Multilevel block subcodes for coded phase modulation

zyxwvutsrqp zyxwvutsr zyxwvutsrq zyxwvutsrqpon zyxwvutsrq zyxwvutsrqp 100 104 Case Periodof bursterrors bit Required Eb/No A B C M = 40, L = 2048 N = 50 Burst length bit 21 dB dB 9.21 4.81 ,i2 dB I e b -3 10 ; .E 1 Simulation results: Table 1 compares the required EbIN, to obtain BER = I W : A the fixed block interleaving system, B the pseudor- andom interleaving system, and C the equivalent random error channel system. Four different burst patterns (cases 1 4 ) and the same interleaver delay are assumed. In cases 1 and 2, the parameters of burst errors and the deinterleaver meet the conditions of BER degradation. In these cases, the required E,/N, for the fixed block interleaving system is larger than that for the equivalent random error channel system; meanwhile the required E,INo for the pseudorandom interleaving system is equal to that for the equivalent random error channel system. I 2 -5 10 E b / N O, d B m Fig. 3 BER performance with interleaving techniques: case 4 X (i) no coding, no interleaving o (ii) coding, no interleaving A (iii) coding, fixed block interleaving 0 (iv) coding, pseudorandom interleaving 0 (v) coding, equivalent random error channel pseudorandom interleaving is an effective way of compensating for radar interference. In addition, the proposed pseudorandom order generating method has been proven to perform satisfactorily. 0 IEE 1994 Electronics Letters Online No: I9940653 I 1 April 1994 N. Nakajima, T. K. Matsushima and J. Murakami (Research Laboratory I, Communication and Information Systems Research Laboratories, Research and Development Center, Toshiba Corporation, I Komukai-Toshiba-cho,Saiwai-ku, Kawasaki 210, Japan) References s., OKUNO,T., and OHMOTO, R.: 'Bit interleaving technique as a radaar interference canceller', IEICE Tram. B-II, 1993, J76-BU,(8), pp. 679489 (in Japanese), 2 MUI,S.Y.: 'The performance of pseudorandom interleaving in conjunction with Viterbi decoding of convolutional codes'. ICC'83, pp. 509-513, 1983 1 AIKAWA, zyxwvutsrq zyxwvutsrqp Fig. 2 BER performance with interleaving techniques: case I X (i) no coding, no interleaving o (i) coding, no interleaving A fii) coding, fixed block interleaving 0 (iv) coding, pseudorandom interleaving Multilevel block subcodes for coded phase modulation 0 (v) coding, equivalent random error channel On the other hand, cases 3 and 4 do not fulfdl the conditions of BER degradation. The fixed block interleaving system, therefore, performs well. In contrast, the required EbIN, for the pseudorandom interleaving system is equal to or slightly larger than that for the equivalent random error channel system. It is supposed that the small degradation of the BER for the pseudorandom interleaving system in case 4 occu~sbecause the pseudorandom deinterleaver generates consecutive errors; however, the degradation is very small in comparison with that for the fmed block interleaving system in cases 1 and 2. Fig. 2 shows the BER against EJN, curves in cases 1 and 4, respectively. R. Baldini Filho and P.G. Farrell zyxwvutsrqp Conckbn: We have shown the conditions under which BER is degraded when conventional fixed block interleaving is adopted to compensate for radar interference. Further, we have used computer simulation to investigate BER degradation under these conditions. The results of the computer simulation indicate that ELECTRONICS LETTERS 9th June 1994 Vol. 30 Indexing terms: Block codes, Phase modulation The aim of this Letter is to show a new coded phase modulation based on fields. A class of multilevel block codes based on fields are also presented and tho% codes can perform better in terms of asymptotic coding gain than their equivalent codes over rings of integers modulo-Zm. Introduction; In general, trellis coded modulation (TCM) schemes based on Ungerboeck [l] set partitioning have shown to be highly