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Maximum Throughput of FHSS Multiple-Access. Networks Using MFSK Modulation. Kwonhue Choi, Associate Member, IEEE, and Kyungwhoon Cheun, Member ...
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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 52, NO. 3, MARCH 2004

Maximum Throughput of FHSS Multiple-Access Networks Using MFSK Modulation Kwonhue Choi, Associate Member, IEEE, and Kyungwhoon Cheun, Member, IEEE

Abstract—Optimum values for the modulation order , code rate , and the number of frequency-hop slots maximizing the network throughput are obtained based on simulations for frequency-hopped spread-spectrum multiple-access networks, where -ary Reed–Solomon (RS) code symbols are transmitted per hop, and each -ary RS code symbol is transmitted using log -ary frequency-shift-keying-modulated signals. Network throughput is evaluated under additive white Gaussian noise and Rayleigh fading channels. For the case when the received RS symbol is not interfered by multiple-access interference (MAI), a closed-form expression for the symbol-error probability is derived, and for the case when the symbol is interfered by MAI, simulated symbol-error probabilities are used. It is shown that the optimum is four or eight, irrespective of the channel environment and the number of users. The optimum code rate is determined primarily based on the channel environment and or . It is also shown does not show much dependence on that for the case of synchronous hopping under Rayleigh fading at high signal-to-noise ratios, the difference in instantaneous power among the interfering users significantly improves the performance, compared with the case when there is no fading. We also consider the case when the receiver erases the symbols that are interfered and compare the performance with the case of the hard decisions receiver. Index Terms—Frequency-hop (FH) communication, frequencyshift keying (FSK), multiple-access communication.

I. INTRODUCTION

I

N THIS PAPER, optimization is carried out on the system parameters of frequency-hopped spread-spectrum multiple-access (FHSS-MA) networks employing Reed–Solomon using -ary frequency-shift keying (RS) codes over (MFSK) modulation based on simulated symbol-error probabilities (SEPs). Some previous works on system parameter optimization for FHSS-MA networks using MFSK modulation are given in [1]–[8]. In [1] and [2], optimization of the code rate and the number of FH slots is performed using a simple upper bound to the error probability, i.e., the error probabilities for symbols interfered

Paper approved by G. Cherubini, the Editor for CDMA Systems of the IEEE Communications Society. Manuscript received March 27, 2000; revised September 15, 2000 and March 13, 2003. This work was supported by the Ministry of Information Communication in the Republic of Korea, under the Information Communication Fundamental Technology Research Program. K. Choi is with the School of Electrical Engineering and Computer Science, Yeungnam University, Gyeongsangbuk-do 712-749, Korea (e-mail: [email protected]). K. Cheun is with the Division of Electronic and Computer Engineering, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Korea (e-mail: [email protected]). Digital Object Identifier 10.1109/TCOMM.2004.823616

, irby at least one other user (hit) is assumed to be respective of the modulation alphabet size . Although these results are meaningful in that they explicitly give analytical expressions for the optimum selection of system parameters and resulting network throughput, they lack accuracy due to the fact bound to the SEP is excessively that the underlying pessimistic [3], [4]. It is, therefore, necessary to investigate the problem of optimizing the system parameters in connection with the accurate SEP analysis, as introduced in [3] and [4]. In [5], a simple approximation to the -ary SEP was derived for a synchronous hopping system, which as a function of as a was used to find the optimum modulation alphabet size function of the number of active users in the network for a given number of FH slots and code rate . However, the opin [5] is different from the global optimum, which timum is obtained in this paper by jointly optimizing with and in the entire space of the set, and thus, the maximum throughput in [5] is far off from the true achievable throughput. Furthermore, the approximation formula for the SEP used in [5] cannot be applied to the case with fading,1 nor to the case of asynchronous hopping. In [6], the tradeoff among code rate, the are inprocessing gain, and the modulation alphabet size vestigated by using the same approximate error formula used , where the modulain [5] for a given total bandwidth, and tion alphabet size was restricted to be equal to the RS code less than 32 were symbol size, and thus, small values of not considered. However, it was shown in [4] that the optimal modulation alphabet size which maximizes the throughput of the FHSS-MA network employing capacity-achieving codes is four or eight. This implies that it is necessary to consider system models where the modulation alphabet size is smaller than the RS code symbol size. In this paper, we evaluate the performance of RS-coded FHSS-MA networks using MFSK modulation for various values of code alphabet size , modulation alphabet size , code rate , the number of FH slots , and the number of code symbols transmitted in a hop. For the case when the symbol is hit by other users, which means that there exist other users’ signals in the corresponding FH slot during the symbol duration, simulated SEPs are used. For the case when the received symbol is not hit, a closed-form expression for the code SEP is derived. The performance with respect to these system parame-triples achieving ters is investigated, and the optimum the maximum throughput are obtained for several values of . In order to obtain fully optimized system parameters, we set no constraint on the total system bandwidth, and thus, no 1We will show that there is a significant difference between the approximate error formula used in [5] and the simulation results for the case with fading.

