2.3 Downlink Transmission in IEEE 802.16m OFDMA [11]
2.3.4 Cell-Specific Resource Mapping
The content of this section is mainly taken from [11]. P RUF P is are mapped to LRUs.
All further PRU and subcarrier permutation are constrained to the PRUs of a frequency partition.
2.3.4.1 CRU/DRU Allocation
The partition between CRUs and DRUs is done on a sector specific basis.Let LSB−CRU,F P i
and LM B−CRU,F P i denote the number of allocated subband CRUs and miniband CRUs for
F Pi (i ≥ 0). The number of total allocated subband and miniband CRUs, in units of a subband (i.e. N1 PRUs), for F Pi (i ≥ 0) is given by the downlink CRU allocation size, DCASi. The numbers of subband-based and miniband-based CRUs in F P0 are given by DCASSB,0 and DCASM B,0, in units of a subband and miniband, respectively. When DFPC
= 0, DCASi must be equal to 0.
ForF P0, the values of DCASSB,0 is explicitly signaled in the SFH as a 5, 4 or 3-bit field to indicate the number of subbands in unsigned-binary format, with DCASSB,0 ≤ KSB,F P. A 5, 4 or 3-bit Downlink miniband-based CRU allocation size(DCASM B,0) is sent in the SFH only for partition F P0, depending on FFT size. The number of subband-based CRUs for F P0 is given by
LSB−CRU,F P0 = N1· DCASSB,0. (2.19)
For F Pi (i > 0, F P CT 6= 2), the number of subband CRUs (LSB−CRU,F Pi) and miniband CRUs (LM B−CRU,F Pi) are derived as follows:
LSB−CRU,F Pi = N1· min{DCASi, KSB,F Pi}, (2.20) LM B−CRU,F Pi =
½ 0, DCASi ≤ KSB,F Pi,
(DCASi− KSB,F Pi) · N1, DCASi > KSB,F Pi. (2.21) When FPCT = 2, DCASSB,i and DCASM B,i for i = 1 and 2 are signaled using the DCASSB,0 and DCASM B,0fields in the SFH. Since F P0 and F P3 are empty, LSB−CRU,F P0 = LMB−CRU,F P0 = LDRU,F P0 and LSB−CRU,F P3 = LM B−CRU,F P3 = LDRU,F P3. For i = 1 and 2, LSB−CRU,F Pi = N1·DCASSB,0and LM B−CRU,F Pi is obtained from DCASM B,0using the map-ping in Table 2.6. The total number of CRUs in frequency partition F Pi, for 0 ≤ 1 < F P CT , is denoted by LCRU,F Pi, where
LCRU,F Pi = LSB−CRU,F Pi+ LM B−CRU,F Pi. (2.22) The number of DRUs in each frequency partition is denoted byLDRU,F Pi, where
L = F P S − L (2.23)
Table 2.6: Mapping Between DCASM B,0 and Number of Miniband-Based CRUs for F P0 for 1024 FFT Size (Table 809 in [11])
and F P Si is the number of PRUs allocated to F Pi. The mapping from P RUF Pi to CRUF Pi is given by:
CRUF Pi[j] =
½ P RUF Pi, 0 ≤ j < LSB−CRU,F Pi,
P RUF Pi[k + LSB−CRU,F Pi], LSB−CRU,F Pi ≤ j < LCRU,F Pi, (2.24) where k = s[j − LSB−CRU,F Pi] with s[ ] being the CRU/DRU allocation sequence defined as s[j] = {P ermSeq(j) + DL P ermBase} mod (F P Si− LSB−CRU,F Pi). (2.25) We have 0 ≤ s[j] < F P Si− LSB−CRU,F Pi in(2.25), P ermSeq() is the permutation sequence of length (F P Si− LSB−CRU,F Pi) and is determined by SEED = {IDcell · 343} mod 1024 and DL P ermBase is set to preamble IDcell. The mapping of P RUF Pi to DRUF Pi is given by
DRUF Pi[j] = P RUF Pi[k + LSB−CRU,F Pi], 0 ≤ j < LDRU,F Pi (2.26) where k =s[j + LCRU,F Pi − LSB−CRU,F Pi]. Fig. 2.9 presents an example to illustrate the various steps of subband partitioning, miniband permutation, frequency partitioning, and
CRU/DRU allocation for the case of 10 MHz system bandwidth. For this example, KSB = DSAC = 7, F P CT = 4, F P Si = 12(f ori ≥ 0), DF P SC = 2, DCASSB,0 = 1, DCASM B,0= 1, DCASi = 2 and IDcell = 0.
2.3.4.2 Subcarrier Permutation
The downlink DRUs are used to form two-stream DLRUs by subcarrier permutation. The subcarrier permutation defined for the DL distributed resource allocations within a frequency partition spreads the subcarriers of the DRU across the whole distributed resource alloca-tions. The granularity of the subcarrier permutation is equal to a pair of subcarriers.
After mapping all pilots, the remainders of the used subcarriers are used to define the distributed LRUs. To allocate the LRUs, the remaining subcarriers are paired into contiguous tone-pairs. Each LRU consists of a group of tone-pairs.
