Design of a Constrained High Data Rate CDMA System

Transcription

1 esign of a Constrained igh ata Rate CA yste andita Lavanis, Vinay Gangadhar,. Vijay Kuar, A. Chockalinga Electrical Counication Engineering ndian nstitute of cience, Bangalore {nandita,vinay,vijay,achockal}@ece.iisc.ernet.in..ash, A. as, A. awar,. Reddy Research Center arat. O. Kanchanbagh yderabad Abstract This paper deals with the design of a high data rate code-division ultiple-access (CA) syste under a specified jaing argin specification as well as hardware and bandwidth liitations. everal choices had to be ade in coing up with the design such as specifying the nuber of subcarriers, choice of spreading codes and the nature of the odulation. The rationale behind each of the choices ade is given. escriptions of transitter and receiver are also included. Relevant siulations of crosscorrelation are also provided.. ntroduction This paper is concerned with the design of a high data rate direct-sequence CA (-CA) syste satisfying the requireents listed in the table below: otation Values yste bandwidth (W ) ρ W z ata rate () ρ bps Jaing argin (J) ρ J db Chip rate (R c = T c ) ρ Rc cps uber of users sall Table : Requireents of a high data rate -CA syste. λ= The restriction on chip rate R c arises since the required speed of any of the hardware coponents eployed in both transitter and receiver is directly proportional to this quantity. The constraints suggested that we eploy ultiple subcarriers to reduce the (required) operating chip rate. eploy soe for of higher-order odulation to reduce the bandwidth requireent. oreover, this higher-order odulation should be built up of K signals since the spreading codes in -CA typically use K signals. With this in ind, we chose a ulti-carrier odulation schee in which there are Λ orthogonal sub-carriers {e jω 0t+ λ t} Λ Tc. urther, each subcarrier is data odulated using a signal that is the superposition of pairwise orthogonal binary pulse wavefors as described below: Let = n and let B denote the linear bi-orthogonal error-correcting code consisting of {±} codewords each of length. Let the set of all codewords be partitioned into subsets B h, h, each of size in such a way that x B h x B h h. We will refer to the subsets B h as subcodes. n our usage, the subcodes will turn out to be the cosets of a linear subcode of the bi-orthogonal code B of size. et = = and note that = n + log. The input binary essage strea fro the source is partitioned into blocks each of size Λ bits. The corresponding real R transitted signal x R (t) is shown below: Λ x R (t) = R{ p(t kt c ) e j(ω 0t+ λ Tc t) () k= λ= [ ( ) c k f(u λ,h, k) + j ( ) b k f(v λ,h, k) ] }, where λ identifies the subcarrier, h identifies the particular subcode B h within the bi-orthogonal code B, {u λ,h = (u λ,h,, u λ,h,,, u λ,h, )} and {v λ,h = (v λ,h,, v λ,h,,, v λ,h, )}, together represent the underlying Λ essage bits. The functions f(u λ,h, k) and f(v λ,h, k) represent the Walsh functions along the and channels associated with the essage vectors u λ,h and v λ,h, respectively. f(.) perfors higher-order orthogonal odulation as well as code ultiplexing of coplex subchannels per subcarrier. inally, {( ) c k + j( ) b k } k= denotes a coplex pseudonoise () spreading sequence, drawn fro a faily of sequences possessing low cross-correlation and out-of-phase autocorrelation values; this code identifies the user, ω 0 is the carrier frequency and T c is the subcarrier spacing, and p(t) is a pulse wavefor that extends only over [0, T c ], where T c is the chip tie. oe coents relating to the transitted signal are now in order: (a) The transitted signal is the superposition of Λ signals which are pairwise orthogonal either on account of the inter-subcarrier frequency spacing or on account of the bi-orthogonal nature of B. Thus, under the assuption of perfect receiver synchronization, the The corresponding {0, } version of this code is the first-order Reed-uller code.

