Hello everybody!
Do I understand correctly following items?
Is the channel frequency selective?
To consider the channel as frequency flat the bandwidth of the signal should not exceed coherence bandwidth of the channel. In other words, symbol rate (baud rate) Rs should be desirably selected according to the coherence bandwidth Bc (and hence according to the root mean square (r.m.s.) delay spread ) related restrictions [1].
E.g. Rs of the considered modem lies between 0.5 and 2 MBd (S-band) and this fact also relates to the measured coherence bandwidth Bc = 0.5 – 2 MHz [2].
Is the channel time variant?
To consider the channel as time-flat the symbol (frame) period should not exceed the coherence time of the channel. Coherence time can be estimated by the maximum Doppler shift (according to Jakes model) as Tc = 1/ fD,max. Possible doppler shifts can be estimated by well-known formula.
Symbol duration Ts should be at least 10 times smaller than the Tc to avoid time selectivity [1].
E.g. for the LEO satellite channels (orbit altitudes: 200-2000 km) symbol duration will be approximately 1.6 microseconds and therefore Rs,min = 625 kHz (since Rs = 1/Ts in case of linear modulation schemes).
Does that mean that the channel is flat in a range from 625 kHz to 2 MHz?
References:
[1] Goldsmith A. Wireless communications. – Cambridge university press, 2005. – p. 88-92
[2] Kanatas A. G., Panagopoulos A. D. (ed.). Radio Wave Propagation and Channel Modeling for Earth–Space Systems. – CRC Press, 2016. - p. 107
As you know in a channel, amplitude fluctuations are not the only effect. Wireless channel can be frequency selective (i.e. not flat) and time-varying. To understand this you have to consider the channel effect as a filter, see the added figure for a simple explanation.
A frequency selective channel is generally defined by its coherence bandwidth compared to the modulation bandwidth of the signal in space (SIS). If the coherence bandwidth is larger than the SIS modulation bandwidth, then the channel is referred to as flat fading, and the effects of frequency selectivity are generally negligible on link performance.
But time invariance is not so simple to define. Basically, for the channel to be considered time invariant it must by slow fading compared to all time scales of the waveform and receiver, e.g., the modulation period, the frame time, the interleaver span if applicable, and the tracking loop settling times (~1/BL, the loop-noise bandwidth of the tracking filter). When this is the case then the the channel effects are ergodic -- the time averaged performance over the channel fluctuations approaches the ensemble averaged performance (i.e., @averaged over the first-order statistics of the channel fluctuations). So the discussion above on time invariance is incomplete and misleading.
Dear Vladimir,
I will not repeat what did you wrote. You just want to verify you answer.
Yes your channel will be frequency flat and time invariant so long your symbols smaller than Bc and your symbol time smaller equal the coherence time. You have to estimate your channel every coherent time to equalize it.
Best wishes
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