Performance Evaluation of L-PPM Links Using Repetition Rate Coding Timucin Ozugury, Mahmoud Naghshinehz, Parviz Kermaniz, C. Michael Olsenz, Babak Rezvaniz and John A. Copelandy y
Communications Systems Center, Georgia Institute of Technology, Atlanta, GA 30332 z IBM Thomas J. Watson Research Center, Yorktown Heights, NY 10598 E-mail : fozugur,
[email protected] fmahmoud, kermani, cmolsen,
[email protected]
ABSTRACT In this paper, we evaluate the performance of infrared communication methods using repetition-rate coding over LPPM wireless links to provide reliable infrared transmission throughout the indoor environments. All receivers adapt the communication data rate by monitoring the channel, and they instruct transmitters to use highest rate if it is possible. Reducing the users data rate by a factor of RR (rate reduction) results in an RR-fold SNR improvement. We analyze how repetition-rate coding improves the capture probability of the infrared modem over L-PPM links. We also discuss the e ect of RR-fold transmission in utilization using Go-back-N and Selective Reject ARQ schemes.
I INTRODUCTION Infrared (IR) communication systems have exible high performance and robust network supporting the various multimedia applications between portable and mobile computers. Wireless IR systems have important advantages over radio systems, such as use of baseband technology, no need to contribute the congestion of radio frequency spectrum, lower cost and physical size. On the other hand, IR signals are a ected by severe noise and disturbance, such as di use propagation paths, background ambient light producing shot noise in the photo-detector, and physical obstructions of the line-of-sight, which in many cases reduce the reliability of the transmitted information [1]. Since IR systems are subject to large dynamic variations of signal-to-noise ratio (SNR) at the receiver depending on the above mentioned properties of IR medium, the system su ers from unacceptably high error rates or loss of connections at a xed data rate. The required SNR improvements can be achieved by reducing the signaling bandwidth accordingly and accepting the reduction of user data rate [1]. Reducing the user data rate by a factor of RR (rate-reduction) results in an RR-fold SNR improvement. With this concept, the receiver monitors the channel conditions and requests up or down-scaling of the user data rate from the transmitter whenever the channel warrants it. The receivers receive the data at the highest data rate possible. Reducing the user data rate can be devised by introducing redundancy in the channel symbol stream. This redundancy
is introduced as the repeated transmission of each symbol. The error rate on the IR channel is the parameter to determine a recommended rate-reduction for future data streams. In this paper, we investigate the capture probability of IR receivers using power-ecient L-position modulation (L-PPM) format with adaptive repetition-rate coding resulting in variable data rates. In order to derive the capture probabilities as a function of SNR, we work on the receiver characteristics to introduce the SNR at the IR receiver. We also show the utilization on repititive-rate coded IR channels where Go-Back-N (GBN) and Selective Reject (SREJ) automatic-repeat request (ARQ) schemes are used for retransmission.
