REDUCEDSTATE SEQUENCE ESTIMATION FOR COMPLEMENTARY CODE KEYING Christof Jonietz  Wolfgang H
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REDUCEDSTATE SEQUENCE ESTIMATION FOR COMPLEMENTARY CODE KEYING Christof Jonietz Wolfgang H

Gerstacker and Robert Schober Chair of Mobile Communications University of ErlangenN urnberg Cauerstrasse 7 D91058 Erlangen Germany Email jonietz gersta LNTde Department of Electrical and Computer Engineering University of British Columbia Vancouve

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REDUCEDSTATE SEQUENCE ESTIMATION FOR COMPLEMENTARY CODE KEYING Christof Jonietz Wolfgang H




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REDUCED–STATE SEQUENCE ESTIMATION FOR COMPLEMENTARY CODE KEYING Christof Jonietz , Wolfgang H. Gerstacker , and Robert Schober Chair of Mobile Communications, University of Erlangen–N¨ urnberg, Cauerstrasse 7, D-91058 Erlangen, Germany, Email: jonietz, gersta @LNT.de Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, Canada, Email: rschober@ece.ubc.ca Abstract - In this paper, reduced–state sequence estimation (RSSE) designed for complementary code keying (CCK) transmission over frequency–selective fading channels is investigated. An

Ungerboeck–like set partitioning of the multidimensional CCK symbol constellation is given. For the proposed RSSE algorithm based on this partitioning, numerical results are provided for a typical indoor wireless channel. A comparison is made with optimum detection and suboptimum decision–feedback equalization (DFE), respec- tively. Keywords - WLAN IEEE 802.11b, complementary code keying, set partitioning, reduced–state sequence estimation I. I NTRODUCTION In the last few years, the increase in wireless and mobile communications as well as internet users has been tremen- dous. High–rate

standards for indoor use with up to 11 Mbit/s have been developed by the IEEE 802.11b committee for wireless local area networks (WLANs). For transmission with and 11 Mbit/s complementary code keying (CCK) [1] has been adopted. In IEEE 802.11b receivers, an equalizer is mandatory for high performance, since radio transmission in offices or densely built outdoor areas suffers from intersymbol interference (ISI) caused by multipath propagation. Previous proposals for equalization schemes for IEEE 802.11b can be found in [2], [3], [4]. In [5] and [6] suboptimum decision–feedback

equalization (DFE) approaches for CCK modulation have been investi- gated. Optimum maximum–likelihood sequence estimation (MLSE) is not feasible when the delay spread of the channel becomes large. An approximation of the MLSE performance for CCK has been derived in [5] for Ricean multipath fading channels and confirmed by numerical results. It has been shown for practical scenarios, that DFE suffers from a performance loss of about dB compared to MLSE. In this paper, suboptimum reduced–state sequence estimation (RSSE) for CCK transmission over frequency selective fading channels is

proposed, which is a promising candidate to close the performance gap between DFE and MLSE. The paper is organized as follows. A short overview of CCK modulation is given in Section 2. In Section 3, a chip–based and a symbol–based system model for CCK transmission, respectively, is established. In Section 4, RSSE tailored for CCK transmission and a corresponding set par- titioning of the multidimensional CCK symbol constellation are introduced. Numerical results are given in Section 5, which demonstrate the good performance of the proposed suboptimum RSSE scheme. Section 6 concludes the paper.

II. C OMPLEMENTARY ODE EYING CCK is a variation of –ary orthogonal keying modu- lation, where one of orthogonal signal code words is chosen for transmission in each time step. In [7], it has been shown that a high power efficiency can be obtained for ISI channels using CCK signals for transmission. The IEEE 802.11b standard employs data rate modes of and 11 Mbit/s. We consider the 11 Mbit/s mode here, since it is most relevant for high–rate applications. In this case, the binary input data sequence is partitioned into vectors of length 8, =[ ...d ∈{ , where refers to transposition

of a vector. The complex–valued code words (also denoted as symbols) are chosen from set with cardinality |C| =2 = 256 according to the rule [1]: =[ ,c ,c ,c ,c ,c ,c ,c =[ j (1) Hence, each code word is composed of 8 quaternary phase- shift keying (QPSK) chips, where is transmitted first in time. The phases , and are determined by the dibits ,d ,d ,d , and ,d respectively, according to the mapping rule } } π/ } , and } π/ III. T RANSMISSION ODEL A. Chip–Based Model First, we consider a discrete–time equivalent complex baseband chip–based model for CCK transmission over