susceptible to phase rotations of the signal set. Moreover, the TCM binary codes are very strict in terms of coding rate. On the other hand, coded modulation techniques based on rings of integers modulo-q have high flexibility of coding rates and can be easily made invariant to phase rotations of the carrier [2 - 41. Coded q-PSK modulation schemes based on codes over rings have also No. 12 927 zyxwvutsrqpo zyxwvutsr zyxwvutsrqponm zyxwvutsrqp zyxwvutsrqpon zyxwvuts zyxwvutsrqp shown a similar performance in respect of TCM schemes. Although block coded q-PSK modulation based on rings of integers modulo-q (Z,) presents good asymptotic coding gains over its basic uncoded modulation, there is no simple soft-decision decoding scheme that performs at or near to the maximum likelihood decoding bound. This is mainly due to the algebraic structure of the rings of integers modulo-q, that is, there exists no multiplicative inverse for all elements in a ring and, therefore, a division operation cannot be defmed. The division operation is crucial for a decoding process using algebraic methods. This problem could be easily overcome if the multilevel codes were defined over a field instead of a ring. The aim of this work is to analyse multilevel block subcodes over Z, suitable for coded q-PSK modulations, where q is a prime number. Note that a necessary and sufficient condition for a ring 2, to be a field is that q must be a prime number. Moreover, a subcode is defmed as a subset of codewords of a given (n, k ) multilevel block code over Z,. Note that the vector operations performed over the codewords of a subcode are not generally closed. 41x X) m Fig. 2 Coded 5-PSK modulatwn (0, 1, 2, 31, however, the encoder performs algebraic operations onto the field Z,. TnMe 1: Multilevel block subcodes for coded 5- and 7-PSK modulation Mltilevel source 4 6 8 10 12 14 16 I8 20 22 24 -911 g12 ' . ' glr 0 0 911 g12 " ' 91. . . .. G= j : : . .. .. .. .. . . 0 0 . . ..' ' ' . I Coded 5-PSK Fig. 1 Encoder structure 0 0 ... .. . 0 0 ... .. . 0 0 911 ' ' _ 0 .. . ... .'. 0 "' 0 i g12 "' (1) glr- 8 3.01 8 3.01 IO 3.98 12 4.77 12 4.77 12 4.77 14 5.44 16 6.02 I6 6.02 16 6.02 18 6.53 14 15 24 92 68 I21 6.38 1131 7.76 I0243 9.15 120334 10.53 31424ll 11.91 I1134111 13.29 113314404 14.67 1112414311 15.52 11142?41101 16.91 I Coded 7-PSK 2.03 4 113 1132 2.88 8 3.59 6 11223 4.20 2 112653 4.74 I2 113Zul 5.22 13 l w 3 2 I l 5.64 5 111245556 5.89 8 1112455556 6.26 5.31 7.75 9.26 10.77 12.31 14.30 15.36 17.68 1.23 2.87 3.65 4.30 4.88 5.53 5.84 6.45 2 3 1 3 5 1 4 4 zyxwvuts 48 5a 255 76 102 A subcode suitable for the coded 5-PSK modulation has to be rate equal to 112 for comparison with uncoded 2-PSK modulation. The same is also true if the expanded modulation set 7-PSK is chosen. Notice, however, that the coded 7-PSK modulation will have three modulation symbols with no bit assigned. Table 1 shows the minimum squared Euclidean distance DE ."*, the asymptotic coding gain g, over the uncoded 2-PSK m&latlon of codewords with minimum Euclidean weight and the number N,, for some (n, k ) multilevel subcodes suitable for coded 5- and 7PSK modulation. Table 1 also shows some parameters of block For small valcodes defmed over a ring of integers modulo4 [I. ues of code length, the asymptotic coding gains over uncoded 2PSK for both coded 5- and 7-PSK are smaller than those obtained for coded CPSK. However, for code length 12 and over, this trend is inverted, that is, coded 5- and 7-PSK present better asymptotic coding gain than coded 4-PSK. Moreover, the coded 7-PSK scheme performs better than the coded 5-PSK for almost all code lengths. The block subcodes are represented by the first r elements of the first row of the generator matrix G. zyxwvutsrq zyxwvutsr Table 2 Multilwel block submdes for coded 1 I- and 13-PSKmodulation I$+[ gm = lOlog,, E [dB] (2) DEu I25 where E, and E. are the average energies to transmit with coded and uncoded transmission, respectively, and Dmz and 0.' are the minimum squared Euclidean distances of the coded and uncoded scheme, respectively. Assume a coded 5-PSK modulation scheme. Fig. 2 shows the Gray mapping of all combination of two bits into the symbols of 2, . No bit is assigned to modulation symbol 4. Therefore, symbol 4 is used only as redundancy in the multilevel subcode. Notice also that the multilevel source only generates symbols from the subset 928 ._ I 3.24 2.09 13 136 1 I 1.99 4 . 