II INFRARED SYSTEM MODEL In infrared system, the multiple access protocol is implemented using a slotted-based scheme, where the user has a new packet to transmit, it does so in the following slot. We consider L-PPM technique, in which we have L slotspin a symbol in which there is only one pulse with power P LT where T is the duration of the slot and P is constant, and the rest is zero. The PPM pulse is chosen to be a raised-cosine signal, which is denoted by ( t) y(t) = sint(t) 1cos ? 4 2 t2
(1)
where is a raised-cosine factor, which can be in the range of [0,1]. Figure 1 shows the eye-diagram display of PPM pulses generated by raised-cosine signals where raised-cosine factor is 0.75 and interference-signal ratio is 10 percent. For calculation of the error probabilities, interfering signal from other stations are taken into consideration. Interfering signal is also assumed as raised-cosine signal shape. The phase of the interfering signals with respect to the intended signal is random. Thus, at the time of sampling, the signal level of the interfering signal may be any value of the signal within the PPM symbol period. Signal-interference is quantized in order to get discrete-time probability density function (pdf). Quantization is the process of breaking the amplitudes of the signals up into a prescribed number of discrete amplitude levels. Quantization process of
1.2
Interfering signal ISR
31ISR/32
1
15ISR/16
PPM pulse amplitude
29ISR/32
14ISR/16
0.8
Quantization steps
0.6
0.4
3ISR/16 4ISR/32
2ISR/16
0.2
3ISR/32
ISR/16
ISR/32
0
0
t1 t2 −0.2 −0.5
−0.4
−0.3
−0.2 −0.1 0 0.1 0.2 Time (normalized PPM pulse duration)
0.3
0.4
0.5
T
Figure 1: Eye-diagram of raised-cosine signal for = 0:75 used for 4-PPM pulse with an interference-signal ratio of %10. interfering signal is portrayed in Figure 2. The total amplitude swing of interference- signal ratio (ISR) is divided into 16 equally spaced amplitude levels. The quantized amplitude levels are taken as ISRi = ISR((i ? 1)=16 + 1=32), i = 1; : : : ; 16: The probabilities of each ISRi can be de ned as pi = (ti+1 ? ti )=T , where T is the duration of L-PPM symbol, and (ti+1 ? ti ) is the duration, which covers the speci c quantization level. For example, the probability of quantization level of 31ISR=32 is (t2 ? t1 )=T according to Figure 2. With these assumptions, the received power at the slot where the pulse is originally placed, can be expressed as p ISRi + noise y1 = P LT 11++ISR M (2) = A1 + noise; i = 1; : : : ; M; where ISRi is the quantized interference-signal ratio, M is the number of quantization levels, and in our case, we take M = 16. Noise at the receiver is white Gaussian with zero mean and variance 2 . The received power at the slot in which no pulse is placed originally, can be expressed as i
i
p i y0 = P LT 1 +ISR ISRM + noise = A0 + noise; i = 1; : : : ; M: i
(3) After this point, we talk only about a \1", which corresponds to the slot with the original pulse in it, hence, a \0" corresponds to the slot without the pulse. The conditional error probabilities in L-PPM slots can be expressed as i
pe1 = pe0 =
M X i=1 M
X i=1
pi Q( Th ? A1 )
(4)
i
pi (1 ? Q( Th ? A0 )) i
(5)
where Q(x) is referred to as standard error function. Th is the normalized threshold where the normalized threshold
Figure 2: Quantization of interference-signal ratio generated by raised-cosine pulse refers to the magnitude of the receivers eye pattern, so that for example a threshold of %50 is right in the middle of the eye, and what the receiver sees is the sum of the desired signal plus the interfering p signal(s). Note that SNR can be de ned as SNR = 10log((P LT )2 =2 ): The conditional error probabilities, pe0 and pe1 , are plotted versus p SNR in Figure 3-4, + ISRM ) is used respectively. Note that, Th = 0:3P LT (1 p in Figure 4-5, where M is 16. If Th < 0:5P LT (1+ ISRM ), it provides a small pe1 probability. Since error in \1" is more important than error p in \0" for L-PPM modulation, we need to take Th < 0:5P LT in order to get small pe1 . Note that, above 14 dB (approximately), the error probabilities decrease very rapidly with small increases in signal. In the next section, we investigate repetition rate coding on IR channels.