0090-6778/04$20.00 © 2004 IEEE

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Fig. 1. Block diagram of the considered system.

explicit relation between and . Instead, the throughput is appropriately normalized by the bandwidth expansion, due to these parameters. It is shown that the optimum is four or eight, irrespective of and , and the channel environment which agrees with predicted by analysis based on networks emthe optimum ploying capacity-achieving codes [4]. The optimum code rate is determined primarily based on the channel environment, and or , and the opdoes not show much dependence on . timum number of FH slots is approximately proportional to We also consider the case when the receiver erases the symbols that are hit using perfect side information and compare the performance with the hard decisions receivers. For synchronous hopping systems, where all hit symbols suffer full hits, a receiver erasing hit symbols offers significantly higher maximum throughput than a hard decisions receiver. For the hard decisions receiver, comparison between asynchronous and synchronous hopping systems is included. Under Rayleigh fading, there is a little difference in the maximum throughputs between asynchronous hopping systems and synchronous hopping systems. On the other hand, without fading, asynchronous hopping systems perform significantly better than the synchronous hopping systems. In addition to the optimization of system parameters, we also make some interesting observations on the uncoded error performance of different systems. For example, for the case of synchronous hopping, the error probability under Rayleigh fading actually turns out to be smaller than that corresponding to the nonfading additive white Gaussian noise (AWGN) channel. For the case of asynchronous hopping, we extend the results of [3] , and the dependence of the SEP on to the case when is investigated. This paper is organized as follows. In Section II, the system model is presented and the decision variables used for the semianalytic simulations are derived. In Section III, the normalized throughput is defined and the numerical optimization for the -triple is described. In Section IV, the uncoded error performance of different systems are investigated, and the nu-triple and the maxmerical results for the optimized imum normalized throughputs are presented. Finally, conclusions are drawn in Section V. II. SYSTEM MODEL The block diagram of the considered system is shown in identical Fig. 1. We consider a FHSS-MA network with active users (transmitter–receiver pairs) which is similar to those described in [3] and [4].2 The considered system model may be employed in the variety of applications, such as 2The reader may refer to [10]–[12] for the complexity of the signal processing and the practical implementation issues associated with designing a FHSS modem.

uplink cellular mobile networks, wireless local area networks (WLANs) or wireless personal area networks (WPANs). In this paper, we generalize the system model of [3] and [4] to include may be smaller the case where the modulation alphabet size than the code symbol size , so that one code symbol may be transmitted using multiple MFSK signals with a requirement should be an integer. We consider the that -ary RS block codes with symbol size , block length information symbols per block. Each encoded -ary symbol is modulated with , and noncoherently -ary FSK signals and RS code symbols are orthogonal transmitted during each hop duration. Fig. 2 illustrates the hopping model of the considered system. We assume perfect interleaving so that symbol errors within a given codeword are independent. users in total, i.e., one desired user When there exists interfering users, in the same FH slot during a symbol and is the bit duration) duration (say of the desired user, the complex baseband equivalent of the reis given as follows: ceived signal

