Optimization of adaptive coded modulation schemes for maximum average spectral efficiency

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Optimization of adaptive coded modulation schemes
for maximum average spectral efficiency

• H. Holm, G. E. Øien, M.-S. Alouini, D. Gesbert,
  and K. J. Hole
• Joint BEATS-Wireless IP workshop
• Hotel Alexandra, Loen, Norway
• June 4-6, 2003

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Adaptive coded modulation (ACM)

• Adaptation of transmitted information rate to
  temporally and/or spatially varying channel
  conditions on wireless/mobile channels
• Goal
• Increase average spectral efficiency (ASE) of
  information transmission, i.e. number of
  transmitted information bits/s per Hz available
  bandwidth.
• Tool
• Let transmitter switch between N different
  channel codes/modulation constellations of
  varying rates R1lt R2 lt RN bits/channel symbol
  according to estimated channel state information
  (CSI).
• ASE (assuming transmission at Nyquist rate) is
• ASE ? RnPn
• where Pn is probability of using code n
  (n1,..,N).

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Generic ACM block diagram
Informa tion str eam
Demodu- lation and decoding
Adaptive choice of error control coding and
modulation schemes according to information
about channel state
Wireless channel
Coded information pilot symbols
Estimate channel state
Information about channel state and
which code/modula- tion used
Information about channel state
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Maximization of ASE

• Usually
• Codes (code rates) have been chosen more or less
  ad hoc, and system performance subsequently
  analyzed for different channel models
• Now
• For given channel model, we would like to find
  codes (rates) to maximize system throughput.
• Approach
• Find approachable upper bound on ASE, assuming
  capacity-achieving codes available for any rate
• Find the optimal set of rates to use
• Introduce system margin to account for deviations
  from ideal code performance

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A little bit of information theory

• For an Additive White Gaussian (AWGN) channel of
  channel signal-to-noise ratio (CSNR) ?, the
  channel capacity C information bits/s/Hz is
  Shannon, 1948
• C log2(1 ?)
• Interpretation
• For any AWGN channel of CSNR ? ?, there exist
  codes that can be used to transmit information
  reliably (i.e., with arbitrarily low BER) at any
  rate R lt C.
• NB
• This result assumes that infinitely long
  codewords and gaussian code alphabets are
  available.

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Application of AWGN capacity to ACM

• With ACM, a (slowly) fading channel is in essence
  approximated by a set of N AWGN channels.
• Within each fading region n, rates up to the
  capacity of an AWGN channel of the lowest CSNR -
  sn - may be used.

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ASE maximization, contd

• For a given set of switching levels s1, s2, sN,
  (an approachable upper bound on) the maximal ASE
  in ACM (MASA) for arbitrarily low BER is thus
• MASA ? log2(1g) sn?sn1 pg(g )dg
• where pg(g ) is the pdf of the CSNR (e.g.,
  exponential for Rayleigh fading channels).
• We may now maximize the MASE w.r.t. s s1, s2,
  sN by setting
• ?s MASA 0.

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Assumptions

• Wide-sense stationary (WSS) fading, single-link
  channel.
• Frequency-flat fading with known probability
  distribution.
• AWGN of known power spectral density.
• Constant average transmit power.
• Symbol period ?? Channel coherence time (i.e.,
  slow fading).
• Perfect CSI available at transmitter.

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ASE maximization Rayleigh fading case

• Maximization procedure leads to closed-form
  recursive solution (cf. IEEE SPAWC-2003 paper by
  Holm, Øien, Alouini, Gesbert Hole for details)
• find s1
• find s2 as function of s1
• find sn as function of sn-1 and sn-2 for n3,,
  N.
• Optimal component code rates can then be found as
  
• R1log2(1s1), , RN log2(1sN).

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MASA optimum w.r.t. CSNR level 1
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Optimal switching levels for CSNR (N1,2,4)
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Individual optimized information rates (N1,2,4)
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Capacity comparison AWGN Rayleigh (N1,2,4,8)
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Probability of outage
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Extensions and applications (1)

• Practical codes do not reach channel capacity
• May introduce CSNR margin 0 lt l lt 1 in achievable
  code rates Replace log2(1g) by log2(1lg)
  slight, straightforward modification of
  formulas.
• Other possible approach Use cut-off rate instead
  of capacity. yields performance limit with
  sequential decoding
• Worst-case (over all rates ? 0,4 bits/s/Hz, at
  BER0 10-4) theoretical margins for some given
  codeword lengths n Dolinar, Divsalar Pollinara
  1998

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Extensions and applications (2)

• CSI is not perfect
• Analytical methods exist for adjustment of
  switching levels to take this into account done
  independently of level optimization.
• For a Rayleigh fading channel with H receive
  antennas combined by maximum ratio combining
  (MRC), we have that
• Pr(g gt gng(p) g(p)n) QH(Hgn/gbar(1-r),
  Hg(p)n/gbar(1-r))
• where QH(x,y) is the generalized Marcum-Q
  function, gbar is the expected CSNR, and r the
  correlation coefficient between true CSNR g and
  predicted CSNR g(p).
• This may be exploited to adjust switching levels
  g(p)n for g(p) to obtain any desired certainty
  for g gt gn, given g(p) ? g(p)n. ASE-robustness
  trade-off

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Extensions and applications (3)

• True channels are not wide-sense stationary
• Path loss and shadowing will imply variations in
  expected CSNR
• May potentially be used for adaptation also with
  respect to expected CSNR
• E.g., in cellular systems Use different code
  sets (and number of codes) within a cell,
  depending on distance from user to base station.
• Rates may also be optimized w.r.t. shadowing and
  interference conditions.
• Dividing a cell into M gt 1 regions and using N
  codes per region is better than using MN codes
  over the whole cell Bøhagen 2003.

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Conclusions

• We have derived a method for optimization of
  switching thresholds and corresponding code rates
  in ACM - to maximize the ASE.
• Corresponds to optimal discretization of
  channel capacity expression (analogous to
  pdf-optimization of quantizers).
• Analytical solution for Rayleigh fading channels.
• Performance close to Shannon limit for small
  number of optimal codes (for a given average
  CSNR).
• Results can be easily augmented to take
  implementation losses and imperfect CSI into
  account.
• Adaptivity with respect to nonstationary channel
  models and cellular networks possible.
• NB Results do not prescribe a certain type of
  codes.