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I'm new to OFDM modulation. During OFDM modulation in the frequency domain, are the negative frequencies modulated with a conjugate version of the data of the positive frequencies, or do the negative and positive frequencies carry completely different data?

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There are independent sub-carriers in both the positive and negative frequencies. In other words, yes, they have completely different data.

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Both mapping techniques have practical significance:

  • For bandpass channels every subcarrier can be modulated with an individual complex value. The resulting time-domain signal (after inverse discrete Fourier transform (IDFT)) is generally complex-valued.
  • For lowpass channels one often uses the complex-conjugate symmetry you describe in your question. It yields a real-valued time-domain signal (after IDFT). These systems are often referred to as discrete multitone (DMT). For more details see this recent question about Hermitian symmetry.
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For multi carrier OFDM systems, each subcarrier frequency is modulated with different data. As an example with 48 subcarriers, wherein each subcarrier is modulated using BPSK, results in 48 data bits. QPSK (2 bits per symbol) corresponds to 96 data bits and again 48 subcarriers. Conversely, for single carrier OFDM systems only one frequency subcarrier is used and only that subcarrier is modulated with data.

Those modulated bits are sent or received over one OFDM symbol time (different definition of the word symbol as compared with BPSK/QPSK symbol).

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