V.Bota, Zs.Polgar, M.Varga Communications Department, Technical University Cluj-Napoca

1
V.Bota, Zs.Polgar, M.VargaCommunications
Department,Technical University Cluj-Napoca

• Performance Evaluation of H-ARQ Adaptive Coded
  QAM Transmissions
• over Multipath Mobile Channels

2
Overview

• The computation of the average spectral
  efficiency provided by the adaptive use of a set
  of (non-)coded QAM modulations over a mobile
  Rayleigh-faded multipath channel within an OFDM
  transmission scheme governed or not by an H-ARQ
  protocol involves the following steps
• Describe the ODFM transmission scheme
• Establish the set of (non-)coded QAM
  configurations (code modulation), the SNR
  domains where each of them is optimum (channel
  states) and their performances (BER, CER and
  spectral efficiency) within the domains
• Establish the user-chunk allocation method (BFP,
  FH)
• Model the channel and compute the channel state
  probabilities, i.e. the average probabilities to
  employ each configuration (code modulation)
• Compute the average efficiency of a non-ARQ
  transmission and evaluate the average
  performances for various coding schemes
• Compute the average efficiency of a H-ARQ
  transmission and evaluate the average
  performances for various coding schemes

3
1. ODFM Transmission Scheme

• Nsbc 416 payload subcarriers with a frequency
  separation fs 39.0625 kHz
• an user-chunk that consists of A subcarriers x E
  OFDM symbol periods (A 8, E 12) that contains
  L-QAM payload symbols, L 81
• the maximum number of users NusM Nsbc/A 52.
• the chunk rate Dch 2983.5 ch/s, for a
  guard-interval Gi 0.125,
• the user-chunk bandwidth BWch 312.5 kHz. 1

4
2. Set of non-coded QAM modulations - ANCM

• the ANCM set consists of non-coded QAM
  modulations with nk 1,..,11 bits/symb separated
  by thresholds Tk
• figure 1 presents the SNR domains where the QAM
  constellations are employed (channel states) for
  nk 1,,8 on a AWGN channel

nk bit/sb 1 2 3 4 5 6
Tk dB T1 -2 T2 8.3 T3 13.2 T4 16.2 T5 20.2 T6 23.6
nk bit/sb 7 7 8 9 10 11
Tk dB T7 26.6 T7 26.6 T8 29.8 T9 33 T10 36.2 T11 39.4
5
2. Set of LDPC-coded QAM modulations - ACM
Set ACM - chunk coded configurations Set ACM - chunk coded configurations Set ACM - chunk coded configurations Set ACM - chunk coded configurations Set ACM - chunk coded configurations Set ACM - chunk coded configurations Set ACM - chunk coded configurations Set ACM - chunk coded configurations Set ACM - chunk coded configurations
code code code code nk nk
  k j p nc nn Rcfg Tk dB GcdB
  8 3 11 1 0 0.59 -? 4.5
  8 4 23 2 0 0.43 3.3 7.5
  13 3 13 2 0 0.76 6.3 4.5
  9 4 37 4 0 0.55 10.1 8.
  9 5 19 2 2 0.84 12.5 7
  10 3 17 2 2 0.84 13.9 5
  12 4 41 6 0 0.66 16.4 7.5
  12 4 29 4 2 0.76 17.9 6.5
  10 3 17 2 4 0.89 20.7 4
  8 4 41 4 4 0.74 22.8 8
  15 3 29 4 4 0.86 25.4 5.5
  10 3 17 2 6 0.92 26.8 4.5

• The ACM set consists of 12 LDPC-coded QAM
  configurations shown in table 2.
• The LDPC are L2q codes of girth 6, defined by
  parameters k, j, p 10.
• The configurations are defined by the numbers of
  coded and non-coded bits/symbol, by their coding
  rates and by the coding gains.
• The coding gains are referred to the non-coded
  QAM modulations with the same numbers of
  bit/symbol, nk.

• The thresholds Tk of the SNR domains (channel
  states Sk ) where each configuration is optimum
  are also shown.

