Performance of asynchronous slow frequency-hop ... - IEEE Xplore

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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 48, NO. 2, FEBRUARY 2000

Performance of Asynchronous Slow Frequency-Hop Multiple-Access Networks with MFSK Modulation Kwonhue Choi and Kyungwhoon Cheun, Member, IEEE

Abstract—In this paper, the performance of asynchronous slow frequency-hop spread-spectrum multiple-access networks where each user transmits , -ary symbols per hop using -ary frequency-shift keying (FSK) modulation with noncoherent demodulation is investigated. Expressions for the decision variables are derived for a given multiple FSK (MFSK) symbol within a hop hit by 0 interfering users under additive white Gaussian noise and Rayleigh fading channel models. For the special case when = 2, an accurate analytic approximation for the average error probability is derived as a function of and 0 and semianalytic Monte Carlo simulations are performed to estimate the probability of error for larger than 2. The results are used to investigate the dependence of the average symbol error probability on and . Finally, the effect of enforcing phase transition between the MFSK symbols within a hop is investigated.

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Index Terms—Error analysis, frequency-hop communication, frequency-shift keying, multiaccess communication, spread-spectrum communication.

I. INTRODUCTION

I

N THIS paper, average symbol error probabilities are obtained to accurately analyze the performance of asynchronous frequency-hop spread-spectrum multiple-access (AFHSS-MA) networks. We concentrate on slow hopping networks employing noncoherently orthogonal multiple frequency-shift keying (MFSK) modulation to transmit , -ary symbols per hop along with matched filter demodulation at the receivers. The lowest level of performance criteria on which all other performance criteria are based in such networks is -ary symbol error probability, given that the hop in the interfering users. which the symbol is transmitted is hit by What is usually done in analyzing slow frequency-hop systems (or is to upperbound the error probability by 1) whenever a symbol is hit by other users in the network. Recently in [1] and [2], research on average symbol error probability caused by multiple-access interference (MAI) was performed for the case when one MFSK symbol is transmitted bound may per hop, and it was observed that the lead to gross inaccuracies. In [1], an analytic approximation for the average error probability was derived that very accurately . In [2], fits the simulation results for the case when

Paper approved by B. Aazhang, the Editor for Spread Spectrum Networks of the IEEE Communications Society. Manuscript received January 17, 1997; revised October 31, 1997. This work was supported by the Korea Science and Engineering Foundation (KOSEF) under Grant 923-0800-004-2. The authors are with the Department of Electronic and Electrical Engineering, Pohang University of Science and Technology (POSTECH), Pohang 790-600, Korea (e-mail: [email protected]). Publisher Item Identifier S 0090-6778(00)01575-0.

estimates for the average symbol error probabilities were obtained via semianalytic Monte Carlo simulations using the expressions of the decision variables derived for the case when . Using the estimated symbol error probabilities, it was that maximizes shown that there exists an optimum value of the normalized throughput taking into account the bandwidth and time expansion associated with the modulation order . Here, we extend the results of [1] and [2] to the case of slow frequency hopping where , MFSK modulated symbols are transmitted per hop. Previous efforts aimed at specifying the effect of MAI on slow FHSS-MA networks can be found in [3] and [4]. In [3], an approximation was derived for the conditional interfering users for probability of error when a hop is hit by a synchronous hopping system using MFSK modulation. The synchronous hopping assumption considerably simplifies the problem due to the fact that the hop and thus the symbol epochs among the users are synchronized. This reduces the problem to computing the error probability of the MFSK receiver under continuous multiple tone interference which can be solved using techniques similar to those employed in [2] and [6]. It was also assumed in [3] that signal magnitudes of different tone positions, where at least one user is transmitting, are identical regardless of the number of users transmitting the tone, which is a rather unrealistic assumption. In [4], approximations for the symbol error probabilities were derived using the characteristic function approach for asynchronous slow frequency-hopping system using MFSK modulation with phase continuity maintained between symbols in a hop. An assumption was that the separation between the MFSK frequencies is large enough so that the interference possessing a given MFSK frequency has no effect on the outputs of the filters matched to other MFSK , frequencies. For the binary FSK (BFSK) case and it was observed in [1] that this assumption (Geraniotis’ assumption) gives optimistic results compared to results when the separation between the two BFSK frequencies is set to ( : symbol duration), the minimum frequency separation required for orthogonality. For the slow hopping case , we show that with phase continuity maintained with between the MFSK signals within a hop, Geraniotis’ assumption results in a slight lower bound to the actual symbol error probabilities. However, with 180 phase transitions between the MFSK signals within a hop,1 we find that Geraniotis’ assumption results in a significant deviation from the exact , an approximation based value. For the case when 1We shall show that 180 phase transitions between MFSK signals within a hop provide significantly improved performance over the phase continuous case under the additive white Gaussian noise (AWGN) channel.