Let LSC,l denote the number of data subcarriers in lth OFDMA symbol within a PRU, i.e., LSC,l= PSC − Nl, where Nl denotes the number of pilot subcarriers in the lth OFDMA symbol within a PRU. Let LSP,l denote the number of data subcarrier-pairs in the lth OFDMA symbol within a PRU and is equal to LSC,l/2. The DL subcarrier permutation is performed as follows. For each lth OFDMA symbol in the subframe:
1. Allocate the Nl pilots within each DRU as described in Section 2.3.4.3. Denote the data subcarriers of DRUF P i[j] in the lth OFDMA symbol as
SCDRU,j,lF P i [k], 0 ≤ j < LDRU,F P i, 0 ≤ k < LSC,l. (2.27)
2. Renumber the LDRU,F P i · LSC,l data subcarriers of the DRUs in order, from 0 to LDRU,F P i · LSC,l − 1. Group these contiguous and logically renumbered subcarriers into LDRU,F P i · LSP,l pairs and renumber them from 0 to LDRU,F P i · LSP,l − 1. The
renumbered subcarrier pairs in the lth OFDMA symbol are denoted as
RSPF P i,l[u] = {SCDRU j,lF P i [2v], SCDRU j,lF P i [2v + 1]}, 0 ≤ u < LDRU,F P iLSP,l, (2.28) where j = bu/LSP,lc and v = {u} mod (LSP,l).
3. Apply the subcarrier permutation formula to map RSPF P i,l into the sth distributed LRU, s=0,1,. . . ,LDRU,F P i-1, where the subcarrier permutation formula is given by
SPLRU s,lF P i [m] = RSPF P i,l[k], 0 ≤ m < LSP,l, (2.29) with
k = LDRU,F P i· f (m, s, l) + g(P ermSeq(), s, m, l, t). (2.30) In the above,
1. SCLRU s,lF P i [m] is the mth subcarrier pair in the lth OFDMA symbol in the sth distributed LRU of the tth subframe;
2. m is the subcarrier pair index, 0 to LSP,l− 1;
3. l is the OFDMA symbol index, 0 to Nsym− 1;
4. s is the distributed LRU index, 0 to LDRU,F P i− 1;
5. t is the subframe index with respect to the frame;
6. P ermSeq() is the permutation sequence of length LDRU,F P i and is determined by SEED = {IDcell × 343} mod 210;
7. g(P ermSeq(), s, m, l, t) is a function with value from the set [0,LDRU,F P i-1], which is defined according to
g(P ermSeq(), s, m, l, t) = {P ermSeq[{f (m, s, l) + s + l} mod {LDRU,F P i}]
+DL P ermBase} mod LDRU,F P i. (2.31)
where DL P ermBase is set to preamble IDcell, and f (m, s, l) = (m + 13 ∗ (s + l))mod LSP,l.
2.3.4.3 Random Sequence Generation
The permutation sequence generation algorithm with 10-bit SEED (Sn−10, Sn−9, ..., Sn−1) shall generate a permutation sequence of size M according to the following process:
• Initialization:
1. Initialize the variables of the first order polynomial equation with the 10-bit seed, SEED. Set d1 = bSEED/25c + 619 and d2 = SEED mod 25.
2. Initialize an array A with size M to contents 0, 1, . . . , M − 1 ( i.e., A[i] = i), for 0 ≤ i < M .
3. Initialize the counter i to M − 1.
4. Initialize x to −1.
• Repeat the following steps if i > 0:
1. Initialize the counter j to 0.
2. Loop as follows:
(a) Increment x by i.
(b) Calculate the output variable of y = {(d1· x + d2) mod 1031} mod M. If y ≥ i, set y=y mod(i+1)
(c) Swap A[i] and A[y]
(d) Decrement i by 1.
• P ermSeq(i) = A[i], where 0 ≤ i < M.
Figure 2.8: Frequency partitioning for BW = 10 MHz, KSB = 7, FPCT = 4, F P S0 = F P Si
= 12, and DFPSC = 1 (Fig. 502 in [11]).
Figure 2.9: Frequency partition for BW=10MHz, KSB = 7, F P CT = 4, F P CT = 4, F P S0 = F P Si = 12, DF P SC = 2, DCASSB,0 = 1, DCASM B,0 = 1, DCASi = 2 and IDcell = 0 (Fig. 503 in [11]).
2.3.4.4 Test Case for Subcarrier Permutation
In this subsection, we provide an example of the subcarrier permutation. It is also used in the later channel estimation simulation.
• NPRU = 48
• DSAC = 7
• KSB = 7
• KM B = 20
• LSB = 28
• Nsub = 12
• DFPC = 2
• FP0 : FP1 : FP2 : FP3 = 1:1:1:1
• FPS = 12
• ID Cell = 2
• SEED = 686
• DL PermBase = 2
Fig. 2.10 shows the original positions of LRUs permutation before subcarrier permutation.
And we give the number for each pair (every two subcarriers as a pair) as shown in Fig. 2.11.
Figs. 2.12 to 2.15 show the subcarrier permutation for each DRU. In these figures, each number pair X Y indicate the DRU number (X) and the subcarrier index (Y ).
Figure 2.10: LRU positions before subcarrier permutation.
Figure 2.11: Subcarrier pairs before subcarrier permutation for each frequency partition.
Figure 2.12: Subcarrier permutation for FP0.
Figure 2.13: Subcarrier permutation for FP1.
Figure 2.14: Subcarrier permutation for FP2.
Figure 2.15: Subcarrier permutation for FP3.