IMPROVING PERFORMANCE OF MULTIDESTINATION ARQ SCHEMES UNDER HIGH ERROR RATE CONDITIONS

(1)

.

References

1 BERGMANN, 1. R., BROWN, R. C., CLARRICOATS, P. 1. B., and ZHOU, H.: 'Synthesis of shaped-beam reflector antenna patterns', IEE Proc.

H , 1988,135, pp. 48-53

CRONE, G. E.: 'A reconfigurahle mesh reflector antenna'. Proc. of the 6th international conference on antennas and propagation, Warwick, 1989, pp. 112-116

BROWN, R. c., CLARRICOAIS, P. 1. B., and HAI, z.: 'The performance of a prototype reconfigurahle mesh reflector for spacecraft antenna applications'. Proc. of the 19th European microwave conference, London, 1989, pp. 876878

2 CLARRICOAIS, P. 1. B., HAI, Z., BROWN, R. C., POULTON, 0. T., and

3

IMPROVING PERFORMANCE OF MULTIDESTINATION ARQ SCHEMES UNDER HIGH ERROR RATE CONDITIONS

Indexinq terms: Data transmission, Information theory

The throughput eficiencies of a class of continuous multidestination A R Q schemes are evaluated. The operation of the proposed schemes is simpler than that of the schemes studied previously. Numerical results also show that the optimal proposed scheme offers a better throughput performance than the optimal one investigated previously.

Introduction: Because of the increasing demands of point-to- multipoint communication over a broadcast links such as file distribution or teleconferencing links, various multidestination automatic repeat request (MARQ) schemes have been recently proposed and evaluated.14 For example, the performance of the Moeneclaey and Bruneel,' the Sastry6 and Morris' schemes for multidestination environments were examined in Reference 4. It was found that the Morris scheme offers the best throughput performance of the three whereas the Moene- claey and Bruneel scheme is the simplest t o implement a n d provides almost the same throughput performance as the Morris scheme under very high error rate conditions. In Ref- erence 8, a class of MARQ schemes which can achieve a better performance under high error rate conditions were proposed.

The class of MARQ schemes investigated in Reference 8, however, have to distinguish whether a data block is transmitted for the first time or is being retransmitted, resulting in a complicated operation. I propose another class of MARQ schemes with repeated transmissions which can improve the throughput performance and simplify the operation as well.

Investigated ARQ schemes: In the continuous ARQ schemes investigated here, each data block is transmitted with m or fewer copies contiguously t o the receivers. At each receiver, a n error detection procedure is performed on each received copy. A positive (ACK) or a negative acknowledgment (NAK) is sent back to the transmitter according t o whether the copy is received successfully or erroneously. A data block is considered to be successfully delivered as long as each receiver receives successfully at least one of the transmitted copies. If at least one receiver detects all the m copies with error, then, just as in the go-back-N ARQ scheme, the transmitter goes back to and retransmits that data block against with at most m copies. This process is repeated until the data block is successfully delivered.

For convenience, the time to transmit a copy of a data block is called a slot. Consider the transmission of a particular data block. We assume for simplicity that the round-trip delay between the transmitter and any receiver is equal t o N slots. As a result, if m I N , all the m copies of a data block have t o be transmitted before any response can arrive at the transmit- ter. If m > N, then the transmitter may receive an ACK for the data block from each receiver before all the m copies are transmitted. When this occurs, the transmitter will start trans- mitting the next data block rather than continuing transmit- ting the rest copies. Therefore, the phrase 'or fewer' was used

ELECTRONICS L E T E R S 31sr January 1991 Vol. 27 No. 3

.-T.

. -~~ ~ _ _ _ _ ~

in the description of the operation of the investigated ARQ schemes.

It should be obvious that, given the round-trip delay N and the block error probability P,, the optimal maximal allowed number of copies in each transmission depends on the number of unacknowledged receivers. In other words, t o maximise the throughput efficiency, the maximal allowed number of copies should be adaptively adjusted according t o the number of unacknowledged receivers. However, such adaptive protocols could be too complicated and thus may not be favoured from an implementational point of view. Therefore, the MARQ schemes proposed in this Letter are worth studying.

Throughput performance: Let K denote the number of receivers in the system. For simplicity, we assume that transmission errors between copies of data blocks occur independently at each receiver and the feedback channel is error-free.

Consider a particular value of m. Let q , denote the throughput efficiency. Clearly, q(m) = l/L,(K), where L,(K)

represents the average number of transmissions required to successfully deliver a data block. T o compute the value of L,(K), we have t o consider three cases separately.

(i) Case I: m = CO.

The scheme when m = 00 is actually the Moeneclaey and Bruneel scheme and has been examined in Reference 4. The result is

L , ( K ) = S(P,, K )

+

N - 1 ₍₁₎ where

represents the average number of copies transmitted until each of the K receivers receives at least one copy successfully. (ii) Case 2: 1 I m I N .

For this case, all the m copies are transmitted before the transmitter can receive any response. Therefore, L,(K) can be computed recursively by ; = o \ ' I x (P:)'-'[N

-

1

+

Lm(K - i)] (3) with m

+

P:(N - 1) 1 - P: Lm(l) =

Notice that, to compute Lm(K), the values of Lm(l), Lm(2),

.

. . ,

and Lm(K

-

1) have t o be determined first.

(iii) Case 3: N

<

m

<

00.

When m

>

N , the transmitter may receive an ACK from each receiver before all the m copies are transmitted. Let Q j K )

denote the probability that all the K receivers receive successfully the data block in j copies, i.e.