0090–6778/00$10.00 © 2000 IEEE

CHOI AND CHEUN: ASYNCHRONOUS SFH MULTIPLE-ACCESS NETWORKS WITH MFSK MODULATION

on the union bound and the Geraniotis’ assumption is derived in [4]. Though the union bound/Geraniotis’ assumption bound and results in a large improvement over the Gaussian approximation, simulation results reveal that its accuracy degrades as the number of interfering users increases. The main issue of this paper is to provide an accurate evaluation of the average symbol error probabilities for slow , , AFHSS-MA (SAFHMA) networks as a function of . In addition to the AWGN channel, the error probaand bility analysis is also performed for the fading channel where the amplitude of the signals received from the active users in the network is assumed to suffer from independent Rayleigh , an accurate analytic apfading. For the case when proximation for the average error probabilities as a function and are derived using methods similar to those of of is larger than 2, semi[1] and [4]. For the case when analytic Monte Carlo simulations are performed to estimate the error probabilities using the expressions derived for the decision variables. We find that without fading and with continuous phase between symbols in a hop, the average symbol -ary symbol transmitted within a error probability of an ) abruptly increases hop hit by one interfering user ( as increases and eventually saturates for large , whereas , the average symbol error probability is virtufor ally independent of . With Rayleigh fading, the average symbol error probability shows only a minor variation as a for all values of . function of Another issue of interest is the effect of introducing phase transitions between the MFSK signals transmitted within a hop in order to reduce the effect of MAI. Numerical and simulation results reveal that the average symbol error probability gradually decreases as the phase transition value increases and reaches a minimum at 180 phase transitions resulting in a significant decrease in the average error probability compared to the phase continuous case under the AWGN channel. This result should be practically useful since 180 phase transitions can be implemented simply by alternating the polarity of successive MFSK signals within a hop. With Rayleigh fading, introducing phase transition between symbols has only a small effect on the average symbol error probability. The organization of this paper is as follows. In Section II, the system and channel models assumed in this paper are briefly described, and in Section III, the decision variables are derived interfering for a given MFSK symbol within a hop hit by users. In Section IV, an accurate analytic approximation for the for the error probability is derived as a function of and . In Section V, results from the previous sections case of are used to analyze the dependence of the system performance on and . Finally, conclusions are drawn in Section VI.

II. SYSTEM AND CHANNEL MODEL The system considered in this paper is identical to the identical active users (transAFHSS-MA network with mitter–receiver pairs) described in [1] and [2] except that multiple -ary symbols may be transmitted during a hop.

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The transmitters send , -ary symbols per hop using noncoherently orthogonal MFSK modulation in one of the available frequency slots. At baseband, the MFSK frequencies alsymbols are lotted to the Hz

(1)

being the duration of one -ary symbol. Assuming with that the hopping pattern of the receivers are perfectly synchronized to those of the corresponding transmitters, the complex baseband equivalent of the signal presented to a given receiver (for example, receiver number one) during a hop duration (for ), when the hop is hit by interfering example, duration users, may be written as follows:

(2) where received signal power of the th transmitter. • ’s Assuming perfect power control2 without fading, , and under independent have a constant value of ’s are independently, identically Rayleigh fading, distributed (i.i.d.) Rayleigh-distributed random variables with probability density function (pdf)

• • •

number of -ary symbols per hop. hop duration equal to . if otherwise.

delay of the th user assumed to be uniformly disand independent between users.3 It tributed on is assumed that perfect synchronization is maintained be. tween paired users giving the th symbol transmitted by the th user • , assumed to be independent for during different and taking on values in with equal probability. random phase of the MFSK signal corre• , assumed to be independent sponding to symbol and uniformly distributed on . for different In order to consider the case when phase discontinuity is introduced between symbols within a hop, we let be , where denotes the phase transition value between consecutive MFSK signals within a hop. For the case when the phase continuity •

2It is straightforward to generalize the results to the case when the received signal power is different, as in [1]. 3The results for the case of synchronous hopping may be obtained as a special case of the results presented in this paper by setting t = 0 for all k .