frequency–selective channels. The CCK encoder maps the input data words to symbols : time index at symbol level). A fixed channel or a block fading channel
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CCK encoder CCK demapper RSSE Fig. 1. Block diagram of the symbol–based transmission model. (random impulse response, varying from packet to packet, but being constant within each packet) is assumed. The discrete–time received signal for each packet is given by ]= =0 ]+ (2) which is obtained from –spaced sampling of the continuous–time received signal ( : chip interval, here: =90 ns). ∈{ ,..., q : channel

order), is the discrete–time overall channel impulse re- sponse (CIR), which contains the combined effects of the continuous–time transmit filter, channel, and receiver in- put filter. is a discrete–time additive white Gaussian noise (AWGN) process corresponding to a receiver input filter with square–root Nyquist characteristic and ]= [1] ,c [1] ,c [1] ,...,c ,c ,c is the transmit sequence of an entire packet (frame) consisting of suc- cessive code words with chips ∈{ , ..., B. Symbol–Based Model For block–oriented transmission a symbol–based model is more suitable.

Instead of single chips , entire received vectors are considered, which correspond to transmitted symbols . The block diagram of the symbol–based model is depicted in Fig. 1. The received symbol sequence can be written as the convolution of a finite–length matrix filter impulse response and the transmitted symbol sequence, ]= =0 ]+ (3) where are CIR coefficient matrices, which can be calculated in a straightforward manner from , cf. [5]. is a zero–mean white complex Gaussian vector process with components of variance , and denotes the order of the matrix filter, :

smallest integer ). IV. R EDUCED –S TATE EQUENCE STIMATION A. RSSE for CCK transmission Now, RSSE tailored for continuous transmission of CCK symbols over ISI channels is considered. Recall, that in MLSE a trellis state at a given symbol time is defined as the concatenation of the most recent symbols, ]= 1] 2] ,..., ]] , where ’ denotes the hypothesis for a symbol. Therefore, the ML trellis has |C| states and |C| transitions to and from each state. The underlying idea of RSSE is the construction of a trellis with a reduced number of states [8]. The states of the reduced trellis are

formed by combining the states of the MLSE trellis into hyper states using set partitioning of the multidimensional CCK symbol constellation . The CCK symbol constellation with cardinality |C| = 256 is partitioned into subsets, where ≤|C| and ∈{ ,..., , cf. also [8]. For each delay an individual partitioning level may be selected. Partitioning level has subsets, where the condition ... has to be fulfilled in order to obtain a proper trellis diagram. The symbols are represented by the number of the corresponding subset, which contains . A state at symbol time of the reduced

trellis is defined as ]=[ 1] 2] ,..., ]] (4) representing the subsets of the most recent symbols in the corresponding partitionings. If |C| |C| /J parallel branches emerge from each state to any allowed next state, which form a hyper branch. Each hyper branch represents an ensemble of symbols which are elements of the subset given by Here, two special variants of RSSE with low complexity are adopted. In the first variant set partitioning is applied only to symbol 1] , whereas the past symbols , are taken into account by pure state dependent decision feedback. This means, the state

number corresponds to the subset number of symbol 1] ∈{ ,...,J . Therefore, the number of trellis hyper states corresponds to the number of subsets in the used partitioning. Here, =4 or =8 is used. The corresponding algorithms are denoted by RSSE4 and RSSE8, respectively. In the second variant, set partitioning is applied to symbols 1] and 2] , using =4 and =4 (RSSE4x4), whereas the past symbols , are taken into account only by state–dependent decision feedback. The number of trellis hyper states is =16 In Fig. 2, the trellises of RSSE4 and RSSE4x4 are depicted (RSSE8 is constructed

similarly to RSSE4). In both cases, parallel transitions are shown by single lines and the corresponding trellis states are defined on the left. The performance of RSSE can be improved if a finite impulse response (FIR) matrix feedforward filter is introduced, transforming the overall CIR into its minimum–phase equivalent s,min in order to concen- trate the energy of the overall CIR in the first matrix tap, cf. [5]. Then, the RSSE branch metric for a branch with
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+1] +1] RSSE4x4 trellis RSSE4 trellis [0 0] [0 1] [0 2] [0 3] [1 0] [1 1] [1 2] [1 3] [2 0]