(1)

where index for numbering users, which include one desired user and interfering users. We take for the desired user without loss of generality; received MFSK signal energy from the th transmitter. Assuming uplink power control that the received instantaneous and average powers from all users are identical for nonfading and Rayleigh fading channels, respectively, have a constant value of , given by where is the bit energy, and under Rayleigh fading, are mutually independent exponential random variables with an identical probability density function (pdf) ; number of -ary symbols per hop; MFSK signal duration; if otherwise;

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Fig. 2.

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 52, NO. 3, MARCH 2004

Hopping model of the considered system.

delay of the th user. It is assumed that perfect synchronization is maintained . between paired users, giving For the case of asynchronous hopping, is assumed to be independent between users and uniformly distributed on . The results for the case of synchronous hopping may be obtained as a special case by setting for all ;

In order to demodulate the th MFSK signal of the first user, in the interval and the receiver observes decision variables given below computes the

th -ary subsymbol value transmitted by the th user during , assumed to be independent for different , and taking on values in with equal probability;

III. NORMALIZED THROUGHPUT AND OPTIMUM -TRIPLE

random phase of the MFSK signal corresponding to , assumed to be independent for different , and uniformly distributed on . We let be , i.e., a 180 phase transition is introduced between the consecutive MFSK in a hop symbol, which was found to offer the minimum average error probability in [3]; complex white Gaussian noise (WGN) process with , where is the two-sided power spectral density (PSD) of the AWGN at the receiver input. Also, is the Dirac delta function, and denotes the complex conjugate of .

(2) The index of the largest decision variable is chosen as the estiof the th symbol. mate

A. Average SEP When a code symbol is hit by interfering user(s), the interference may last for several MFSK signals, or even the enMFSK signals comprising the code tire duration of the symbol. Then, the consecutive MFSK signals belonging to the code symbol undergo highly correlated interference, and thus, the error events of consecutive MFSK signals are not indepeninterfering users, the -ary code dent. Thus, when there are SEP, given denoted by , is obtained by generating and simulating the following probability:

(3) is the th -ary subsymbol value belonging to where the corresponding -ary symbol of the reference user.

CHOI AND CHEUN: MAXIMUM THROUGHPUT OF FHSS MULTIPLE-ACCESS NETWORKS USING MFSK MODULATION

When there is no interfering user, i.e., , a closed-form expression for the SEP can be derived. Without fading, the error MFSK signals belonging to the -ary symbol events of are independent. Thus, is calculated as (4) where as [14]

is the

-ary FSK signal error probability given

for synchronous hopping, and hopping [10].

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for asynchronous Markov

B. Normalized Throughput and Optimum

-Triple

, defined as the The normalized throughput average number of successfully transmitted information bits per second per Hertz, is given by [5], [6] b/s/Hz

(5) , and is the PSD of with background noise. When the received signal undergoes fading, there exists the dependency of the error events of MFSK signals belonging to a -ary symbol, even without interference, since the MFSK signals belonging to a -ary symbol undergo the same fading process that remains constant during the symbol duration. Under Rayleigh fading, the instantaneous signal-to-noise ratio (SNR) is given by , where is an exponential random variable with . Thus, under Rayleigh pdf fading is given as follows:

(12) where

denotes bandwidth of one FH slot given by denotes the -ary symbol duration given by denotes correct decoding probais the code rate. With bility of the RS codeword, and and into (12), can the substitution of be written as follows: [b/s/Hz] (13) For the case when the receiver simply makes hard decisions on each symbol, is given as [15]

(6) By using the polynomial expansion technique, (6) can be calculated as follows [9]: (14)

(7)

For the case when the receiver erases the symbols that were hit is given as using perfect side information [2], [15]

where

(15) (8)

where and bilities, given as

denote erasure and error proba-

(9) (10) active users in the network, the avWhen there exist erage error probability of -ary RS code symbol denoted by is obtained by averaging over the possible values of as follows:

