Channel Impulse Response (CIR) in Wireless Communication

 

Channel Impulse Response in wireless communication is a crucial parameter to give answers to a lot of queries. Typically, the wireless channel is considered a linear time-invariant system (LTI) because we receive the same signal as transmitted with attenuated amplitude and slightly different in phase. And multi-path is a common phenomenon in this case.

For a typical wireless communication system,

Received signal, y = h*x + n 

where, x is the transmitted signal and n is the AWGN noise.

Due to multi-paths channel impulse response looks like this

h = [0.8288022873178911    1.0400938302264099    0.9424830276250771    0.3019643679270881    -0.5947514354335648    -1.3007824537001517    -1.2534870210140514    -0.7381779467768559    0.07381938414922966    0.7797542454500325    1.0632467316101784    0.8469514322363529    0.30203449329894005    -0.26719874911268726    -0.5999808394073104    -0.6134160146789202    -0.39101760064376856    -0.07265278504693483    0.21168715002474983    0.34729791990462994    0.26862030429356454    0.024895985835635216    -0.20771798984043073    -0.2758366088353594    -0.07955007818175588    0.2630873783534531    0.5205905558337094    0.48726646804136836    0.1271472047123772    -0.39135049354818147    -0.7905138999971242    -0.8380580696257237    -0.4695577591044186    0.17037988097232765    0.7795852936028065    1.0417316758598383    0.8073627272543262    0.1933759418574037    -0.4791294212121494    -0.871894772283266    -0.8199299553736871    -0.4049774898633317    0.11931538388685506    0.4818158838540853    0.5320365528639177    0.30126070038538827    -0.03248531608367147    -0.2569258928772116    -0.2504567844235932    -0.04353309043268273
]

You know, we can do many things using channel impulse responses. For example, you can tell whether the channel is noisy or not just by seeing the plot of the channel impulse response. For a more noisy channel, the more zigzag plot of the channel impulse response.

You can compare transmission techniques for the same environment by analyzing the channel impulse response. Beamforming, channel combining, etc., are all techniques that use channel impulse responses. For example, in the Maximum Ratio Combining technique, we combine the channels where we give more weightage to the stronger signal and less weightage to the weak signals.

 

 

Fig: Channel Impulse Response of the above-mentioned channel 'h'

 

 

In general, we find channel impulse response by channel estimation. In wireless communication, you can find channel impulse response by comparing received known signals like pilot signals.

 

 

Fig: This is an example of an ideal channel impulse response. For robust LOS communication between the transmitter and receiver is represented by a single impulse

 

So, it is clear from the above discussion why we find channel impulse responses like 'h'. For typical wireless communication, the transmitted signal reaches up to the receiver through different multi-paths but they are copies of the same transmitted signal.

Also Read about

 [1] MATLAB Code for Generating Channel Impulse Response

[2] Fundamentals of Channel Impulse Response (CIR)