6
3. User-Chunk Allocation Method

• the user-chunk allocation method ensures the
  frequency diversity, to compensate the variable
  attenuation of the Rayleigh fade of the mobile
  multipath channel
• the method employed is Best Frequency Position
  (BFP), i.e. each user-chunk is allocated the
  group of Cu sub-carriers that ensure the best
  average SINR for the bin-period envisaged,
  2,3,4
• involves the state-prediction of all available
  bins, over a prediction time-horizon, performed
  by the user mobile station.
• the channel prediction is assumed to be perfect

7
4. Computation of the channel state probabilities

• The computation of the average throughput over a
  time-varying channel employs the channel modeling
  as a Markov chain with S states, each state
  having an average probability of occurrence wk, k
  1,S.
• The computation of the state probabilities wk
  requires a detailed description of the particular
  radio channel analyzed and has two consider the
  combination of the Rayleigh fading and multipath
  propagation 6 and the user-chunk allocation
  algorithm performed by the scheduler of the
  base-station 4, 7, on the other hand.
• This method provides a good accuracy when
  compared to the simulation results, 3, but it
  requires a significant amount of computation that
  should be performed for every average level of
  the first arrived path.
• The probability distribution also depends of the
  average SNR0 .

8
4. Computation of the channel state
probabilitiesApproximate method

• an approximate method to compute the p.d.f. of
  the received signal level (and the SNR at the
  receiver), for any given average SNR0 of the
  first arrived path, which could be applied for
  any SNR0 and Nus.
• it requires a smaller amount of computation and
  consists of three steps
• determine the probabilities of the receivers
  SNR to vary between an imposed set of thresholds
  Tk, for a given SNR0 of the first arrived path
  and Nus, either by the approach 3 or by
  computer simulations
• find an interpolation function f(x) that
  approximates the distribution of the SNR on the
  channel, fulfilling the conditions imposed by
  step a.
• translate and scale the f(x) around the desired
  SNR of the first arrived wave, SNRa.

9
4. Computation of the channel state
probabilitiesApproximate method

• the interpolation function f(x) should fulfill
  conditions (1) condition (1.b) includes an
  additional upper threshold Tk1 which insures the
  solvability of the system of equations (2).
• f(x) should also 0 lt f(x) lt1, it should have only
  one maximum across the whole range of x
  considered.
• by choosing f(x) to be a polynomial function of
  order S, (2.a) and using the state probabilities
  wk, the coefficients of f(x) are computed by
  solving the system of equations defined by (2.b)
  and (2.c).

(1)
(2)
(2)
10
4. Computation of the channel state
probabilitiesApproximate method - example
Tk dB T1 -2 T2 8.3 T3 13.2 T4 16.2 T5 20.2 T6 23.6
Nus 1 0 0 0 210-5 1.410-3 3.910-2
Nus 25 0 0 0 510-5 3.210-3 5.510-2
Nus 50 0 0 3.110-4 6.810-3 2.610-2 8.810-2
Tk dB T7 26.6 T7 26.6 T8 29.8 T9 33 T10 36.2 T11 39.4
Nus 1 3.410-1 3.410-1 5.310-1 8.710-2 7.810-4 0
Nus 25 3.510-1 3.510-1 5.010-1 8.810-2 7.910-4 0
Nus 50 3.110-1 3.110-1 4.810-1 8.910-2 1.010-3 0

• the WP5 Urban Macro channel model (18 paths) 9,
  for SNR0 16 dB, 3
• the SNR values were split into 11 domains
  (channel states), separated by thresholds Tk,
  table 3, ANCM. The user- chunk allocation is BFP.
• the state probabilities wk of the total SNR to
  lay within each domain are shown in table 3
  (obtained by simulations), for Nus 1, 25 and
  50.

Nus Tkm-1 dB TkM1 dB Ndomains Order of f(x)
1 20.2 36.39 6 8
25 20.2 36.39 6 8
50 16.2 36.39 7 9

• for a simpler computation only
• the states with high probability were retained,
  see table 4

11
Computation of the channel state
probabilitiesApproximate method - example

• the graphs f(SNR) vs. SNR obtained for SNR0 16
  dB and Nus 1, 25 and 50 are shown in fig. 2
• the probabilities of the SNR to lie within each
  interval are obtained by integrating f(x) between
  the corresponding thresholds (2.a).
• the values obtained (C )are shown for SNR0 16
  dB in table 5 and compared to the values obtained
  by computer simulation (S), for Nus 1.

