In many books and papers, they used to use the complex form of the channel effect response. However, in reality, the signal is real values and also the channel.
Is it correct to use the following approximation? (in MATLAB)
% Rayleigh channel fading
eta = 4; %Path loss exponent
d = 200; %Distance from BS to the user
h_var = sqrt(d^-eta); % channel effect variance, mean is zero
h = h_var*randn(1,length(tx))/sqrt(2);
The question whether a QAM signal should be considered as a real or a complex signal is a little bit confusing. If you are talking about the RF signal (i.e. RF wave) transmitting in the real world, yes, it is real. However, if you are talking about and working on the baseband QAM signal, it is complex. I guess you are doing simulation in baseband. If this is true, then you should consider both the QAM signal and the channel complex.
From your MATLAB code, it seems that you assume both I and Q components of the QAM signal experience an equal Gaussian attenuation independent from time to time. These seem incorrect to my understanding. (1) In Rayleigh fading channel, I and Q of the QAM should experience Rayleigh attenuations with random phase rotation as well. (2) The attenuations from time to time shouldn't be independent, which depends on how fast the channel changes.
Good luck.
Shouxing Qu Thanks for replying. I am actually concerned about the actual signal transmitted (RF wave) because I want to develop both the transmitter and receiver. Is there any way to simulate that real channel response?
Even you want to develop both the transmitter and receiver in your simulation, still you only need to do your simulation in baseband to include all effects of the channel. Actually, as I know, none one is doing such simulation in RF band, because all channel effects can represented in baseband simulation, while simulation in RF band is much expensive but provides none extra value.
Let's have a quick review of some concept. In general an RF signal (also referred to as bandpass signal) is:
P(t)=I(t)*cos(w*t)+Q(t)*sin(w*t),
where w is the angular frequency of the RF carrier, I(t) and Q(t) are the in-phase and quadrature-phase components of P(t) which is a real signal. For convenience, usually a complex signal S(t) = I(t)+j*Q(t) is defined and referred to as the baseband signal of P(t). Correspondingly, the bandpass (RF) signal can be expressed as:
P(t) = Real{S(t)*exp(j*w*t)},
where Real{x} stands for the real component of x.
With these notations, when the system (including the transmitter + channel + receiver) is studied, we only need to investigate the baseband signal S(t) and its changes (due to the channel).
In short, what you can do is as follows.
(1) Generate a sequence of baseband QAM symbols (denoted by S(t)).
(2) Generate a sequence of complex Rayleigh fading coefficients, such as
h(t) = a(t)+j*b(t), where a(t) and b(t) are independent Gaussian random processes with proper power spectral density depending on how fast the channel changes.
(3) The received baseband signal is r(t) = s(t)*h(t)+n(t), where n(t) is the optional noise. Your receiver then further works on this baseband signal r(t).
If you really want to see the waveform of the received RF signal, simple take the real component of {r(t)*exp(j*w*t)}.
Hope these helpful to you. Good luck.
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