# Meaning: channel unknown and known at the transmiiter

What does "channel unknown" and "known at the transmitter" mean?

In books about signal processing, it has always mentioned it if capacity or transmission (estimation) is discussed. I can't understand the difference.

If I simulate the transmission, the channel is given to me (the channel is known at the Transmitter). I can model it using the standard function in Matlab or as a random function. In estimation algorithms, like ZF, it is also used as a channel ( inverse of channel matrix) for an estimate. What is the difference? How can channel be unknown?

edit 1.

It is unclear what difference is between CSI unknown and known. If I simulate transmission system, I need a channel. If H is given as a matrix or via rayleigh-function, it means CSI is known, isn't'? The Capacity is computed using a channel matrix (in its equation). I cant understand then why there are two difference equation: CSI known and unknown to the transmitter.

• I'm not quite sure what to explain here. Your channel is random. You can either have knowledge of the channel, or you don't. That's it. – Marcus Müller Feb 4 at 10:00
• what is ZF? Can you please expand it – jomegaA Feb 4 at 10:06
• In general, the answer in @MarcusMüller's comment is what people imply in talking about known/unknown channel. If it is still not clear, you can quote several paragraphs that show your point and we will discuss them. – AlexTP Feb 4 at 10:38
• @jomegaA I'd bet it's "Zero Forcing" – Marcus Müller Feb 4 at 10:39
• @jomegaA ZF is zero-forcing – Jang Lee Feb 8 at 8:58

You need to distinguish between transmitter (TX) and receiver (RX) here. For the receiver it is generally quite easy to gain knowledge of the channel: have the transmitter send a few known symbols, then the receiver can estimate the channel coefficients (e.g., via Least Squares or MMSE). The receiver needs this channel estimate for equalization. For example, the ZF receive strategy you mentioned essentially means you divide out the channel coefficient, i.e., if you receive $$y = h \cdot s + w$$ where $$h$$ is the channel, $$s$$ your unkown information symbol and $$w$$ the noise, the simplest you can do to estimate $$s$$ is divide out $$h$$ (use $$y/h$$ as an estimate), for which you need to know it.

The question you asked about is knowing the channel at the transmitter. This is much harder since in general, the receiver would need to send its estimated channel coefficient back to the transmitter to know it. This requires extra communication resources. And time, which is a problem since the channel information might be outdated by the time it reaches the transmitter, if your channel is time-varying. Another option is to assume the channel between TX and RX are "symmetric", in communication parlance referred to as reciprocity. Then, the TX can estimate its own received channel for data it got from the RX and assume that the same channel coefficient applies for the reverse link. For this to work, in general we need to assume that TX and RX work on the same frequency (e.g., when they use time division duplexing).

The real question here is what would it help the TX to know the channel? Does that improve capacity? As I'm sure you read it does help in the MIMO case as this allows the TX to send data in the "proper directions", i.e., excite the strong eigenmodes of the channel and thus get more power across. There are other cases where it helps, e.g., when dealing with multiple users, interference, and other things.

• I have just read an implementation in Matlab: the channel is defined as Matlab function rayleigh, data as a random vector. It was written in a description " the channel state information is given", what does it mean? Does it mean the channel $H$ is given ( defined as rayleigh channel via Matlab function), isn't? if yes, then what it means if "channel state information is not given"? – Jang Lee Feb 8 at 8:58
• Yeah I guess given and not given refers to the channel matrix $H$. – Florian Feb 9 at 20:46

For simulation "known at the transmitter" could mean how you model the channel. A simple AWGN or some other distribution to simulate multiple interference...

But it is unknown what it could incur on the transmission.