0 3 3.31 2.19 1 I Table 2 shows the performance of some (n, k ) multilevel subcodes suitable for coded 11- and 13-PSK modulation. These coded modulation schemes, as coded 8-PSK modulation, have uncoded CPSK as reference. The parameters shown for coded 8-PSK modulation were obtained by using block codes defined over a ring of integers modulo-8 [5]. ELECTRONICS LETTERS 9th June 7994 Vol. 30 No. 12 zyxwvuts zyxwvutsr zyxwvutsrqpon zyxwvuts zyxwvutsrqp zyxwvutsrqpo Table 2 shows that both coded 11- and 13-PSK modulation schemes present better asymptotic coding gain over uncoded 4PSK than their equivalent coded 8-PSK modulation. Moreover, the coded 13-PSK scheme has better performance than coded 11PSK for all code lengths. Concluswn: Block coded q-PSK modulation based on fields of integers modulo-q appears to have good asymptotic coding gains when block subcodes with adequate length are used. Further, these unconventional coded modulation schemes have a more tractable algebraic structure than coded modulation based on rings of integers modulo-2m.This more convenient algebraic structure can help in devising a practical soft-decoding algorithm with low complexity and good performance. receiver owing to channel fading has heen addressed by several researchers and is the problem we address in this Letter. Varanasi [2] proposed two schemes in which noncoherent differential decision logic is applied to outputs from a D F or LDF. Wijayasuria et al. [3] proposed a block processing decorrelating algorithm called the sliding window decorrelating algorithm (SLWA) which also employs noncoherent differential detection. SLWA has a much lower recomputation cost in response to changes in configuration compared to the standard LDF for infinite sequence length. However, these noncoherent schemes exhibit an irreducible error floor at high SNRs over Rayleigh fading channels with nonzero Doppler spread and have SNR loss compared with the coherent detection. In this Letter, we propose a practical coherent decorrelating detection arrangement for infinite sequence length data over asynchronous up-link DS-CDMA channels of star-topology mobile radio networks. We address only frequency-nonselectiveRayleigh fading in this Letter because a diffuse multipath fading multiuser channel can be considered as an equivalent nonselective fading multiuser channel, treating each path component as an additional user so that decorrelation can be applied [4]. zyxwvutsr 0 IEE 1994 5 April 1994 Electronics Letters Online No: 19940641 R. Baldini Filho (DECOM - FEE - UNICAMP Universidade Estadual de Campinas, PO Box 6101, 13.081-970 Campinas - SP, Brazit) P. G. F a l l (Communications Research Group Department of Electrical Engineering, The University of Manchester, Manchester A413 9PL, United Kingdom) zero energy ReferUNGERBOECK, G.: ‘Trelliscoded modulation with redundant signal sets: Part 11: state of the art’, IEEE Commun. Mag., 1987, 25, (2). zyxwvutsrq pp. 12-21 BALDMI F., R., PESSOA, A C F., and ARANTES, D.s.: ‘Systematic linear codes over a ring for encoded phase modulation’. Int. Symp. Information and Coding Theory (ISIff87), 27-1 July-August 1987, Campinas, SP, Brazil BALDINl F., R., and FARRELL. P.G.: ‘Coded modulation with convolutional codes over rings’.EUROCODE 90,Udine, Italy, 59 November 1990, MASSEY. J.L., and MITTELHOLZER, T : ‘Codes over