(4) Q,(K) = ( 1 - Pi)"

Furthermore, let R j K ) denote the probability that the K receive the data block successfully exactly at the j t h copy, i.e.

= Q,tK) - Q j - i(K) ( 5 )

Then L J K ) can be evaluated recursively by

m - N m

L J K ) =

1

R j K K + N - 1)+ m R j K )

j = 1 j = m - N + I

x (P:)"-'[m

+ N

-

1

+ Lm(K

-

i)] ₍₆₎ 293

(2)

Again, the values of Lm(l), Lm(2),

. . .

,

and L,(K

-

1) have t o be determined before L,(K) can be computed.

Numerical results and discussions: Fig. 1 shows the throughput efficiencies of the multidestination selective repeat (MSR), the multidestination go-hack-N (MGBN), the optimal scheme studied in Reference 8 (labelled as SUBOPT), and the optimal scheme investigated here (labelled as OPT) against P, for N = 5 and K = 5. The throughput efficiencies of the MSR and

MGBN schemes are equal to l/S(P,, K) and 1/[1 - N

+

N S ( P , , K)], respectively. We can see that OPT is consis-

g 0 4 0 -

L /

\)

3 0 L2 0 : \ \ ‘ x : * ; J El

r

0 0 0 2 0 0 4 0 0 6 0 0 80

,-

M S R OPT

r

0 0 0 2 0 0 4 0 0 6 0 0 80 1 Pe

m

Fig. 1 Throughput eflciency against P , for N = 5 and K = 5

0 80 >.

”

$0 60

”

c

-

a r m TO 4 0

s

5 0 20 0 0 0 2 0 OLO 0 6 0 0 8 0 162512/ P e

Fig. 2 Throughput eflciency against P, for N = 5 and K = 20

2

5

7

2 o L

I

r - 0 0 2 0 0 4 0 0 6 0 0 8 0 1

1675131

P e

Fig. 3 Optimal maximal allowed number of copies against P , N = 5 K = 2 0

_ _ _ _

- N = 5 K = 5

294

tently greater than SUBOPT. The percentage of improvement is about 12.3% at P, = 0.15. Fig. 2 shows similar results for N = 5 and K = 20. Again, the optimal proposed scheme offers a net increase in throughput efficiency with respect t o that studied in Reference 8. According to numerical results, the percentage of improvement decreases as K increases. Fig. 3 illustrates the optimal maximal allowed number of copies m* against P,. We can see that m* is an increasing function of P,

and tends to he larger as K becomes larger.

T.-H. LEE 26th November 1990

Department of Communication Engineering National Chiao Tung University Hsinchu, Taiwan 30050, Republic of China

References

GOPAL, I. s., and IAFFE, J . M.: ‘Point-to-multipoint communication over broadcast links’, IEEE Trans., 1984, COM-32, pp. 10361044

MASK K., TAKENAKA, T., YAMAMOM, H., and SHINOHARA, M.: ‘Go-

back-N ARQ schemes for point-to-multipoint satellite communi- cations’, IEEE Trans., 1983, COM-31, pp. 583-590

SABNANI, K., and SCHWARTZ, M.: ‘Multidestination protocols for satellite broadcast channels’, IEEE Trans., 1985, COM-33, pp. 232-239

CHO, Y. I., and UN, C. K.: ‘Continuous multidestination ARQ schemes for high error-rate channels’, Electron Lett., 1988, 24, pp. 694-895

MOENECLAEY, M., and BRUNEEL, H . : ‘Eficient ARQ scheme for high error rate channels’, IEEE Trans., 1984, 20, pp. 986987 SASTRY, A. R. K.: ‘Improving automatic repeat-request (ARQ) per- formance on satellite channels under high error rate conditions’,

IEEE Trans., 1975, COM-23, pp. 436-4439

MORRIS, I. M . : ‘On another go-back-N ARQ technique for high error rate conditions’, IEEE Trans., 1978, COM-26, pp. 187-189 LEE, T.-H.: ‘Some continuous multidestination ARQ schemes for high error rate conditions’, Electron. Lett., 1990, 26, pp. 168&1687

FREQUENCY ASSIGNMENT FOR SATELLITE MULTILEVEL SCPC SYSTEMS

Indexing terms: Satellite links, Algorithms

A rule-based strategic search method for frequency assignment for satellite multilevel SCPC systems is presented. The quality of solutions improves significantly on published results. In addition, little computation time is required.

Introduction: In

a

recent communication,’ a fast method for searching for the frequency assignment for satellite equal carrier SCPC systems is proposed. It suggests that a carrier he deleted and inserted alternately until no change results in the assignment. In brief, the carrier in a slot containing the largest amount of intermodulation (IM) products is deleted while a carrier is inserted in an unoccupied slot which contains the least amount of IM products. By adding a few practical stra- tegies, the method is extended for the case of multilevel SCPC systems.

T o evaluate the effect of IM noise in satellite communication systems, only third order IM products are considered because the third order IM product dominates the I M power spectrum.’ There are two kinds of third order IM product, triple product, (A

+

E - C), and double product, (2A

-

E). In

the search for quasioptimum assignments, only the triple product is taken into account. This is because there are many more triple than double products and because the triple product is 6 d B higher than the double product in power In multilevel SCPC systems, C / ( N + I M ) is t o be maxi- mised during system design. As N is known and constant, maximisation of C / I M is suflicient in this Letter. T o assess the quality of an assignment, a parameter (C/IM advantage) is defined.5 The C / I M advantage is defined as the ratio of the