signal working well.
I also change sim card.
I suggest call sony service let them send you new one.
Sent from my C6903 using xda app-developers app
htc touch/ htc cruise /htc hd/ hd2/nexus one/hd7
htc incredible s/Htc sensation /htc hd7(again)/ galaxy s2/ galaxy s3
sony tx / xperia ZL / xperia z1/htc m8/xperia z2