[2 1] [2 2] [2 3] [3 0] [3 1] [3 2] [3 3] [0] [1] [2] [3] Fig. 2. Subset trellises for RSSE4 and RSSE4x4. hypothesis emerging from state is ]) = s,min [0] =1 s,min m, ]] (5) |||| :L –norm of a vector). is the output signal of the feedforward filter and ]] ,..., ]] denote state–dependent decisions (path register contents). The block diagram of the CCK transmission system with RSSE receiver is shown in Fig. 1. and denote the estimates of the transmitted symbols and the transmitted input data word , respectively. In this paper, the overall channel impulse response is assumed to be

known at the receiver. B. Set Partitioning of the CCK Symbol Constellation In this section, the partitioning of the multidimensional CCK symbol constellation is discussed in more detail. As mentioned before, each hyper trellis state consists of the union of a number of MLSE trellis states, which is defined by a suitable set partitioning of the signal constellation. The set partitioning should be such, that the minimum intra subset Euclidean distance min is maximized [8]. Fig. 3 illustrates an Ungerboeck–like partitioning tree of the CCK symbol constellation. Therein, the number of

subsets , the number of symbols in each subset, and the minimum intra subset squared Euclidean distance (MISED) min is specified for each partitioning level ∈{ ,..., In Table 1, the possible squared Euclidean distances α, between symbol pairs are summarized ∈C ) along with the corresponding number Table 1 Mutual squared Euclidean distances α, of symbol pairs α, Number of symbol pairs 83072 122048 1622272 202048 243072 32128 of symbol pairs with that distance (total number of pairs: 256 = 32640 ). The starting point of our considerations for set partitioning is

=3 with =32 subsets. mutual orthogonal symbols are collected in one subset, i.e., within each subset Re Im =0 holds. Therefore, a MISED of min || || || || || || Re =16 results, corresponding to a dB distance increase compared to the minimum distance of =8 subsets for =2 are generated by subsuming four subsets from =3 in each case in such a way that the MISED of min =16 is maintained, but the orthogonality condition within each subset no longer holds because Im =0 occurs. =4 subsets for =1 are generated by subsuming two appropriate subsets of =2 in each case. Then, a MISED of min =12 results.

In =4 128 subsets with min =32 can be found. The subsets are generated by collecting a single symbol (corresponding to subsets at =5 ) and its antipodal partner. The subsets of =3 may be alternatively generated by subsuming four appropriate subsets of =4 in each case. Three other partitionings with =2 16 and 64 subsets may be derived by subsuming two appropriate subsets from =1 and , respectively. But these partitionings do not play any role for RSSE and are disregarded in the following, since they yield just an increased complexity but achieve no gain in the MISED compared to =0 and ,

respectively. In the following, generation rules are given to create the four dibit phases i, for the symbols within each subset ∈{ ,...,J at each partitioning level, where ∈{ refers to the dibit phase index. Basically, the generation rules may be derived by analyzing the phase tables for each subset. For given dibit phases, the corre- sponding symbol is calculated using Eq. (1). With the given generation rules, the set partitioning is completely specified. 1) =0 The phases i, of the symbols are obtained as i, (6) where any choice of ∈{ ∈{ ,is possible.
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256 64 64 6464 32 32 22 11 =0 =1 min =8 =1 =4 min =12 =2 =8 min =16 =3 =32 min =16 =4 =128 min =32 =5 =256 min Fig. 3. Partitioning tree of the CCK symbol constellation. : partitioning level, number of code words per subset within the circle, : number of subsets, min : minimum intra subset squared Euclidean distance. 2) =1 The four dibit phases i, of the th subset are obtained as i, i, (7) where ∈{ ∈{ . The index depends on values of and and can not be chosen independently. i, denotes the initial value of the th dibit phase within the th subset. In Eqs. (8)-(11), the initial

phase values ,..., and the values of depending on and are given. =0: =0 =0 =0 =0 if ∈{ } ∈{ if ∈{ } ∈{ (8) =1: =0 =0 =0 if ∈{ } ∈{ if ∈{ } ∈{ (9) =2: =0 =0 =0 if ∈{ } ∈{ if ∈{ } ∈{ (10) =3: =0 =0 if ∈{ } ∈{ if ∈{ } ∈{ (11) ( ’ denotes logical ’or’.) 3) =2 The four dibit phases i, of the th subset are obtained as , π, π, π, (12) with ∈{ and ∈{ ∈{ The possible initial phase values i, are given by any combination of =0 ∈{ ∈{ ∈{ (13) 4) =3 The four

