I am a little confused about the BER. I found that the BER of 16QAM is better than that of 32QAM. is this right, if so, why we go to higher QAM (i.e. 32, 64, and etc).
thank you in advance
If one would target the best BER, you wouldn't even go up to 16QAM and stick at 4QAM / QPSK. You'll have a secure transmission, with the downside of a low spectral efficiency.
16QAM can achieve a spectral efficiency of 4 Bits/s/Hz, where 64QAM has already 6 Bits/s/Hz. This means, you can increase the bitrate by 50% compared to the previous setting. This is especially important if you have limited resources like channels or bandwidth. In Wireless transmission you'll have a bandwidth of a few MHz and there's no parallel channel for other users, so spectral efficiency is the key to increase data throughput. (In fact there's something like an parallel channel, called MIMO, but you get the key)
See the table here for an overview of wireless transmission systems and their spectral efficiency. Spectral Efficiency
Even for more robust transmission systems (in case of BER) you can pick relatively high modulation grades and use the increased number of bits for redundant information. In case of a bit error the receiver is able to repair the original content. This is called Forward Error Correction