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between MFSK signals within a hop is maintained, is . set to 0 so that we have complex white Gaussian noise process with • where is the two-sided power spectral density (PSD) of the AWGN at is the Dirac delta function the receiver input. Also, denotes the complex conjugate of . and In order to demodulate the th symbol of the first user, the rein the interval and comceiver observes decision variables given below [10] putes the Fig. 1.

Patterns of symbol hit.

(3) The index of the largest decision variable is chosen as the estiof the th symbol. mate III. DECISION VARIABLES In this section, we derive expressions for the decision variused for the computation of the probability of error ables and the semianalytic Monte Carlo for the case when . simulations for , By substituting (2) into (3) and normalizing by are obtained as folnew equivalent decision variables lows:

say that a partial hit by the th transmitter has occurred if the interference from the th transmitter is present for only a fracis tion of the th symbol duration, in which case set to (1,0) or (0,1) corresponding to a hit from the left and from the right, respectively. Finally, there is the case when the th user’s signal is absent during the th symbol duration in spite of the fact that a hop hit has occurred. For this case, the value of is set to (0,0). Using the fact that is uniformly , the probability of a full hit denoted by distributed on , the probability of a partial hit denoted by , and the probability of a symbol hit (either full hit or partial hit) denoted by as a function of are given as follows:

(6) (4)

and zero otherwise, and for the case when there is no fading and follows the Rayleigh distribution with pdf for the case with Rayleigh fading. is a complex Gaussian random variable repreThe term with zero senting the contribution of the AWGN on , where . The mean and is the MAI contribution of the th interfering user on term and can be written as follows:

where

for

(5) and denote the normalized outputs of where the terms the th branch of the demodulator due to the two symbols transmitted by the th interfering user during the observation interval denoted by , , as shown in Fig. 1. is used to distinguish the The binary random vector hit patterns by the th interfering user as shown in Fig. 1. The hit pattern may be categorized into the following three cases. We say that a full hit by the th transmitter has occurred for the th symbol if the interference from the th transmitter is present for the entire duration of the th symbol , in which case is set to (1,1). Second, we

(7) (8) Under the assumption that the users employ independent Markov hopping patterns, only partial hits are possible for . However, as increases, decreases to zero, and and converge to . Hence, for large values of , and full hits will be dominant. We also note that do not depend on the location of the symbol within a hop. taking on the four From (6)–(8), the probabilities possible values are obtained as follows:

(9)


Since we have assumed that the users employ independent is independent hopping patterns, the random vector for different . relative Denoting the normalized delay of the symbol as , which are i.i.d. and unito formly distributed on [0,1) and the phases corresponding to two , as , , respectively, can be shown in symbols (10) and (11) (see Appendix), shown at the bottom of the page, are 1 for the case when there is no where fading and are i.i.d. random variables following the same distrifor the case with fading. For the special case when bution as with phase continuity between symbols within a

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(16) and denote the magnitude and the argument of a and complex number , respectively. Since a constant phase transiis maintained between BFSK symbols within a hop, tion of , (12) may be simplified as follows: i.e., (17) where

simplifies to . hop, Equations (4) with (5) and (9)–(11) are used in the semianalytic Monte Carlo simulations to estimate the average symbol interfering users and error probability within a hop hit by . also in the analytical computations for the case when IV. ANALYTIC APPROXIMATION ERROR PROBABILITY FOR For the case when

FOR THE

(19)

, we may rewrite (5) as follows:

(14)

’s are independent for different and are uniformly Since , so are the ’s. Thus, ’s are indedistributed on pendent for different and spherically symmetric conditioned , , , , , on the random vectors . When the phase continuity beis zero tween the BFSK symbols within a hop is maintained, . For the special case of a full hit with and we have equal to can easily be seen to be with phase continuity. We first compute the error probability conditioned on the . Substituting from (17) random vectors and : into (4) yields the following expressions for

(15)

(20)

(12) where

,

,

(18)

,

are defined as

(13)

(10) otherwise

(11) otherwise

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where we have assumed that without loss of generality.4 Since the demodulator chooses the index of the larger and , the probability of error given and of conditioned on is given as

where denotes the expectation with respect to . Since are independent for different , we may write