(11) is the hit probability, where is the number of FH slots, and defined as the probability of another transmitter hopping to the same FH slot in any part within the symbol duration, with

(16) (17) Substituting (14) and (15) into (13), we obtain the normaland . Thus, for ized throughput as a function of , the normalized throughput is a function a given value of and . We divide the of three independent variables optimization process into two steps as follows. First, for a and , the optimum pair, denoted given value of maximizing the normalized by throughput, is found numerically as follows:

(18)

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P

TABLE I

K ) FOR Q = 256 AND L = 1

(

Next, we optimize for the given with replaced by to complete the optimization -triple that maxiprocess, resulting in the optimum mizes the normalized throughput as follows: (19) where

(20)

IV. NUMERICAL RESULTS AND DISCUSSIONS For all the numerical results given in this section, we assume uplink power control that the received instantaneous and average powers from all users are identical for nonfading and Rayleigh fading channels, respectively. Table I shows the simulated SEPs for asynchronous hopping systems and synchronous hopping systems with various modulation alphabet sizes for and . We note that there is significant difference between the simulated SEPs and the bound, as with the case when the modulation alphabet size is equal to the code symbol size [3]. For example, the simulated error probability of 0.105 for the case of asynchronous hop with is much smaller than the bound, . which corresponds to 0.9961 for For the case of synchronous hopping, a more accurate approximate error formula is found in [5], where the MFSK symbol interfering users, is given as follows: error, when there are (21) and the

-ary SEP

is calculated as follows: (22)

However, there is also considerable difference between the simulated results and the approximate error formula given in (22), especially under Rayleigh fading and high SNRs. For example, the simulated SEP of 0.527 for the synchronous case, when and dB under Rayleigh fading, is much smaller than 0.9, which is predicted by (22). This is because (22) is based on the assumption that the error events of the MFSK signals belonging to a -ary code symbol are independent, however, the error events of the MFSK signals are highly correlated, due to the constant fading amplitude within the -ary code symbol. We also observe from Table I that the SEPs under Rayleigh fading are smaller than those without fading for the case of synchronous hopping. The difference in the SEPs is especially at high SNRs. To explain significant for small values of this, consider the case when the background noise is negligible. Then, without fading, the error probability of a -ary code symbol is close to for small values of , even . Although is approximately when [6], which is just half of the worst-case error probability of MFSK signal, the -ary code SEP increases and approaches as the number of MFSK signals debelonging to a -ary code symbol increases, i.e., as creases. This is because the MFSK signals belonging to the code symbol have the independent error events, and all of them should be successfully demodulated for a correct -ary code symbol demodulation. On the other hand, with Rayleigh fading, the fading amplitudes are assumed to remain constant throughout a -ary code symbol duration. Therefore, the MFSK signals belonging to a -ary code symbol are correctly demodulated all together if the desired user’s fading amplitude is larger than that of the interfering user under a negligible background noise environment. The fading amplitudes are assumed to be identically distributed among the users, and thus, the probability that the desired user’s fading amplitude is larger than that of the interfering user is equal to 0.5. This explains the ’s are off from and are maintained reason that

CHOI AND CHEUN: MAXIMUM THROUGHPUT OF FHSS MULTIPLE-ACCESS NETWORKS USING MFSK MODULATION

P (K ) for Q = 256; M = 4; q = 100, asynchronous hopping, = 1; 2; 10; 100, and E =N = 10 dB.

