DESIGN OF REED-SOLOMON FREQUENCY-TIME HOPPING SEQUENCES

Am6rico M. 6. Gorreia Institarto Superior Tknico - DEEC/Telecom. R. Rovisco Pais 1, 1096 Lisbor; Codex, Portugal

email: americo.corre~a~1x.it.pt

his work considers an hybrid A with and without GDMA

e access system where joint frequency and time ~ o p p i n ~ sequences are employed to

pe~Qrmance. The system radio access system

S ~ ~ l t i p l ~ Access) d TDMA with and

w ~ t h o ~ t s p ~ e a d ~ n ~ (CDMA component). The users are o~ho~ona l ly separated into time

ots (in each cell), and within each time slot an a d ~ ~ t i ~ n a l s e p ~ ~ a t i o ~ by spreading codes can be used. This paper deals with how to design hQpp~ng s e ~ u e n c ~ as orthogonal as possible.

The FMA can be operated in F’DD and in TDD. The channel spacing is 1.6MHz both in FDD and in TDD mode, the total available band is 15MHz. TDD does not need separate uplink and downlink bands but operates with a single carrier and is therefore flexible if new asymmetric bands are allocated to UMTS. The multiframe structure of FMA is designed to provide compatibility with the GSM multiframe structure, to make handovers between F’MA and GSM possible, and to offer an efficient realisation of a packet access protocol (MAC).

The TDMA frame length is 4.615ms like in the GSM and it consists of e 64 1/64 time slots of length 72ys (15/208ms)

or

16 1/16 t h e slots of length 288ps (15/52ms)

0 8 1/8 time slots of length 577ps (15/26ms) or

any mix of these time slots of different lengths fitting together in the TDMA frame.

Or

0-7803-4281-x/97/$10.00 01998 ‘BEE

The nonspread bursts of M A are assigned to the 1/64 and 1/16 slots while the spread bursts are assigned to 1/8 slots El].

The physical content of the time slots are bursts of corresponding length. Within each time slot of length 72ps and 288ps, one burst of corresponding length can be transmitted. Within each time slot of length 577ps, up to 8 bursts of corresponding lengthh, separated by different spreading codes, can be transmitted. These multiple bursts within the same time slot can be allocated to different users or partly or all to one and the same user. Each burst consists of a training sequence, two data blocks, and a guard period. Besides the traffic bursts which carry user data, also burst types carrying control information are specified, like e.g., frequency correction burst, synchronisation burst and access burst.

Reed Solomon codewords presented as sequences are adequate for slow frequency hopping (SFH). SFH has inherent frequency diversity, and has the property of randomising cochannel interference, referred as “interferer diversity”. If the system has time synchronous hopping it is possible to design RS frequency sequences orthogonal to each other, i.e., sequences such that no two sequences have the same value at the same time slot. When the number of users is much greater than the number of available sequences (frequencies), the use of RS codewords as frequency hopping sequences allows to minirslise the hits (two or more users hopping to the same &equency at the same time slot). According to the ‘interference averaged’ concept presented in [2] we can include an additional averaging introducing time hopping to increase the capacity of the system To average the interference even more RS hopping sequences

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can be used in this joint frequencyhme hopping scheme.

In the ]literature we can find a lot of papers about time hopping multiple access THMA and also about frequency hopping multiple access FHMA. Only a few deal with joint TH/FH Multiple Access, for instance [3,4]. However, the medium access control (MAC) presented in these papers are different from the one used in FRAMES and those results are not applicable to the MAC of this paper.

To increase the throughput the FRAMES' TDMA frames are time synchronous on adjacent cells (clusters) [2). This assumption will allow us to specify Reed Solomon orthogonal sequences for joint frequency/time hopping. For time asynchronous TDMA frames another set of Reed Solomon hopping sequences is also specified in this document according to the suggestions presented in [5,6]. The expected increase of throughput is equal to the increase of throughput of the Slotted-ALOHA compared to the ALOHA. The easiest way to design the sequences is to think of the problem in one dimension (l-D) and then extend to the 2-D. The design should consider the minimisation of hits. The extension to 2-D gives us an additional degree of freedom to avoid hits. In this document details will be given on how to assign optimally to different services (data rates and/or different frames format) orthogonal frequencyhime hopping sequences. To speclfy the RS sequences we need the background about finite fields (see [7]).

