CDMA, OFDM

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CDMA, OFDM
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CDMA

• Code Division Multiplexing

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CDMA

• Used in 3G networks.
• Direct Sequence Spread Spectrum spread a data
  bit into multiple chips.
• Each sender has a unique chip sequence, that is
  orthogonal with other chip sequences.

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Simple Examples of CMDA

• A (-1 -1 -1 1 1 -1 1 1 )
• B (-1 -1 1 -1 1 1 1 -1 )
• C (-1 1 -1 1 1 1 -1 -1 )
• D (-1 1 -1 -1 -1 -1 1 -1 )

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Orthogonal Frequency-Division Multiplexing

• From the highest level, OFDM divides the
  communication bandwidth into a number of
  sub-channels, each occupying a fraction of the
  bandwidth.
• Each sub-carrier is modulated by BPSK, QPSK, or
  other schemes.
• Used in 802.11a and 802.11g.

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OFDM

• Why OFDM?
• More resilient to multi-path fading.
• Fast Fourier Transform (FFT) algorithm makes the
  computation efficient.

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OFDM

• How OFDM is implemented (following Tse
  Viswanath book Ch. 3.4.4).
• Assume the received sample is
• hl is the channel coefficient at tap l. This is
  caused by multi-path as we discussed earlier, a
  weak path will have a different delay compared to
  the main path. When we are taking sample at time
  m, the response excited by other data symbols
  will not be 0 at this point. As a result, the
  sample voltage contains some fraction from data
  symbols other than the symbol at time m.

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OFDM

• In this explanation, it is assumed that hl0 for
  l lt0 and lgtL.
• Basically, we need to assume that the channel
  coefficients are not all nonzero, which it quite
  reasonable the delay spread is usually bounded,
  and the impulse response is fast approaching 0
  after several symbol time.

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OFDM

• Suppose we need to send Nc data symbols denoted
  as d0 to dNc-1.
• With OFDM, we not only send these data symbols,
  but also append a prefix of length L to it at the
  beginning. That is, we send
• dNc-L1 , dNc-L2 ,, dNc-1 ,d0,
  d1,., dNc-1.
• With these data symbols as input, the output at
  time m for LltmltNcL-1 is
• Cyclic convolution. ym is the cyclic
  convolution of h and d.

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OFDM

• Given two series h and d, both are non-zero only
  within 0,N-1, the cyclic convolution of h and
  d is defined as
• Cyclic convolution. Let the DFT of hm, dm and
  ym be Hk,Dk and Yk,respectively. We have
  YkHkDk.

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OFDM

• Cyclic convolution. If there is n such that
• for all m-n,
• Note that this is true if
• n (m-n) mod N.

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OFDM

• The implication of this is that we may transmit
  the data symbols in the frequency domain. That
  is,
• the data symbols are actually Dk, 0ltkltNc.
• Then we do a IDFT on Dk to get dn, 0ltnltNc.
• Then we append the cyclic prefix, and send out
  the block, called an OFDM block or an OFDM
  symbol.
• The OFDM symbol will go through multipath, say we
  received y0, y1,, yL-1, yL,, yNcL-1.
• We then take only yL-1, yL,, yNcL-1 and
  do a DFT on them.
• Because yL-1, yL,, yNcL-1 is the cyclic
  convolution of dn and hl, the result of DFT is
  DkHK!

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OFDM