2 receiver can proceed to decode each of these pairwise orthogonal signals independently. (b) The use of the Λ pairwise orthogonal signals allows us to transit Λ bits in chip ties. (c) nterestingly, the transitted signal can also be viewed as the superposition of Λ signals each odulated using a ( +) -A constellation, where = q, corresponding to the signal points { (a + ıb) a, b Z, a, b }. (d) ote that a syste with Λ = and > corresponds to a single-carrier -CA syste whereas setting = and Λ > causes the syste to reseble an O syste (except that no cyclic prefix is used as the channel is assued to be frequency flat).. Transitter and Receiver n this section, we describe the transitter and the receiver of the syste introduced in the previous section. The rest of the paper is divided into the following sections. The transitter and receiver are described in ection. Jaing argin and bandwidth considerations in the design are described in ection. We also present a design exaple in this section. iscussion on the choice of spreading sequences is presented in ection V. A. Transitter The block diagra of the transitter is shown in ig.. This includes the use of an outer rate- EC to reduce the overall bit error rate. The coded essage bits (-bits) are apped on to Walsh functions (-chips) as described in the previous section. The Walsh spreading plays two vital roles, naely, (i) it perfors higher-order orthogonal odulation, and (ii) it also perfors code ultiplexing of data subchannels on each subcarrier. As we will see in ec., the Walsh spreading, in addition to identifying the subchannels, provides jaing argin as well (since Walsh spreading can be viewed as an exaple of the EC spreading discussed in [7]). The signalling rate at the output of Walsh spreader is R c, which is the chip rate. The function of spreading is to perit the desired signal to be separated fro the ultiple-access interference (A) as well as to provide a self-synchronization capability. ote that the spreading does not result in any bandwidth expansion, i.e., the signalling rate at the output of the spreading is also R c. The ulticarrier signal generation is ipleented using the principles of O [],[4], and this explains the presence of the T and blocks. n order to facilitate robust low-ipleentation-coplexity code acquisition, a low rate orthogonal pilot signal is code ultiplexed with data. The pilot code could be the all- Walsh function. The output of the converter is A converted and the resulting coplex signal K odulates the R carrier. B. Receiver The block diagra of the receiver is shown in ig.. The receiver perfors the following functions: (i) R and deodulation, followed by A conversion in the analog front-end, (ii) T operation on the A output saples to generate the individual subcarrier saple streas. followed by (iii) despreading and deodulation, (iv) deodulation block on each subcarrier is a bank of correlators; (v) ilot code acquisition and tracking is perfored using a ypothesis Testing evice (T)[5].. Jaing argin and Bandwidth Considerations A. Jaing argin t can be shown that each subcode B h inherits the iniu distance d in of the parent bi-orthogonal code which equals. The design in ec. and, ay be regarded as one in which spreading is carried out using an EC code and the jaing argin of such a syste can be found discussed in [7] (see ec. 3.). Our syste is different fro that described in [7] in two respects. irstly, our syste eploys ultiple subcarriers, and secondly, we have ultiple pairwise orthogonal signals odulating each subcarrier as opposed to a single signal in [7]. The use of subcarriers reduces the ipact of jaing arising fro a wideband jaer. owever, in the presence of narrowband jaing, the jaing argin of the ulticarrier syste is that possessed by a single subcarrier. Thus it suffices to calculate the jaing argin associated with a single subcarrier signal. Each subcarrier is odulated using a signal that is the superposition of signals. owever, since these are pairwise orthogonal, and are hence easily separable at the receiver end, we ay assue that we are dealing with a subcarrier signal of the for { } x R(t) = R f(u, k)( ) c k p(t kt c )e jω 0t, () k= which is of the for of the signal considered in [7]. Assue that a axiu-likelihood (L) soft-decision decoder is eployed at the receiver. Consider a jaer with power J av. This jaer could be either a narrowband or wideband jaer. Let av = E b T b denote the average power av of the transitted signal. The ratio J av av then represents the jaing-to-signal power ratio. The jaing argin of a CA syste is the largest value of J av av that the syste can tolerate before the perforance, as judged by the bit error probability, becoes unacceptable. n the presence of jaing, the perforance of the L decoder can be given by the following along the lines of

3 Λ Λ R = = c R c Λ = bps Walsh spreading Walsh spreading ilot preading preading λ = x R (t) Rate - EC ilot preading T A Conversion and R odulation Walsh spreading Walsh spreading Λ ilot preading preading λ=λ bits chips chips preading ig.. Transitter for the ulticarrier -CA syste with Λ subcarriers and real subchannels per subcarrier. The processing rates at each odule are shown. the discussion given in [7] : where e ( ) (x) = π ( ) av d in J av t=x (3) e t dt. (4) This indicates that the signal-to-jaing power-ratio av J av is enhanced by a factor of total gain (T G), given by T G = Total Gain roc. Gain d in Coding Gain = d in =. The processing gain here is the ratio of length of the EC code in chips () to the diension of the EC code (). Thus, Jaing argin (db) = Coding Gain (db) + rocessing Gain (db) R 0 (db), (5) where R 0 is the R needed to achieve target bit error rate. or exaple, R 0 is typically about 6 db for K odulation with a rate- outer EC including soe ipleentation argin. We thus have ( ) Jaing argin (db) = 0 log 6.0 ρ J. (6) The J requireent yields ρ J 0( +0.6) 0. (7) B. Bandwidth and chip rate considerations ro ig., the chip rate R c is R c = where = log and = rate constraint R c = ince ρ bps, we have Λ, (8) which yields the chip Λ log ρ R c. (9) ρ ρ R c Λ log. (0) The transission bandwidth W is given by Λ T c W = Λ T c = ro the bandwidth restriction, we have ro (0), () and (), we get { ρrc Λ log ρ in. ence, log. () W ρ W z. (), ρ } W log. (3)