2 RS Hopping Sequences

Frequency and time hopping will be considered in this document as mixed time and frequency division multiple access. In the Frames Multiple Access, traffic channels are designated as combinations of time slot positions and carrier frequency (and codes when spreading is employed). Let q be a prime number, or q = p"' where p is a prime, pick an integer v 2 2 . It can be shown that we can find a set of q" - 4 sequences of length q-l such that any two sequences in the set have at most (v-l) symbols in common (i.e. hits).

If we allow constant sequences then we can have q" sequences.

We need to differentiate between RS hopping sequences based on a prime number q from the other RS sequences based on a number q = p"' , where we need to apply the polynomial representation of the extension field.

2.1 Synchronous RS Hopping Sequences Design

Each sequence is represented by an element of

Sequence period = 4-1. Two sequences hit in at most v-1 positions.

Define P,(X) = C C i X J , where

ci E G F ( q ) .

For each c=(cQ,c~, . . , ,cPl) we get a sequence. We exclude the zero coefficients since this gives a constant sequence.

The sequence is defined as follows:

W q ) .

v-1 .

i=O

fn = S( Pc( ))

where a is a primitive element of G F ( q ) , and S(.) maps field elements to frequencies or time slots. Another way to represent each RS sequence or pattern with length q-1 is

f n = CO ( I , I I . +cI ( I , ad , . . , . , d-2) =

cQ(1,1,1, ..., 1 )+a"(], a , 2, .... , d-')

For two sequences characterised by (co,cl) and

(do 'C',)

if c, = c', then the sequences are orthogonal.

if c, # c', then the two sequences hit at most once. if C I # C'I and CQ = c'g then the two sequences are cyclic shifts of one another.

Taking into account the last property, a shift of certain amount of elements to the left (or right) causes q-l symbols to coincide. This has the effect that time shifted version of transmitted sequences from different users have a high tendency to coincide and cause interference. This

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Frequency and time hopping sequences will be combined, where q is the number of available carriers and q’ is the number of available time slots, N0=qq9.

Generally we can find a set of NI=q(q-l)q’ hopping sequences where there is (at most) one hit between sequences, Lea9 same resource occupied by dzerent users in different cells or clusters (adjacent interference not null), For an assignment of p1 resources to one user Nf=q(q- I)q’/n is the maximum number of active users in different cells, where occurs one bit between users in every sequence period (q-l)(q’/n-l) For both FMA with and without spreading there are different services with different bit rates. Namely 8 Kbps, 64 144 Kbps, 384 Kbps 1024 Kbps and 20 s. This means that instead of a simple nt of n resources to one user, different users might have assigned with nd, n2, n3, n4 different resources, one for each service. For instance, nonspread speech with 8 Kbps requires nI=U.5 physical channel (time slot with 1/64 of frame duration) per sf.ame. This means that in every two frames bits are sent in one time slot. Nonspread data with 144 Kbps requires n2-2 physical channels ( t k slot with 1/16 of frame duration) per frame. Nonspread data with 384 Kbps requires n3=5 physical channels (time slot with 1/16 of frame duration) per frame.

And nonspread data with 2048 Kbps demands n4=I4 time slots with 1/16 of frame duration, per frame.

There is a mix of services and frames in UMTS. Figure 1 shows an example of physical channels (9 frequency carriers and 16 time slots), where a particular mix of services and frames is presented.

imposes strict time synchronism between TDMA frames in adjacent cells.

se que^^^ is represented by an element of

Sequence period = q-1. Two sequences hit in at most v-d positions.

Define where i=O

ci E G F ( q ) .

For each C=(GO,CI , . . . ,c,-l) we get a sequence. We exclude the zero coefficients since this gives 8 constant sequence.

