# Can someone explain or elaborate on the channel estimation and noise variance estimation algorithms used in HF receiver?

For different type of communication, there is different type of algorithms to acquire CSI. For instance 4G (LTE) network have SRS or DMRS to estimate the channel based on pilots.

I am designing a similar algorithm based on probes (or pilots) in order to have the time based channel estimate of groundwave HF channels (this is for my equalization block). The Doppler spread measuring the rapidity of channel time variations seldom exceeds 1 Hz on HF channels.

Let $$y(t) = h(t) \ast s(t) + n(t)$$, where $$s(t)$$, the pilots symbols, have an autocorrelation given by $$R_s (t) = \delta (t)$$.

The pilot (or training) symbols are chosen so that the intercorrelation between $$s(t)$$ and $$y(t)$$ is given by: $$R_{y,s} = R_s (t) \ast h(t) \approx \delta (t) \ast h(t)$$ if one neglects the noise,

I have 15 kHz of bandwidth and I need 300 estimates. The sampling frequency is $$F_e = 30\,\text{kHz}$$. That's one channel coefficient every 100 Hz. One estimate takes at least 300/(30 kHz) = 0.01 s.

The channel coherency time (channel span) is about 0.5s up to 1.5s (mean value) .

For a 1800 Bd symbol rate and a maximum time spread of 5 ms, N = 22 coefficients are needed to (almost) fully represent the channel.

I will make simulation for noise and propagation conditions, with SNR varying between 5 and 15 dB.

• As in your last question, the way you estimate the channel depends on what kind of temporal and frequency resolution and precision you need. So, what are your needs. – Marcus Müller Mar 16 at 9:30
• Have you addressed all points in the comment to your question? what is the channel estimation technique used for HF communication? – Marcus Müller Mar 16 at 9:31
• the channel estimation if for the DFE equalization block, in term of precision I have let"s say 30 KhZ and I need 300 estimates – Abby_DSP Mar 16 at 10:00
• That's one channel coefficient every 100 Hz (meaning your channel coherency bandwidth should be larger than 100 Hz), and means that one estimate takes at least 300/(30 kHz) = 0.01 s. What is the maximum propagation loss for which you still want to be able to estimate the channel? What's your TX power, and your RX noise figure? (PS: Could you add that to your question?) – Marcus Müller Mar 16 at 10:06
• (also, I removed the unrelated tags) – Marcus Müller Mar 16 at 10:12