Spectral Efficiency of MC-CDMA:

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• Spectral Efficiency of MC-CDMA
• Linear and Non-Linear Receivers
• Aditya Gupta
• 11/05/2209

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Purpose

• Analyzes the spectral efficiency
• Randomly-spread synchronous multicarrier
  code-division multiple-access (MCCDMA) channel
  subject
• Analyze the spectral efficiency for uplink and
  downlink conditioned on sub carrier
  frequency-selective fading
• Analysis is focused in the asymptotic regime

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Spectral Efficiency

• The spectral efficiency of a CDMA system is the
  total number of bits/s/Hz that can be transmitted
  arbitrarily reliably.
• For multicarrier CDMA (MC-CDMA), it is also the
  aggregate capacity per subband supported by the
  system.
• Eb/N0 (the energy per bit to noise power spectral
  density ratio) is an important parameter in
  Digital communication. It is a normalized signal
  to noise ratio (SNR) measure, also known as the
  "SNR per bit". It is especially useful when
  comparing the bit error rate(BER) performance of
  different digital modulation schemes without
  taking bandwidth into account.

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Previous Work and What's New in this Paper

• The spectral efficiency for randomly spread
  non-fading as well as at-fading direct-sequence
  CDMA (DS-CDMA) is studied in the wideband limit
  and large number of users for the jointly optimum
  receiver as well as linear receivers.
• Model analyzed in this paper is MC-CDMA.
• Impact of frequency-selective fading is also
  observed.

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Multi-Carrier Code Division Multiple Access

• Multi-Carrier Code Division Multiple Access
  (MC-CDMA) is a multiple access scheme used in
  telecommunication systems, allowing the system to
  support multiple users at the same time.
• MC-CDMA spreads each user symbol in the frequency
  domain.
• Each user symbol is carried over multiple
  parallel subcarriers, but it is phase shifted
  (typically 0 or 180 degrees) according to a code
  value.
• The code values differ per subcarrier and per
  user.
• The receiver combines all subcarrier signals, by
  weighing these to compensate varying signal
  strengths and undo the code shift.
• The receiver can separate signals of different
  users, because these have different (e.g.
  orthogonal) code values.

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Advantagesof MC-CDMA

• The requirement of having a continuous band of
  frequency for transmission as in DS-CDMA is
  dropped
• For equally spaced subcarriers, FFT can be used
  to implement the modulation/demodulation.

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What is analyzed

• Jointly optimum receiver
• Linear MMSE receiver
• Decorrelator
• Single-user matched filter
• Find analytically the spectral efficiency of the
  four receiving schemes for both uplink and
  downlink MC-CDMA channels conditioned on fading
• The effect of multicarrier transmission on the
  spectral efficiency of CDMA systems is examined

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Uplink and downlink MC-CDMA Conditioned on Fading

• For MC-CDMA the received spreading sequences are
  transformed from the original sequences by
  subband fading.
• Complex instantaneous fading coefficient at the
  i-th subcarrier of user k by Hik (1ltkltK),
  (1ltiltN)
• The received spreading sequence of user k is sk
  Hksk, where Hk diag
  (Hk1,.HkN)
• The spectral efficiency is calculated conditioned
  on the fading coefficients. This is advantageous
  because in this way we can then find the effect
  of an arbitrary frequency-selective fading
  distribution on capacity, and possibly further
  average capacity with respect to an ensemble of
  those fading distributions.
• For the downlink all users experience the same
  fading.
• Denote the subcarrier fading coefficients by
  H1,.,HN. User k's received sequence is sk
  Hsk, where H diag H1,,HN.

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Linear MMSE Receiver

• Let p(x, y) (0 lt x lt 1 0 lt yltb ) be the
  two-dimensional asymptotic allocation function
• pk(x) (0 ltx lt 1) be the one-dimensional
  asymptotic allocation
• The average received energy among users is Q.
• The average received signal-to-noise ratio (SNR)
  is snr
• Q can be interpreted as the power constraint of
  the users' codewords
• snr is the per-symbol SNR constraint of the
  users.

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Linear MMSE Receiver

• Conditioned on the fading coefficients, the MMSE
  multiuser efficiency of user k converges almost
  surely as K,N -gtinfinity with K/N b where K is
  the number of users and K/N b is the system load

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Linear MMSE Receiver

• Conditioned on the fading coefcients, the
  spectral efficiency of the MMSE receiver
  converges almost surely as K,N -gtinfinity with
  K/N b
• In the downlink involved expressions simplify
  significantly

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Optimum Receiver

• Uplink Capacity Conditioned on Subcarrier Fading
• In the asymptotic regime, we obtain an
  interesting closed form relation between the MMSE
  spectral efficiency and the optimum spectral
  efficiency.
• The capacity gain attained by optimum non linear
  processing depends only on the linear uncoded
  performance measure U(y snr), which is
  proportional to the output SINR of the by yN th
  user.

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Optimum Receiver

• Downlink Capacity Conditioned on Subcarrier
  Fading
• The conclusion is that the high-load Copt is
  reduced by the subband number reduction effect
• the optimum spectral efficiency converges to

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• The MMSE spectral efficiency is bounded for bP /
  C gt 1, and that the capacity loss due to
  subcarrier fading vanishes as Eb / N -gt infinity
• Figure 2 shows the optimum spectral efficiency
  vs. Eb / N0 of MC-CDMA and DS-CDMA for b 25.

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Decorrelator

• Uplink Capacity Conditioned on Subcarrier Fading
• Conditioned on the fading coefcients, the
  spectral efficiency of the MMSE receiver
  converges almost surely as K,N -gtinfinity with
  K/N b

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Decorrelator

• Figure shows Cdeco as a function of Eb / N0

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Single-user Matched Filter

• Uplink Capacity Conditioned on Subcarrier Fading
• Conditioned on the fading coefficients, the
  spectral efficiency of the MMSE receiver
  converges almost surely as K,N -gtinfinity with
  K/N b

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Single-user Matched Filter

• Downlink Capacity Conditioned on Subcarrier
  Fading
• Figure shows Csumf as a function of Eb / N
• Comparing the figures with those of the other
  receivers, we conclude that the matched filter is
  much more sensitive to the subcarrier fading than
  the other three receivers

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Conclusion

• The spectral efficiency of several receivers is
  analyzed for MC-CDMA channels subject to
  multicarrier frequency-selective fading.
• Analyze both the uplink and the downlink
  conditioned on
• The conditioned capacity converges asymptotically
  to an expression that depends, in general ,when
  no assumption on the ergodicity of the channel is
  made, on the empirical instantaneous power
  profile of the subcarriers fading.
• Main results is the expression characterizing the
  extra capacity attained going from optimum linear
  to optimum nonlinear processing as a function of
  the uncoded linear MMSE performance measure.

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Conclusion

• The effect of multicarrier frequency-selective
  fading on the capacity of several multiuser
  receivers is also studied.
• There is generally a capacity loss incurred by
  subcarrier fading.
• Two main causes for the loss.
• The first cause happens when some subbands are so
  deeply faded that virtually all the energy that
  was put into them is wasted.
• The second cause, reflected by Jensen's
  inequality, can be explained by the
  non-uniformity of the subband fading powers
  reducing the effective number of transmitting
  subbands.
• The impact of subcarrier fading is more
  significant for the single-user Matched filter
  than for the optimum receiver, MMSE receiver, and
  decorrelator

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References

• Spectral Efficiency of MC-CDMA Linear and
  Non-Linear Receivers by Linbo Li, Antonia M.
  Tulino, Sergio Verdu.
• Thank You !!!