original:
Explain the principle of OFDM to the "Xiaobai" icon
Time domain angle:
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It is too difficult for a system to implement OFDM in the time domain, and delay and frequency offset will seriously destroy the orthogonality of subcarriers, thereby affecting system performance.
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A communication system is roughly divided into a transmitter and a receiver
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The IFFT corresponding to the transmitter and the FFT corresponding to the receiver mean that the transmitter and receiver are processed in the frequency domain and the air is transmitted in the time domain.
Frequency domain angle:
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The spacing frequencies are orthogonal to each other, so although the F1 and F2 spectrums overlap, they still do not interfere with each other
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OFDM orthogonal sub-carriers, the carrier frequency spacing is Nyquist bandwidth, ensuring maximum frequency band utilization
In this way, the signals outside the bandwidth can be effectively limited, and under the condition of ensuring that the signal of this channel does not have cross-symbol interference, not only can the bandwidth be used to the maximum extent, but also the mutual interference of the signals between the subcarriers can be reduced
Band utilization is the ratio of symbol rate 1 / T and bandwidth B (or W).
Implementing OFDM with IFFT
To understand IFFT to achieve OFDM, the best way is to look at the formula.
f (t) = a1 · sin (2π · Δf · t) +
a2 · sin (2π · Δf · 2t) +
a3 · sin (2π · Δf · 3t) +
...
ak · sin (2π · Δf · kt ) +
b1 · cos (2π · Δf · t) +
b2 · cos (2π · Δf · 2t) +
b3 · cos (2π · Δf · 3t) +
...
bk · cos (2π · Δf · kt) +
= ∑ak · sin (2π · Δf · kt) + ∑bk · cos (2π · Δf · kt) [Formula 1-1: Expression of real numbers]
In order to facilitate mathematical processing, the above formula has the complex expression form as follows:
f (t) = ∑Fk · e (j · 2π · Δf · kt) [Formula 1-2: Expression of complex numbers]
The IFFT here needs to discretize the time domain, so the formula IFFT ≈
IDFT- > fn = 1 / N · ∑Fk · e (j · 2π · k · n / N) [Equation 3-1, n is the discrete time After the serial number, N is the total number of IFFT, n ∈ [1, N]】
OFDM system diagram in the time domain:
Implement OFDM with IFFT:
Signals about the physical layer
To understand the meaning of the signal, the entire physical layer signal transmission process can be decomposed. It can be seen that the signal processing is different in different steps.
Source coding focuses on compressing the capacity of the signal to improve transmission efficiency (bit stream);
channel coding inserts redundant information for variable channels to increase the stability of transmission (bit stream);
signal modulation converts the bit stream into In order to transmit a specific waveform, depending on the modulation method, either one bit corresponds to one waveform, or several bits correspond to one waveform (high-order modulation). So there is a problem that I do n’t know what waveform 0 corresponds to and what waveform 1 corresponds to, because I did n’t understand the modulation process.