4 Λ Λ y R (t) λ = e-spreading spreading deod deod bps R and deod. A Conversion T EC decoder λ=λ e-spreading spreading Tiing signal deod deod ro T output λ = λ = Λ Λ ilot Acquisition and tracking ig.. Receiver for the ulticarrier -CA syste with Λ subcarriers and real subchannels per subcarrier. The inequality in (3) suggests that one should choose W = ρ W, R c = ρ Rc and Λ to be the sallest power of (to perit T ipleentation) such that Λ ρ W ρ Rc. (4) With this choice of Λ, the outer inequality in (3), takes on the for log () ρ W. (5) Equation (5) places an upper bound on, which together with the lower bound on in (7) places a lower bound on =. We illustrate with an exaple:. Let ρ J = db, ρ Rc = 0 cps, ρ W = 80 z and ρ = 5 bps.. Based on (4), we chose Λ = 4. Equation (7) yields 00.3 so we choose = 8 to keep coplexity at a iniu. The constraint (5) forces 64 when is a power of. This yields = 4. electing = 64 ensures = 4 (a saller value of leads to a lesser AR value). 3. This perits us to operate at data rates as high as ρ W log () = = 5 bps. C. eak-to-average-ower-ratio (AR) As described in ec., each subcarrier is odulated using a signal that is the superposition of subchannel signals, and ay be assued to be of the for as in (). Thus, the AR ay be given as AR = eak value of transitted signal Root ean square value of transitted signal Assuing that the code sequence sybols are rando and independent, the ean squared value (V) of the transitted signal in the duration of the kth chip is given by { Λ ) } E cos {(ω 0 + λtc t ( ) c k f(u λ,h, k) + λ= Λ sin λ= ) } {(ω 0 + λtc t = Λ ( ) b k f(v λ,h, k) ence, AR = Λ Λ = Λ. A range of systes can now be obtained, paraeterized by the particular choice of, yielding varying data rates as well as AR. Table presents three systes that satisfy the above constraints.

5 J ata Rate AR (db) (bps) (db) Table : Exaple of systes which satisfy the requireents W = ρ W = 80 z, R c = ρ Rc 0 cps, ρ J = db. V. Choice of preading On account of their excellent periodic correlation properties, the decision was ade to eploy aily A quaternary sequences [3],[], for carrying out the spreading operation shown in ig.. Let the sequences in quaternary aily A be expressed in the for s A (k) = { } ( ) ca(k) + ı( ) b A(k) for a suitable pair of binary {0, } sequences {c A (k), b A (k)}. The spreading operation in ig. involves a stage of Walsh function spreading followed by a stage of spreading eploying the aily A sequence described above. After incorporating Walsh spreading, we ay regard spreading as being carried out by the coposite spreading sequence s(k) given by s(k) = { ( ) c A(k)+W (k) + ı( ) b A(k)+W (k) } = {( ) c(k) + ı( ) b(k)}, where W (k) = f(u λ,h, k), W (k) = f(v λ,h, k) are Walsh functions, each having length = n. A plot of the siulated aperiodic correlation properties of the coposite spreading sequence is shown in ig. 3 which shows that the cross-correlation values are not too high given that the CA syste is to be designed to support only a sall nuber of users. An alternative is to use -sequences in place of Walsh functions and binary spreading codes along and ars which incorporate the -sequences used to carry data in place of quaternary aily A. A replaceent of this type is not expected to change data rate and jaing argin values. uch failies of binary sequences ay readily be constructed using for exaple, either alternative quaternary sequence failies [] or alternately, supersets of binary Gold sequences [8] and are expected to lead to lower values of aperiodic cross-correlation. or lack of space as well as for clarity of presentation, we oit the details. The sequences in aily A are extended to length n fro length n by appending a single at the start of each sequence. This is to ake the copatible with Walsh functions which are of length n. A siilar procedure is followed in the W-CA standard. [6] o of occurances 9 x Correlation agnitude igure 3: istogra of real part of aperiodic cross correlation for the coposite spreading sequence obtained by superiposing length-8 Walsh functions on quaternary aily A sequences, having extended length 8.) V. Conclusion The design of a high data rate -CA syste under a specified jaing argin as well as hardware and bandwidth constraints was presented. t is shown that higher data rates and efficient bandwidth utilization can be achieved by using Walsh functions, which serve the purposes of higher-order odulation as well as EC spreading in conjunction with ultiple, orthogonal subcarriers. The design also akes use of coposite spreading sequences derived fro quaternary faily A sequences and Walsh functions. The constraints placed on the high data rate CA syste are suarized in equations (7)-(5), which also show how one can go about selecting syste paraeters to eet the constraints. References []. ara and R. rasad, Overview of ulticarrier CA, EEE Counication agazine, pp 6 33, eceber 997. []. V. Kuar, T. elleseth, A. R. Calderbank and A. R. aons, Jr., Large ailies of uaternary s with Low Correlation, EEE Trans. nfor. Theory, vol. 4,o., pp arch 996. [3] A. R. aons Jr. and.v. Kuar, On a Recent 4-phase esign for CA, ECE Trans. Coun., vol. E76- B, o. 8, pp August 993. [4] Z. Wang and G. B. Giannakis, Wireless ulticarrier Counication, EEE Counication agazine, ay 000. [5] A. Viterbi, CA: rinciples of pread pectru Counication, Addison-Wesley, June 995. [6] 3 rd Generation artnership roject website: [7] J. G. roakis, igital Counication, cgraw-ill, 4th edition, 00. [8] O.. Rothaus, odified Gold codes, EEE Trans. nfor. Theory, vol. 39, pp , 993.