(21) and conditioned on From (20), it is clear that are sums of independent and spherically symmetric complex random variables, and hence, they themselves are spherically symmetric. Furthermore, in [1], it was observed that the numerical results for the error probability obtained under the assump’s are independent for different , thus implying that tion that and are independent results in a very close fit to ’s can simply the simulation results. With this assumption, be treated as i.i.d. random variables uniformly distributed on . Using the property of complex random variables with circular symmetry, we may write the conditional probability of error as follows [1], [8]:

(27)

and since lows:

’s are i.i.d., this may further be simplified as fol-

(28)

(22) where and

and are the characteristic functions of , respectively, conditioned on , given as follows:

where (29)

(23) (30) (24)

, , and are the characteristic functions of , , and , respectively. Hence, can be computed to be

Here

The next step is to compute can easily be shown to be

,

, and without fading with fading

, which (31)

(32)

(33) is the energy per bit and is the Bessel where function of the first kind of order defined as [13] (34)

(25) Now, in order to evaluate over as follows:

, we need to average (25)

Substituting tity

from (33) into (29) and (30) with the idenyields , as follows: (35)

(26) (36)

M>

4Note that we cannot do this for the case when 2, since the error probability is dependent on which symbol was transmitted [2].

Using (31) and (32), (28) can be computed to be (37), shown at the bottom of the next page, where the signal-to-noise ratio is


defined to be . Numerically evaluating the expectations in (35) and (36) and the integral in (26) with (37) enables us to for the case when . evaluate With frequency-hopping slots, the probability of a hop hit by an interfering user for the asynchronous Markov hopping [5]. Hence, the average error probamodel is given by given that there are active users in a network bility is given as follows:

(38) In order to directly evaluate the above summation, the evaluare required. ations for can be obtained without evaluating the However, in with and above summation by replacing with a new random vector replacing with the distribution given in (39), shown at the bottom of the page. V. NUMERICAL RESULTS First, we assess the accuracy of the numerical computation for the BFSK case and the semianalytical simulation used to ) estimate the symbol error probability for the MFSK ( case. In all of the following results, 5000 errors were colcomlected for each simulation data. In Table I, puted using (26) for the BFSK case under AWGN without fading are given along with the simulation results using the dB for vardecision variables given by (20) for with and without 180 phase ious combinations of transitions between symbols. We observe that the numerically computed values using (26) give very accurate predictions of the simulation results for all cases considered. For the case , semianalytic Monte Carlo simulation results when obtained using (4) were compared with results obtained via waveform level simulation using sampled waveforms of (2). The results verified the accuracy of the semianalytic simulations.

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Before we present the main numerical results, we evaluate the accuracy of the Geraniotis’ assumption and the union bound in [4] when the minimum separation ( Hz) between the MFSK signals for orthogonality is employed for . First, in Table II are shown the values of with and without Geraniotis’ assumption for and dB under AWGN without fading. As was ob, Geraniotis’ served in [1] for the BFSK case with assumption results in optimistic estimates of the error probability. As increases, the deviation is more pronounced with 180 phase transitions within a hop than it is for the case when continuous phase is maintained between symbols. This is due to the fact that the phase discontinuities in the interfering signals increase the cross interference terms which are neglected under the Geraniotis’ assumption. For the Rayleigh fading channel, Geraniotis’s approximation is more accurate than for the AWGN case since the cross interference terms have less effect on the error probability due to the large variance of the Rayleigh fading amplitudes of the interfering signals. Next, Table III compares the results obtained using the union bound with the Geraniotis assumption5 against the accurate results obtained via semianalytic simulations using dB, , and various (4) for . We note that for small values of , the values of Geraniotis’ assumption dominates resulting in a slight lower increases, the union bound dominates rebound, but as sulting in an upper bound. In Fig. 2, the effect of introducing phase discontinuity on the average error probability is shown. The numerical and for , , and simulation results for are plotted as the function of the phase transition . We observe that the average symbol error probability monotonically decreases as the phase transition approaches 180 . This can be explained by the fact that with phase discontinuity, the MAI has a broader power spectrum and 5We note that the union bound can only be applied under the Geraniotis’ assumption, which by itself was observed to give a lower bound.

without fading (37) with fading

(39)

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TABLE I COMPARISON OF NUMERICAL COMPUTATION AND SIMULATION RESULTS FOR P

COMPARISON OF P

TABLE II

(L; K ), WITH AND WITHOUT GERANIOTIS’ ASSUMPTION. M = 32, E =N = 30 dB, NO FADING

Fig. 2. Simulation results and numerical calculation for probability of error as a function of ' for L ,M , and K ; ; . E =N dB, no fading.