The sequence is defined as follows:

fn = S( P,( d )) fn = CO (l,a7a2 ,... . ,~-2)4-c~(l , l , l ,... , I ) =

co(r,a,d ,... *7a¶”) aa“(I,I,I , e . . , I )

where

& = !$O,fi,fit * - fq-2) ~ o ~ p a r i n g the sequence design for asynchronous adjacent base stations to the previous s y n c ~ o n o u ~ case we conclude that there is a permute between the parameters CO , C I . In this case a shift of certain amount of elements to the left (or right) causes q-1 symbols to coincide. However, this happens with the orthogonal

cated to users belonging to same base station (cell). Time shifted versions of user sequences from different cells (base stations) hit at most once in every time hopping period

There are NO orthogonal resources. For an assignment of one resource to one user No is the maximum number of active users without any occurrence of hits (when hopping exists). For an assignment of n resources to one user NJn is the maximum number of active users without any occurrence of hits, considering only multiple access inside of the same cell or cluster (cochannel interference null).

We consider time synchronous and asynchronous TDMA frames in adjacent cells (or clusters).

9x4

FRKXIWCY 1 TlMF

1 2 3 4 5 6 7 8 9 1 0 1 1 12 1 3 1 4 1 5

Depending on the service rate and if real time RT, or non real time NRT (circuit or packet) it might be interesting to separate RT from NRT services. In a system like FMA assuming that the adjacent base stations have time synchronous TDMA frames there are two possibilities two assign the resources (physical channels) to services and users. I. According to [2] each cluster should use the

same time hopping pattern. However, FMA without spreading has different frames structures depending on the service rate. In this case different time hopping sequences must be chosen from the rows of the tables presented in the appendix for 1/16 frame duration (q9=16) and 1/64 frame duration (q’=64). When the traffic is high enough that all the time slots in one frame are occupied (every position in each table row is already in use) then other(s) time hopping sequence(s) must be selected.

To preserve the orthogonality between users we must assign different carriers of the same frequency hopping pattern to different services and/or users. For 8 Kbps services only one carrier should be enough. Most likely, this kind of service is combined with signaling to fill all the time slots in one frame. For FMAl with spreading the frame structure is the same regardless of the service. However for high traffic where all the time slots in one frame are occupied then more than one time hopping sequence must be selected. Different services should use different carriers of the same frequency hopping sequence. This technique requires a constant track of the occupied time slot, carrier frequency

positions and sequences in current use. One drawback of this technique when RS frequency/time hopping sequences are used, each hopping pattern has length N=q’-I or N=q-1, then the maximum number of resources occupied at the same time is N O = (q’-l)(q-l). It would be easy with this method to find orthogonal or almost orthogonal time and frequency hopping sequences (one hit in every hopping period) for adjacent cells.

11. Another choice is to assign different and orthogonal time hopping sequences for different services and users. Taking into account the tables presented in the appendix, instead of assigning resources filling each table row (same sequence), here the assignment of resources is done filling the table columns (different sequences).

As soon as all the orthogonal sequences are used and the traffic keeps growing then to keep the orthogonality we must assign different frequency hopping sequences to different services (again we start fiIhg the columns instead of rows). This technique requires a constant track of the current time slot, carrier frequency positions for each sequence already in use. It is valid for both FMAl modes. This kind of assignment is shown in Figure 1, where it is seen one carrier with some empty time slots for low rate service and four carriers three of them with all time slots occupied and the fourth with five time slots allocated. With this technique the maximum number of resources occupied at the same time would be NO = 4’4. Under full load conditions it would be possible to find only quasi-orthogonal time and frequency hopping sequences (one hit) for users located in adjacent cells,

When we consider that the adjacent base stations have time asynchronous TDMA frames there are the same two possibilities to assign the resources (physical channels) to services and users. In this case, both methods provide the same maximum number of resources occupied at the same time, per cell, which is No=(q’-l)q.

ACKNOWLEDGMENTS This work has been done in the framework of the project ACTS AC090 FRAMES, which is partly funded by the European Community.

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Oct. 1997.

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[7] R. E. Blahut - Theory and Practice of Error Control Codes”, Addison Wesley, 1983.

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