rings - A practical necessity’. AAEC Symp., Toulouse, France, June 1989 BALDMI F., R., and FARRELL, P.G.: ‘C6digos pseudo-ciclicos multiniveis’. Annals of 7’ Sip6sio Brasileiro de Telecommunica@es,4-9 September 1989, Florian6polis, SC, Brazil (in Portuguese) Pilot symbol aided coherent decorrelating detector for up-link CDMA mobile radio communication S. Y. Yoon, S. E. Hong, J. A h and H. S. Lee b time ! Fig. 1 Received data block sequences at base station in proposed arrangement Pilot symbol aided decorrelating detector: In our arrangement, the data sequence transmitted from each mobile user has a block structure, wbere each block consists of a zeroenergy bit, N data bits, and a pilot bit. Mobile transmission is arranged so that the differences in arrival times (in modulo one-block duration sense) of the zero-energy bits at the base station are smaller than the single-bit duration Tb as shown in Fig. 1. This hardly requires any synchronisation overhead as will be discussed in the latter part of this Letter. Thus each block received at the base station is free from edge effects or interference from other blocks. We then perform the block decorrelation of each block separately, rather than use the LDF approach, for computational amenability and flexibility to changes in timing configurations and additionhemoval of users as follows. Numbering the users in ascending order of relative delays modulo Tb,with the same notation as in [2], the matched filter output vector z during a block is zyxwvutsr Indexing terms: Code division and multiple access, Mobile radw systems, Radio receivers, Detectors ~~ ~~~~~~ new decorrelating arrangement for asynchronous uplink direct sequence code division multiple acces communication, which employs coherent detection with pilot symbol aided channel estimation, is proposed. The proposed coherent scheme improves the bit error rate (BER) and exhibits no error floor compared to the pre~ousnoncoherent schemes. The BER performance for BPSK is obtained by simulations over a frequency-nonselective Rayleigh fading channel. A !-i! T I n t r d c t i o n : Among the detection schemes for direct sequence code division multiple access (DS-CDMA) systems, decorrelating detectors have been studied by many researchers because they have low complexity and significantly outperform conventional receivers. Lupas and Verdu [I] proposed two decorrelating detection schemes for asynchronous DS-CDMA communication in which the decision device follows the decorrelating filter (DF) for f ~ t sequence e length and the limiting decorrelating filter (LDF) for s i t e sequence length, respectively. They assumed perfect knowledge of the camer phases of the received signals but require no knowledge of the received energies. The application of decorrelating detectors to asynchronous DSCDMA when the signal phases and energies are unknown at the ELECTRONICS LETTERS 9th June 1994 Vol. 30 z=RAd+y (1) where the diagonal elements of A are complex channel fading gains of average energy Eb, (dlz = 1, and y is the additive noise component of the matched filter output owing to the input AWGN with power spectral density NJ2.After decorrelating z by the procedure described in eqn. 24 [3], we obtain the decorrelated output vector R-lz. Multiplying the decorrelated output at a pilotbit position by the pilot bit value, we obtain a noisy estimate of the fading distortion at the position, where the additive noise terms in different blocks are uncorrelated. Smoothed fading estimates at the other bit positions in the block are obtained by a channel interpolation technique, and the receiver makes decisions for BPSK by the sign of the real part of the product of the decorrelated output and the conjugate of the fading estimate [5]. Simulation results and discussions: The simulation conditions are as follows. The BPSK message data bit rate is 2OkbiWs. The signa- No. 12 929