III
RR-FOLD L-PPM
SYMBOLS
The repetition rate scheme is an adaptive way of changing the data rate on channel depending channel conditions. The receiver monitors the channel conditions and requests up or down-scaling of the user data rate from the transmitter whenever the channel warrants it. The receivers receive the data at the highest data rate possible. In the system, L counters track the number of pulses detected in each slot. The modem is said to capture the symbol if and only if there is a single count with maximum number. If two or more of the L counters share the maximum count, or if all counters are zero, the symbol is not captured. Even though a realistic modem would still pick the original slot as the "winning" slot by a chance, we shall in this analysis neglect this possibility and assume that a symbol that is not captured always causes a packet error. With respect to capturing the symbol, the modem can capture the symbol successfully and unsuccessfully where the unsuccessful capture will also result in a packet error. Figure 5 displays some successful and unsuccessful symbol capture scenarios of 4-PPM symbol for RR=4-fold repetition coding. In scenario A, the receiver counts the pulses for each slot as follows; the number of pulses in the
0
Original 4-PPM symbol
10
X
Y
Z
T
RR=4-fold repetition rate code word for the symbol X X X X −1
conditional error probability
10
Code word received by destination T Y X X
Y
T
X
Y
T
X
−2
10
Scenario A
pe , ISR= %5 0 pe , ISR= %10 0 pe , ISR= %20 0 pe , ISR= %40
−3
10
Decoded symbol at the destination X
Code word received by destination X T Z T
T
0
Scenario B
Decoded symbol at the destination T
−4
10
0
5
10 15 signal−to−noise ratio (SNR) (dB)
20
25
Figure 3: Conditional error probabilities pe0 versus SNR, normalized Th=0.3. −2
10
−4
10
conditional error probability
X RR ?i (1 ? pe0 )i pRR e0 i i=0 3 2 i X RR RR ? j j 41 ? pe1 5 j (1 ? pe1 ) j =0 3L?2 2 i X RR (1 ? p )j pRR?j 5 (6) 41 ? e0 e0 j j =0
+(L ? 1)
0
10
−6
10
−8
10
−10
10
p , ISR= %5 e1 pe , ISR= %10 1 pe , ISR= %20 1 pe , ISR= %40
−12
10
−14
10
1
−16
10
−18
10
Figure 5: Scenarios for capturing the 4-PPM symbol using RR=4-fold repetition coding.
0
5
10 15 signal−to−noise ratio (SNR) (dB)
20
25
Figure 4: Conditional error probabilities pe1 versus SNR, normalized Th=0.3. slots X, Y, Z and T are 3, 2, 0 and 2, respectively. Since the counter has the maximum number in slot X, the receiver decodes the symbol successfully. In scenario B, the counters have the values of 2, 1, 1 and 4 for the slots X, Y, Z and T, respectively. Thus, the receiver decodes the symbol unsuccessfully by putting the pulse of 4-PPM symbol in slot T. The capture probability of L-PPM symbol using RRfold repetition rate coding, can be expressed in terms of pe1 and pe0 , as
Pcapture =
X RR (1 ? pe1 )RR?i pie1 i i=0 3L?1 2 i X RR (1 ? p )j pRR?j 5 41 ? e0 e0 j j =0
RR?1
RR?1
Speci cally, Eq. (6) can be written as Pcapture = Psuccess + Punsuccess . Figures 6-7 depict 4-PPM symbol capture probabilities for RR-fold repetition rates. As seen from the gure, the symbol capture probabilities increase as RR increases. Figure 7 also shows successful and unsuccessful capture probabilities for 16-fold rate. It shows that higher repetition rate would increase not only the successful symbol capture probability, but also the unsuccessful symbol capture probability. Consequently, non-capture probability decreases by the increase in repetition rate.
IV PERFORMANCE ANALYSIS
We now focus on the analytical results of the IR systems discussed in Section 2 and 3 using SREJ and GBN ARQ schemes. The performance of classical ARQ schemes, SREJ and GBN protocols, are commonly introduced by [4, 5]. We can summarize the ARQ schemes as follows: In GBN scheme, if an error is detected in a packet, or the packet is lost, all subsequent packets are discarded by the receiver, until an uncorrupted version of this packet is received. In SREJ protocol, if a corrupted packet is received, it is discarded. Only the discarded packet is resent. Subsequent received packets are not discarded and thus not resent either. The utilizations of GBN and SREJ ARQ schemes are derived in [5] as (7) U = t(1 ? pe ) (1 ? (1 ? p )w ) GBN
USREJ
Rpe = wt(1R? pe )
e
(8)
Symbol capture probability for 4−PPM using RR=16 Symbol capture probability for 4−PPM using RR=1
1
Symbol capture probability
Symbol capture probability
1
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1
(a)
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Successful symbol capture probability for 4−PPM using RR=16
Symbol capture probability for 4−PPM using RR=2
1
symbol capture probability
Symbol capture probability
1
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0
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e0
1
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(b)
e0
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(b)
Successful symbol capture probability for 4−PPM using RR=16
Symbol capture probability for 4−PPM using RR=4
0.9 0.8 symbol capture probability
Symbol capture probability
1
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0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1
0 1
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0.2 0
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(c)
0.4
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1−pe
0.2 0
0
1
1−pe
0
Figure 6: Symbol capture probabilities for 4-PPM link, (a) RR=1, (b) RR=2, (c) RR=4.
