My question may be very basic but I always get confused over this. What is the difference between bit-metrics and LLR. For example, in the attached paper, the author says that bit-metrics are computed as in Eq-5. Is that bit-metric the same as LLR. For example, for a BPSK scheme, the LLR will be:
(Received Sample) / (noise variance)^2
How do I relate bit-metrics as said in the paper and the LLR as said in the weblink.
My final aim : The paper says that in order to perform diversity combining, I can actually add the bit metrics from the antenna branches. So I was wondering if I can add the LLRs !
Thanks in advance
Bit metrics are just some quantification of a characteristic of a bit, usually something reflective of the bit SNR or some quality or reliability metric of some kind. Often that winds up being calculated as an LLR, but not always. So an LLR is just one way to compute a bit metric and is often used because it is fits well into the FEC decoder algorithms being used.
If your FEC decoder or other downstream processing doesn't use or doesn't need LLRs, then you may want to do whatever works best for your particular task. For diversity combining there are a number of different approaches that may also depend on your combining algorithm. e.g., for Chase combining just add the symbols together, for maximum ratio combining compute the SNRs, scale the symbols appropriately, and then add them together. Neither require LLRs, but sometimes it is suitable, if the LLRs are already computed, to just add them together. I wouldn't assume it's the best way to do it unless you're sure it's right for your system and is an efficient approach.
As usual, it depends on what you're trying to accomplish. The bottom line, though, is LLR is just one way to compute a bit metric, but it is a very common method because many FEC decoders expect LLRs for soft-decision input.
Thanks, the idea is more clear to me than before. I know the topic is very old, but can you share any reference (if you remember) about "LLR is just one way to compute a bit metric". I did digging on internet but I think I am getting lost in the mathematical details.