LE DEBRUITAGE DES IMAGES SONAR EN UTILISANT LA THEORIE DES ONDELETTES SORIN MOGA ET ALEXANDRU ISAR ISETc 2010, Timisoara, November 11, 2010 A Study of the Permutation Schemes Used in Mobile Wireless Communications Ioan Eugen Andor, Lucian Ardelean, Horia Baltă, Maria Kovaci, Marius Oltean and Alexandru Isar

LE DEBRUITAGE DES IMAGES SONAR EN UTILISANT LA THEORIE DES ONDELETTES SORIN MOGA ET ALEXANDRU ISAR ISETc 2010, Timisoara, November 11, 2010 Permutations: What for ? - decorrelation - spreading noise /14

ISETc 2010, Timisoara, November 11, /14

ISETc 2010, Timisoara, November 11, 2010 Permutations in Encryption /14

ISETc 2010, Timisoara, November 11, 2010 Permutations in WiMAX WiMAX uses OFDMA at the physical level PERMUTATION = a way to allocate physical subcarriers to users Result: physical resources (subcarriers) are mapped to logical resources (subchannels) Case of Study: DownLink PUSC 512 The available subcarriers are SPLIT in three segments Every segment contains 140 subcarriers (data + pilots) Frequency spreading: the 140 subcarriers are not adjacent in the physical spectrum 5/14

ISETc 2010, Timisoara, November 11, 2010 Example Pilots are different for odd/even symbols Guard band at the edge of the frequency band Segment0=120 Data+20 Pilots The data subcarriers are split in 5 subchannels (5 subch x 24 subcarriers) = 120 subcarriers 6/14

ISETc 2010, Timisoara, November 11, 2010 How it’s a subchannel composed ? The basic formula is: What physical subcarrier corresponds to the logical subcarrier k (k=0,…,23) from the logical subchannel s (s=0,…4) ? nk= (k+13s) mod 24 ps(j)=series obtained by shifting s times to the left the basic permutation sequence DLPermBase = an integer ranging from 0 to 31: is the one providing randomness to the subchannel allocation Ex. Subcarrier (3,2)=5*nk+[ps(nk mod 5)+0] mod 5 = 5 * 5 +3 = 28 Meaning: the logical subcarrier 3 from the logical subchannel 2 is the 28th subcarrier available in the physical spectrum (out of the 120 allocated to segment 0). What is the reason behind…? 7/14

ISETc 2010, Timisoara, November 11, 2010 Turbo-codes Permutations û DEC1 DI DEC0 I I Channel I ex10 y1y1 y2y2 y0y0 LLR1 C1 C0 I u x1x1 x2x2 x0x0 P C1 I ex01 I Interleaver : Rectangular  Random Decorrelation: minimum maximum Spreading: maximum minimum Berrou & others (2004): regular-random Crozier (2000): S-interleaver 8/14

ISETc 2010, Timisoara, November 11, 2010 Distances Spectrum Interleaving / de-interleaving  : I  I, with I =  1,2,... N   -1 : I  I, with  -1 (  (i) ) = i,  i  I Interleaving distance: d(i, j) =  i –j  +  (i) –  (j) ,  i, j  I, i  j Minimum interleaving distance: d min = ids(k) k Distances Spectrum (DS), ids : J =  1, 2,..., 2  N   N ids(k) = pairs number (i, j)  I  I for that d(i, j) = k Spreading Degree (SD): sd = supp  ids(k)  / ids(k) Random-interleaver DS: 9/14

ISETc 2010, Timisoara, November 11, 2010 Frequencies’ Table 10/14

ISETc 2010, Timisoara, November 11, 2010 Frequency positions DS no[d(i,j)=k] d(i,j)=k DS for the S-interleaver with S=13 and N=140 DS for the interleaver defined by the positions’ sequence of the 140 sub-carriers’ frequencies of a BS segment 11/14

ISETc 2010, Timisoara, November 11, 2010 Frequency positions DS The DSs Parameters ParameterS-interleaverFrequencies’ positions permutation system DL-PUSC d min D max s max supp G N /14

ISETc 2010, Timisoara, November 11, 2010 Conclusions - DL-PUSC permutation of the sub-carriers’ frequencies is very good. It minimizes the collision probability also for the case of mobile users, spreading the sub-carriers’ frequencies at an important distance; -the fact that there are permutations with a higher spreading degree, lead us to the idea that this permutation can be improved. A more detailed analysis can leads to results more precise. - the Turbo-codes permutations methods can be used to develop more performant methods for permutation of the sub-carriers’ frequencies in WiMAX. 13/14

ISETc 2010, Timisoara, November 11, 2010 References [1] H. Balta, S. El Assad, „Interleaving Distances Spectrum Comparison between Turcocodes Interleavers”, European Microwave Week, September 2006, Manchester, UK; [2] S. Dolinar, and D. Divsalar, “Weight Distributions for Turbo Codes Using Random and Non-random Permutations”, TDA Progress Report , August 15, [3] IEEE e standard: "Air Interface for Fixed and Mobile Broadband Wireless Access Systems", December 2005; [4] D. Bojneagu, "The mapping of physical subcarriers to logical subchannels in OFDMA DL-PUSC 512 system", Alcatel-Lucent technical memo; [5] C. Berrou, Y. Saouter, C. Douillard, S. Kerouédan, and M. Jézéquel, “Designing good permutations for turbo codes: Toward a single model,” in Proc. IEEE Int. Conf. Commun., Paris, France, Jun. 2004, pp. 341–345. [6] S.N. Crozier, “New High-Spread High-Distance Interleavers for Turbo- Codes”, 20th Biennial Symposium on Communications, Kingston, Ontario, Canada, May 28-31, 2000, pp /14