Tk dB T1 -2 T2 8.3 T3 13.2 T4 16.2 T5 20.2 T6 23.6 T7 26.6 T8 29.8
S 16 dB 0 0 0 210-5 1.410-3 0.039 0.34 0.62
C16 dB 0 0 0 110-5 1.410-3 0.039 0.34 0.62
S 4 dB 0 0.0095 0.138 0.67 0.181 0.0020 0 0
C 4 dB 0 0.0077 0.144 0.665 0.176 0.0067 0 0
S 1 dB 8.710-4 0.146 0.502 0.348 3.510-3 0 0 0
C 1 dB 0.0014 0.150 0.494 0.341 1.510-2 0 0 0

• Comparisons between the computed and simulated
  values performed for Nus 25 and 50 also
  indicated good matching between the two sets of
  values.

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Computation of the channel state
probabilitiesApproximate method - example

• the probabilities of the SNR to lie between the
  given thresholds can be computed, using the
  function f(x), for different values of the SNR0.
• denoting by SNRref the value of SNR0 for which
  the f(x) was derived(16 dB), for the desired
  value of Nus, and by SNRa the actual SNR of the
  first arrived path, the interpolating function fa
  (SNR) can be computed by translating and scaling
  the fr(x), on the x-axis (in dB) which is
  equivalent to

(3)

• the state probabilities wk to lie between the
  imposed thresholds were computed by integrating
  the fa (x) between pairs of thresholds (Tk, Tk1)
  .
• the values of wk for SNRa 4 dB and 1 dB are
  presented in table 5 together with the values
  obtained by computer simulations, for Nus 1.
• additional comparisons performed by the authors
  for different values of SNRa and Nus show that
  the errors of the approximate method are of about
  the same range as those of table 5.
• therefore, this approximate method may be
  employed to compute the probabilities wk of the
  multipath Rayleigh channel to be in state Sk with
  a reasonable accuracy, which would not affect the
  throughput evaluation.

13
5. Spectral efficiency of non-ARQ transmissions

• the transmission scheme uses a M-chunk long
  packet in a system that employs adaptively the
  ANCM set of S 8 non-coded modulations it uses
  the BFP method and assumes perfect channel state
  prediction.
• to evaluate the average throughput we consider
  the QAM-symbol and bit error rates, pek and BERk,
  of configuration k, on a channel in state k, k
  1,S, i.e. the SNRk 10lg (Ps/Pn)k values range
  from Tk-1 to Tk.
• since the pek of a QAM constellation is expressed
  by (4.a) and that, due to the Gray mapping, the
  BERk is expressed by (4.b) 2, the probability
  of an Lnk-bit chunk, transmitted with
  configuration k on a channel in state k to be
  correct after decoding is given by (5).
• for the coded configurations, the SNRkeq are
  increased with their coding gains CGk referred to
  the non-coded constellations with the same
  numbers of bit/symbol.

(4)
(5)
14
5. Spectral efficiency of non-ARQ transmissions

• the average probability of a chunk to be
  correctly decoded, considering all possible
  channel states, is expressed by (6)
• the average probability of an M-chunk long packet
  to be correctible received and the average
  probability of retransmission for such a packet
  are expressed by (7.a, 7.b)

(6)
(7)

• in an application not governed by an ARQ
  protocol, the nominal average bit rate Dnav, the
  average throughput Tn and the average spectral
  efficiency ?av are shown in (8), where Rec
  denotes the rate of an external code applied to
  the whole M-chunk packet.

(9)
(8)

• the average time required for the transmission of
  an U-bit long packet (U not an integer multiple
  of the average chunk length) is given by (9).

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5. Spectral efficiency of non-ARQ transmissions

• the average spectral efficiency of the described
  transmission scheme in a non-ARQ environment is
  computed on a WP5 Macro channel for v30 km/h.
• M 8-chunk packets were considered 1.
• the configurations adaptively employed at the
  chunk level are either non-coded, nk bits/symbol,
  slide 4, or LDPC-coded, ncnn bits/symbol, slide
  5, with coding gain Cgk and configuration rate
  Rck.
• the spectral efficiency and packet error rates
  vs. SNR0 curves are shown in figures 3 and, 4 for
  the following coding schemes
• non-coded, using adaptively configurations of
  table of slide 4
• coded at chunk-level, using adaptively the
  configurations of slide 5
• coded at frame-level with an external LDPC code,
  Rce0.86, CGe6.5 7 dB, using adaptively
  configurations of slide 4
• same as above, but the external LDPC code has,
  Rc 0.91,CGe6 6.5 dB.
• the average numbers of bits mapped/QAM symbol for
  the coding schemes employed are shown in table 6,
  for several values of the SNR0. It also includes
  the lengths of the external codes employed (1
  codeword/ packet).

