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Capacity and Error Probability of a Wireless Channel


Error Probability (Pe) and Capacity

System Error Probability (Pe) Capacity (C)
MIMO Pe ∝ SNR-nt.nr C = min(nt, nr)W log(1 + SNR)
SIMO Pe ∝ SNR-nr C = W log(1 + SNR)
AWGN Pe ∝ e-SNR C = W log(1 + SNR)
Fading Pe ∝ SNR-1 C = W log(1 + SNR)

 

For Doppler spread:

  • Tcoh ∝ vmax-1 (slow fading coherence time > signaling interval)
  • Wcoh ∝ taumax-1 (slow fading coherence time > signaling interval)
  • Frequency-flat fading: coherence BW > signaling bandwidth

where, Tcoh and Wcoh are coherence time,  and coherence bandwidth respectively

vmax-1 , and taumax-1 are maximum frequency delay spread,  and maximum time delay spread respectively

 

OFDM effectively overcomes Inter-Symbol Interference (ISI) issues in fading channels. 

Orthogonal Frequency Division Multiplexing (OFDM)

  • OFDM overcomes ISI by converting frequency-selective channels into multiple (M) frequency-flat subchannels.
  • Multiplexes M information symbols \( X(k) \), where \( k = 0, 1, ..., M-1 \), onto M subcarriers.

OFDM System Diagram


The OFDM system utilizes an Inverse Fast Fourier Transform (IFFT) at the transmitter to create the time-domain signal, and a Fast Fourier Transform (FFT) at the receiver to recover the frequency-domain symbols after the ISI channel.



OFDM Transmitted Signal


x(n) = (1 / sqrt(M)) * sum(k=0 to M-1) X(k) * e^(j * 2 * pi * k * n / M)
 

Further Reading

  1.  OFDM (Theory)

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