(c)
1−p
e0
Figure 7: (a) Symbol capture probability for RR=16fold on 4-PPM link, (b) successful, and (c) unsuccessful capture probabilities.
0.8 1
RR=1
0.7
0.9
0.8
GBN ARQ SREJ ARQ
0.6
0.5 0.6 RR=16
0.5
RR=8
RR=4
RR=2
RR=1
0.4
Utilization
Packet error probability
0.7
RR=2
0.4
0.3
0.3
RR=4
0.2 0.2
RR=8
0.1 0.1
RR=16 0
0
5
10 15 signal−to−noise ratio (SNR) (dB)
20
25
0
0
5
10 15 20 signal−to−noise ratio (SNR) (dB)
25
30
Figure 8: Packet error probability versus SNR for 4PPM and various repetition rates, ISR= %10.
Figure 9: Utilization of GBN and SREJt ARQ schemes versus SNR for RR-fold 4-PPM, ISR= %10.
where t is the transmission time, pe is the packet error rate, w is the window size, R is the window generation time where R = w(t + p1 ) + p2 + p3 + 2d, d is the one-way propagation delay, p1 , p2 , p3 are the processing time of the transmitted packet, the processing time of the received packet, and the processing time of the received acknowledgment packet, respectively. Figure 8 depicts the packet error rate (pe ) for repetition rate coding where the packet length is 128 bytes. pe1 and pe0 are calculated using Eqs. (4)-(5). Then, we calculate pe as pe = 1 ? [Psuccess ]l=log2 L where l is the packet length and L represents the number of slots in a PPM-symbol. According to the Figure 9, doubling RR achieves approximately SNR gain of 3 dB in each case. In particular, the packet error probability increases rather sharply after a certain point, hence, a doubling of RR should occur before pe rises roughly above 0.1. Figure 9 displays the utilization of GBN and SREJ ARQ schemes for various RR rates. The dashed line shows the performance of GBN ARQ as a function of SNR where adaptive data rate is used. The parameters used in the gure are as follows: The packet length is 128 bytes, the window size is 8, ISR is %10, the processor speed is 100 MHz so that p1 = 40 sec., p2 = 20 sec. and p3 = 40 sec., and the channel capacity is 4 Mbps as nominal. The solid line shows the utilization of SREJ ARQ scheme. The dotted lines show the performance of GBN and SREJ ARQ for di erent RR rates. SREJ ARQ scheme has roughly SNR gain of 2 dB over GBN ARQ scheme. As a result, it is good enough to use GBN ARQ method for infrared systems besides repetition rate coding in order not to deal with in nite bu er sizes at the receiver, which is introduced by SREJ ARQ protocol.
tems to utilize the performance even if bit error rate is very high. In the rate-adaptive IR transmission system, the users are willing to trade the data rate in return for reliable connectivity and better network utilization performance. The results clearly demonstrate the e ectiveness of the adaptive data rate concept. It is expected that the symbol capture probability at the receiver increases remarkably with the parameter RR; moreover, a satisfying and convincing utilization performance is observed with adaptive-rate system. The physical layer of wireless transmission systems should be embedded in a special wireless medium access control protocol layer where an automatic settings corresponding to RR values are estimated by the receiver and are reported to the transmitter.
V CONCLUSIONS
In IR medium, system can not support reliable communication throughout the range of realistic oce environments using xed user data rate if signal-to-noise ratio decreases. In this paper, we evaluate repetition rate coding in IR sys-
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