16
5. Spectral efficiency of non-ARQ transmissions
Figure 3 Packet error probabilities vs. SNR0 for
Figure 4 Average
spectral efficiency vs. SNR0 for different
coding schemes 8 chunks/packet,
different coding schemes
8 chunks/packet
SNR0 (dB) nkav bits /symb non-coded ext.-coded nkav bits /symb chunk coded Cwd length 8-chunk/packet
1 3.2179 4.6243 2085
4 4.0308 5.6974 2601
7 4.8479 6.4736 3141
10 5.7611 7.5527 3721
13 6.7219 7.9677 4355
16 7.5793 7.9975 4911
19 7.9478 8 5150
Table 6 Average no. of bits/symbol and external
codeword lengths for M 8 chunk/packet
17
5. Spectral efficiency of non-ARQ
transmissionsComments

• the spectral efficiency of the non-ARQ
  transmissions is affected by two contradicting
  factors
• the average number of bits mapped
  adaptively/symbol as seen from columns 2 and 3
  of table 6, this number is significantly higher
  for the chunk-coded scheme because the set of
  configurations is larger, i.e. smaller
  granularity, and because of the non-coded bits
  mapped, which increase the configuration rate and
  the first factor of (8.c).
• the packet-error probability, which is dependant
  on the packet length and of the correction
  capability of the code, and decreases the second
  factor of (8.c).
• the 1- Pcpav for the chunk level coding is higher
  than the one of the packet level coding, see
  fig. 2. This can be explained two facts
• the SNR thresholds of the coded set of slide 5
  were imposed so that CER 10-2
• the non-coded bits, which increase Rcfg, also
  increase the chunk and packet error rates.

18
5. Spectral efficiency of non-ARQ
transmissionsComments

• the average spectral efficiency is a trade-off,
  see (8.c), between the average nk (including its
  granularity and the coding rates) and Pcpav
  (depending of the CGk).
• the global computation of (8) presented in figure
  2, shows that the chunk-coded scheme has a higher
  spectral efficiency, than the packet-coded
  scheme, though it exhibits higher packet error
  rates.
• this is because the first factor of (8.c) is
  larger for this coding scheme and compensates the
  smaller value of the second factor.
• for a longer packets, e.g. 4 times longer, making
  M 32 chunks, the packet-level coding and the
  chunk-level coding ensure about the same spectral
  efficiency, because of the higher packet error
  probability of the chunk level coding, compared
  to M 8 chunks.
• by imposing the thresholds at higher values, so
  that CER lt 10-3, (1-Pcpav) is decreased but the
  spectral efficiency is also decreased
• the thresholds settings may be adapted to the
  application to ensure the desired trade-off
  between packet-error rate and spectral efficiency

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6. SW H-ARQ average spectral efficiency

• the throughput and spectral efficiency
  performances of the proposed transmission scheme
  are now analyzed within an Stop Wait Hybrid ARQ
  (SW H-ARQ) protocol 4 which employs adaptively
  a set of (non)coded modulations.
• the SWARQ employs an M-chunk long packet,
  performing one transmission and q retransmissions
  of the whole packet before count time-out.
• The count timeout lasts for TT seconds and the
  protocol resumes the transmission, after the
  count timeout, with the packet that generated the
  count time-out (Z-type protocol).
• A perfect (N)ACK transmission across the uplink
  connection is also assumed.
• for application governed by the H-ARQ protocol
  defined above, the average probability of an
  M-chunk long packet to be correctible received
  and acknowledged after its transmission (first
  attempt) P0av and the average probability of
  retransmission are

(10)
20
6. SW H-ARQ average spectral efficiency

• the average probability of such a packet to be
  positively acknowledged after the i-th
  retransmission, i.e. one transmission and i
  retransmissions, Piav and the average probability
  to reach the count time-out state, i.e. to fail
  the transmission and the q retransmissions, PTav
  are

(11)

• the impact of the TT is equivalated by the
  average number of bits that could have been
  transmitted during this state, expressed by a
  multiple dav of the average number of bits of a
  packet

(12)

• the average total number of payload bits that are
  successfully acknowledged, after the (q1)
  attempts, is

(13)

• the average total number of transmitted bits Ntav
  required to successfully acknowledge the Nuav
  bits after the q1 attempts (including the count
  time-out).