dibit phases i, for the th subset are obtained as , π, π, π, (14) with ∈{ ∈{ . The initial phase values i, are given by any combination of ∈{ ,π, ∈{ ∈{ ∈{ (15) 5) =4 is partitioned into = 128 subsets. Each subset comprises two symbols, which are rotated by with respect to each other. Note that is contained in all chip phases (cf. Eq. (1)) and simply corresponds to a rotation of the entire symbol V. N UMERICAL ESULTS For numerical results, we consider the Office-C power delay profile depicted in Table 2. The Office-C

profile is a special case of profiles developed by the Joint Technical Commitee (JTC) to characterize indoor radio environments [9]. The corresponding channel coefficients have Rayleigh distributed amplitudes and the root mean square delay spread is RMS 452 ns. For continuous–time transmit and receiver input filtering, respectively, a square–root cosine frequency response with a roll–off factor is employed. A packet consists of = 1000 symbols. A comparison of RSSE4, RSSE8 and RSSE4x4 with DFE is made in Fig. 4. The bit error rate (BER) and packet error rate (PER),

respectively, are depicted versus /N : received energy per bit). Table 2 JTC Office-C power delay profile Path Excess Delay (ns) Rel. Att. (dB) 100 2100 3150 4500 5550 61125 71650 10 82375 21
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10 12 10 −5 10 −4 10 −3 10 −2 10 −1 BER 10 log 10 (E /N ) PA MLSE DFE RSSE4 RSSE8 RSSE4x4 a) 10 12 10 −2 10 −1 10 PER 10 log 10 (E /N ) DFE RSSE4 RSSE8 RSSE4x4 b) Fig. 4. a) BER and b) PER versus /N for the JTC Office-C channel. ’– –’: performance approximation (PA) for MLSE, ’+’: DFE, ’: RSSE4, ’: RSSE8, ’: RSSE4x4. Also, an

approximation for the BER of MLSE which was derived in [5] is shown. The proposed RSSE schemes yield a gain of about dB over DFE and close the performance gap between DFE and MLSE at high SNR’s. The performance of RSSE8 is slightly better than that of RSSE4, and RSSE4x4 is slightly better than RSSE8. VI. C ONCLUSIONS In this paper, RSSE designed for CCK transmission over frequency–selective channels has been proposed. An Ungerboeck–like set partitioning tree of the multidimen- sional CCK symbol constellation with six partitioning levels was presented. A comparison was made between RSSE (4, 8

and 16 states) and DFE and an approximation for optimum detection. It has been shown, that RSSE is a promising candidate in order to close the performance gap between DFE and optimum detection and may be employed to improve the efficiency of WLAN IEEE 802.11b systems. EFERENCES [1] IEEE Standard 802.11b, Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Spec- ifications – Higher Speed Physical Layer Extension in the 2.4 GHz Band, 1999. [2] M.A. Webster et al. ”Rake Receiver with Embedded Decision Feedback Equalizer”, May 2001. United States Patent, No.: US

6,233,273 B1. [3] M.V. Clark, K.K. Leung, B. McNair and Z. Kostic. ”Outdoor IEEE 802.11 Cellular Networks: Radio Link Performance”. In Proceedings of IEEE Int. Conference on Communications , pages 512 –516, April 2002. New York. [4] H. Luo and R.-W. Liu. ”Apply Autocorrelation Match- ing Method to Outdoor Wireless LAN on Co–Channel Interference Suppression and Channel Equalization”. In Proceedings of Wireless Communications and Network- ing Conference , pages 459–464, March 2002. [5] C. Jonietz, W.H. Gerstacker, and R. Schober. ”Receiver Concepts for WLAN IEEE 802.11b”. In Proceedings of the

5th Int. ITG Conference on Source and Channel Coding (SCC) , pages 443–450, Jan. 2004. Erlangen. [6] W.H. Gerstacker, C. Jonietz, and R. Schober. ”Equaliza- tion for WLAN IEEE 802.11b”. Accepted for the IEEE Int. Conference on Com. (ICC), Paris, June 2004. [7] K. Halford, S. Halford, M. Webster and C. Andren. ”Complementary code keying for Rake–based indoor wireless communication”. In Proceedings of IEEE Int. Symposium on Circuits and Systems , pages 427–430, May 1999. [8] M.V. Eyuboglu and S.U.H. Qureshi. ”Reduced–State Sequence Estimation with Set Partitioning and Decision Feedback”. IEEE

Trans. on Com. , 36(1):13–20, Jan. 1988. [9] Joint Technical Comittee on Wireless Access. Final Report on RF Channel Characterization, Sept. 1994.