Cck -0fdm Wlan Modem

In this paper, we propose a new scheme using (he 1" order Reed-Mullcr (w code with variables 4, RM(I, 4) which improves rhe performance of IEEE 802.1 Ig wireless local mea network (WLAN) modem in terms of peak-lo-average power ralio (PAPR) and symbol error probabilily (SER). We show the equivalence between complemenlary code keying (CCK) codeword and coset of the I" order Reed-Muller code with variables 3 , RM(I, 3 ) . This proposed system shows beller performance than CCK in terms of PAPR ond SER. When the numbers of IFFTpoint is 64. we reduce PAPR by 9dB and gel a codinggain of 3dB alsymbol errorprobabilify of IO4. Since lhe syslem of RM(I, 4) can be implemented using the RM(I, 3). there is a liffle increase in complexily. INTRODUCTION The data rate and reliability required to support the new wireless multimedia service has increased the demand for high-speed wireless communication systems. Recently, both CCK and orthogonal frequency division multiplexing (OFDM) have been adopted as high-speed signaling schemes for IEEE 802.11g WLAN standard [I]. However OFDM carries a serious problem of having a large peak-to-average power ratio when added up coherently. A large PAPR in OFDM system brings disadvantages such as an increased complexity of the analog-to-digital and digital-to-analog converters, and a reduced efficiency of the RF power amplifier. A well-known approach to PAPR reduction is using the correlation properties of complementary sequences translating into a relatively small PAPR of 2 (3dB) when the codes are used to modulate an OFDM signal. In [2], Davis derived that these complementary sequences occur as cosets of the I" order RM code within the Znd order RM code and used these sequences to reduce PAPR in OFDM. The paper is organized as follows. We show the equivalence between CCK and cosets of RM code, and PAPR reduction in the proposed system. Finally we give simulation results to confirm our derivation. EQUIVALENCE B TWEEN CCK AND COSETS OF REEDIn IEEE 802.11g WLAN standard, for a block length of 8, MULLERCODE 256 possible sequences C' can be constructed as follows: c, = y(n+.v?v*i ,&(p\%+%) ,&k+u?%) ,4.(wv4) &~n++!6),&kw3) &w%i,&(yI)) (1) 77 3n 1 2 where q,, ..., q4 E (0, -, A , }. Let G. be the generator matrix of RM (1, m), and xk, k = 1, 2, . , . , m+l be the row vectors of G,, where m is the number of variables. The set of codewords (mod Q) represented by (2) is Golay complementary sequences which have PAPR of 3dB at most [2] : where n is permutation of the symbols and U E (0, 1, .,., QI)"" is information vectors. The first part of the right hand side is coset leader (3) and the second part is I" order RM code. Far m = 3, Q = 4, possible coset leaders based on (3) are [00020020], [00000220] and [00020200]. If coset leader [00020020] is chosen, (2) is equivalent to CCK codes ( I ) after some arrangements. The generator matrix G4 of RM(1, 4) code can be represented by using the generator matrix G, and all-zero and all-one vectors as shown below (4).