1

= 128

(L; K ): M = 2, E =N = 30 dB, NO FADING

=2

=1 3 5

= 30

thus possesses lower PSD levels at the MFSK tone positions compared to the case when the phase continuity between symbols is maintained. This explanation is acceptable

if we consider the fact that tone jamming is approximately 3 dB more effective compared to noise jamming [6], [7] for frequency-hop systems. Also, we observe that the optimal phase transition minimizing the average error probability is 180 . Especially, for , 180 phase transitions significantly decrease the average symbol error probability com). However, as pared to the phase continuous case ( increases, the improvement due to phase discontinuity increases, the is reduced. This is due to the fact that as power spectrum of the MAI component spreads out which is what we aimed to achieve by introducing the phase tran, the sitions between symbols. That is, for large value of power spectrum sufficiently spreads out due to the addition of a large number of independent interfering signals that the additional introduction of the phase transitions has little effect. without fading In Figs. 3 and 4 are the plots of and dB. We obfor as a function of is serve that the behavior of . For initially highly dependent on and saturates for large . The amount of increase with increase is more apparent for the case with continuous phase between symbols in a hop. The reason for this is that for


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TABLE III COMPARISON OF THE UNION BOUNDS AND THE SIMULATION RESULTS FOR P (L; K ), L = 1, E =N = 12 dB, NO FADING

Fig. 4. Average error probability without fading as a function of L with K = 1; 2; 3; 4; 5; for M = 16. E =N = 30 dB with and without 180 phase transitions between symbols.

Fig. 3. Average error probability without fading as a function of L with K = 1; 2; 3; 4; 5; for M = 2. E =N = 30 dB with and without 180 phase transitions between symbols.

, all symbol hits are either a partial hit or a full hit from one interfering user. Full hits result in much higher error probabilities compared to partial hits, especially with continuous phase between symbols in a hop. Since the proband satability of a full hit monotonically increases with . As increases, the MAI urates, so does more closely resembles the Gaussian noise due to the central limit theorem, and thus the error probability is determined by the total average power of the MAI. Since the average interference power of a partial hit is one half of that of a full hit, the average multiple-access interference power observed during a symbol duration is proportional to which is irrespective of . This explains the insenon for larger values of . sitivity of Fig. 5 shows the simulated average symbol error probusing (4) when the signals from the ability active users in the network undergo independent Rayleigh fading. We observe that in this case, the error probability and also on whether or shows minor dependence on

Fig. 5. Average error probability with Rayleigh fading as a function of L with = 30 dB with and without 180 phase transitions K for M = 8. E =N between symbols.

not phase continuity between symbols is maintained. The Rayleigh fading amplitudes of the interfering signals are the determining factor that dominates the signal-to-noise ratio contributions at the correlator outputs which makes the symbol error probability less insensitive to other factors. Another interesting observation is that initially, the symbol even for . error probability slightly decreases with This is due to the fact that the symbol error probability is more dependent on whether or not a symbol is hit than whether it is a full hit or a partial hit since a partial hit with a large power can still cause errors with high probability. This, along with the initial rapid decrease of with explains this observation. Finally, the average symbol error probability with frequency slots for and with and . We observe without fading are shown in Fig. 6 for that the performance degradation due to slow hopping and

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(A.2) By using the definition that gral in (A.1) can be written as

, the inte-

(A.3) which may be evaluated as follows:

Fig. 6. Average error probability with q = 1000 frequency slots and K active users in a network for L = 1 and 28 with and without fading (E =N )(E =N ) = 30 dB.

continuous phase among the symbols is quite large for the AWGN channel whereas the degradation is much smaller for the Rayleigh fading case as may be expected from the results shown in Figs. 4 and 5. In Fig. 6, we observe that the reduction in the number of active users ( ) supported ) with avby the network due to slow hopping ( is 67% and erage symbol error probability equal to 7%, respectively, for the cases with continuous phase and 180 phase transitions between symbols without fading. On the contrary, with independent Rayleigh fading, we observe approximately a 4% and 8% increase in the number of active users supported for continuous phase and 180 phase tran. sition slow hopping networks, respectively, with These observations indicate that different strategies must be employed depending on channel characteristics. VI. CONCLUSIONS In this paper, accurate evaluation of the symbol error probabilities for asynchronous slow FHSS-MA networks using MFSK modulation was performed. Under the AWGN channel, considerable difference in performance between slow and fast hopping systems was observed. On the other hand, only a minor dependence of the network performance on the number of symbols transmitted within a hop was observed for the case with independent Rayleigh fading. In addition, it was observed that markedly improved performance may be achieved by introducing 180 phase transitions between symbols in a hop for the AWGN channel. APPENDIX In order to derive in (10) and (11), we need to evaluate the following integrals:

(A.1)

otherwise. (A.4) The integral in (A.2) can also be evaluated as follows in a similar way:

otherwise. (A.5) Combining these results with the definition we obtain (10) and (11). REFERENCES

,

[1] K. Cheun and W. E. Stark, “Probability of error in frequency-hop spreadspectrum multiple-access communication systems with noncoherent reception,” IEEE Trans. Commun., vol. 39, pp. 1400–1410, Sept. 1991. [2] K. Cheun and K. Choi, “Performance of FHSS multiple-access networks using MFSK modulation,” IEEE Trans. Commun., vol. 44, pp. 1514–1526, Nov. 1996. [3] S. W. Kim, Y. H. Lee, and S. M. Kim, “Bandwidth tradeoffs among coding, processing gain and modulation in frequency hopped multiple access communications,” Proc. IEE Commun., vol. 141, pp. 63–69, Apr. 1994. [4] E. Geraniotis, “Multiple-access capability of frequency-hopped spreadspectrum revisited: An analysis of the effect of unequal power levels,” IEEE Trans. Commun., vol. 38, pp. 1066–1077, July 1990. [5] E. A. Geraniotis and M. B. Pursley, “Error probability for slow-frequency-hopped spread-spectrum multiple-access communications over fading channels,” IEEE Trans. Commun., vol. COM-30, pp. 204–217, May 1982. [6] K. Cheun and W. E. Stark, “Performance of FHSS systems employing carrier jitter against one-dimensional tone-jamming,” IEEE Trans. Commun., vol. 43, pp. 2622–2629, Oct. 1995. [7] M. K. Simon, J. K. Omura, R. A. Scholts, and B. K. Levitt, Spread Spectrum Communications Handbook. New York: McGraw-Hill, 1994. [8] J. S. Bird, “Error performance of binary NCFSK in the presence of multiple tone interference and system noise,” IEEE Trans. Commun., vol. COM-33, pp. 203–209, Mar. 1985.


[9] R. G. Gallager, Information Theory and Reliable Communications. New York: Wiley, 1968. [10] J. G. Proakis, Digital Communications. New York: McGraw-Hill, 1983. [11] S. Kim and W. Stark, “Optimum rate Reed–Solomon codes for frequency-hop spread-spectrum multiple-access communication system,” IEEE Trans. Commun., vol. 37, pp. 138–144, Feb. 1989. [12] M. B. Pursley, “Frequency-hop transmission for satellite packet switching and terrestrial packet radio networks,” IEEE Trans. Inform. Theory, vol. IT-32, pp. 652–667, Sept. 1986. [13] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York: Wiley, 1972.

Kwonhue Choi was born in Mokpo, Korea, on December 5, 1970. He received the B.S. and M.S. degrees in electronic and electrical engineering from the Pohang University of Science and Technology (POSETCH), Korea, in 1994 and 1996, respectively. Since 1994, he has been a Research Assistant at the Department of Electronic and Electrical Engineering, POSTECH, where he is currently working toward the Ph.D. degree. His current research interests are performance analysis of spread-spectrum communications with emphasis on frequency-hopped multiple-access networks and demodulation algorithms for digital modem including GA-HDTV receiver and LEO satellite communication receiver.

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Kyungwhoon Cheun (S’88–M’89) was born in Seoul, Korea, on December 16, 1962. He received the B.A. degree in electronics engineering from Seoul National University, Seoul, Korea, in 1985, and the M.S. and Ph.D. degrees from the University of Michigan, Ann Arbor, in 1987 and 1989, respectively, both in electrical engineering. From 1987 to 1989, he was a Research Assistant at the EECS Department at the University of Michigan, and from 1989 to 1991, he was with the Electrical Engineering Department at the University of Delaware, Newark, as an Assistant Professor. In 1991, he joined the Electronic and Electrical Engineering Department at the Pohang University of Science and Technology (POSTECH), where he is currently an Associate Professor. He also served as an Engineering Consultant to various industries in the area of mobile communications and modem design. His current research interests include cellular and packet radio networks, algorithm and VLSI design for digital modems, military communication networks, synchronization/equalization for radio systems, and turbo codes.