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6. SW H-ARQ average spectral efficiency

• the protocol efficiency, i.e. the ratio between
  the Nuav and the Ntav is then expressed by

(15)

• the average throughput and spectral efficiency of
  the transmission governed by an H-ARQ protocol
  are

(16)

• Comments
• if we remove the protocol requirements, no count
  timeout (dav 0) and no retransmissions (q 0),
  the ?p Pcpav, see (13) and (15), and the
  spectral efficiency is the one of the
  non-protocol schemes, see (11).
• for q gt 0, the ?p is smaller than Pcpav and
  increases with the increase of q for an infinite
  number of retransmissions (q ??) the ?p? Pcpav
  and the spectral efficiency of the protocol
  scheme tends to the one of the non-protocol
  scheme.

• the average time required to transmit an M-chunk
  packet under the H-ARQ protocol is

(17)
22
6. SW H-ARQ average spectral efficiency

• the two contradictory factors that affect the
  ?av, slide 18, (8.c), also affect ?pav in a
  similar manner, but Pcpav is replaced by the
  second factor of ?p, (15).
• the performances of configurations from sets ANCM
  and ACM, slides 4 and 5 were evaluated for an
  H-ARQ protocol in the transmission scheme and
  channel, described before.

• the H-ARQ parameters are q3 retrs. dav 5, M
  8 chunk/packet.
• the average spectral efficiencies provided by the
  coding schemes of table 5 are presented in figure
  5.

• the chunk-level coded scheme provides
• a higher spectral efficiency than the
• packet-level coding schemes as in
• the non-protocol scheme, due to the same reasons,
  for frames of 1 packet.
• for longer packets, the two coding schemes have
  about the same ?pav.

• the values of ?pave are smaller than in the
  non-protocol case due the count time-out interval
  TT, term dav in (15). The increase of TT,
  compared to the packet duration, leads to a
  significant decrease of the spectral efficiency.

23
7. Conclusions

• the average spectral efficiency of such
  transmissions is significantly affected by the
  number of configurations adaptively used for both
  non-ARQ and H-ARQ schemes.
• the coding rates of the employed configurations
  affect in two contradictory ways the ?av
• by decreasing the number of payload bits
  transmitted
• by increasing their probability of correct
  decoding.
• the trade-off between these trends is
  accomplished within a limited range of SNR, where
  the respective coded configuration should be
  employed.
• in both transmission modes, the chunk-level
  coding scheme ensures higher spectral
  efficiencies for small packets, because it allows
  the adaptive employment of more coded QAM
  configurations, while for long packets (more
  chunks) the two coding schemes provide close
  spectral efficiencies.
• this conclusion holds for coding schemes that
  employ only one correcting code, either at the
  chunk-level or at the M-chunk packet level.

24
Questions for Further Study

• the trade-off between the average spectral
  efficiency and packet-error rate might be
  balanced, for chunk-level coding which uses
  adaptively a set of coded modulations, to meet
  the service requirements, by modifying the
  thresholds that separate the SNR domains where
  the modulations are employed. This trade-off
  could also be modified by changing the number of
  configurations of the set that is employed
  adaptively according to the service requirements
• the effects of errors in channel state prediction
  upon the average performances and the possibility
  to increase the number of adaptively used
  configurations, as a countermeasure to these
  effects, should be considered
• a significant increase of the average spectral
  efficiency might be brought by the employment of
  concatenated codes, the outer code at the
  packet-level and the inner code at the
  chunk-level.
• the derivation of the average spectral efficiency
  presented in this paper may be applied for the
  coding scheme employing concatenated codes, both
  for non-ARQ and for H-ARQ transmissions.
• the employment of erasure codes at the
  packet-level coding could also improve the
  reliability of non-ARQ schemes

25
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