Fig. 3. L

to be around 0.5 for and dB, irrespective of in Table I. This suggests that a well-designed intentional power randomization scheme may be found to improve the multiaccess capability of the synchronous hopping networks under nonfading channels.3 Another important observation from Table I is that asynchronous hopping achieves smaller -ary code SEP compared with synchronous hopping for all cases. The amounts of reduction in -ary code SEP via asynchronous hopping are significant, especially for the case of no fading. This is due to the fact that, in the case without fading, asynchronous symbol timing between the MFSK signals of a desired user and an interfering user spreads out the PSD of interference [3], and thus, maintains the maximum of the interference decision variables, given in (2) to components contained in be always smaller than the desired user’s signal component. On the other hand, with fading, although asynchronous symbol timing spreads out the PSD of the interference, the independent fading amplitudes among users makes it still possible that the decision maximum interference component contained in variables is larger than the desired user’s signal component. for The average SEPs versus the number of active users the case of asynchronous hopping are shown in Figs. 3 and 4 for dB and dB, respectively, for , and . Unlike the case when the modulation alphabet size is equal to the code symbol size [3], the SEPs monotonously decrease with increasing for all cases considered. Especially under Rayleigh fading and high SNRs, the decrease in the SEP with increasing is significant. This is due to the fact that with Rayleigh fading, even a partial hit, which denotes the case when the interfering user’s signal is present only for a fraction of the desired user’s symbol duration, is apt to generate symbol errors if the instantaneous power of the desired signal is smaller than that of the interfering signal. Thus, as increases, the SEP decreases and converges, due to 3In the case without multiple-access interference (MAI), i.e., K = 0, the intentional power variation causes performance degradation, since the constant power transmission is optimal for the AWGN channel.

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(K ) for Q = 256; M = 4; q = 100, asynchronous hopping, P = 1; 2; 10; 100, and E =N = 30 dB.

Fig. 4. L

the fact that the hit probability, given as , decreases . For the case of synchronous hopping, we and converges to do not have to compare the cases with different , since the hit probability is not a function of and the symbol timings are synchronized among users, and thus, the characteristics of MAI during a symbol duration is identical, irrespective of . It is also shown in Figs. 3 and 4 that the difference of SEPs between fading and no-fading cases decreases with increasing are SNR. Under low SNR, fading results in , which causes the large differcomparable to between fading and no-fading cases. Howence of is negligible, compared ever, under high SNR, for both cases, and thus, the difference with between the two cases is mainly determined by of . and versus In Figs. 5 and 6, are plotted for various values of , for which is an , and dB without integer for fading and asynchronous hopping. As with previous results given in [1] and [2], obtained by ignoring the background noise error bound for hit symbols, and employing the rapidly converges to a constant with increasing , and increases approximately proportional to . We also note that the dependence of ) on is . However, it is shown minor, except for very small values of and , based on the that error bound, significantly deviate from the results based on error bound simulated error probabilities. The results in a misleading prediction that a much lower code rate and a much larger number of FH slots should be used. In Fig. 7 versus are shown the maximum throughput for various values of . Here also, as with the results is nearly constant, irrespective in [1] and [2], of the traffic level above about 20 active users. However, the maximum achievable throughputs are significantly larger than error bound. For example, those predicted by the , based on the error bound for and , is 0.028 b/s/Hz, which is only about

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Fig. 5. Optimum code rate r (K ; M ) for Q = 256; M = 2; 4; 16; 256, asynchronous hopping, L = 1; E =N = 30 dB, and no fading.

Fig. 7. Maximum throughputs W (K ; M ) for Q = 256; M = 2; 4; 16; 256, asynchronous hopping, L = 1; E =N = 30 dB, and no fading. Solid line: simulation. Dashed line: (Q 1)=Q bound.

0

(25) (26)

Fig. 6. Optimum number of FH slots q (K ; M ) for Q = 256; M = 2; 4; 16; 256, asynchronous hopping, L = 1; E =N = 30 dB, and no fading.

19% of the corresponding result based on the simulated error probabilities given as 0.15 b/s/Hz in Fig. 7. It is also seen is four, regardless of , and from Fig. 7 that the optimal is larger than that that the maximum throughput for even though has twice the bandwidth for . This is due to the expansion per FH slot than that of fact that the -ary SEP with is much smaller than , as shown in Table I, and overrides the larger that of per-FH-slot bandwidth expansion. is approximately proporFrom the fact that tional to , and and converge increases, we compare the asymptotic performance of as the systems considered, using asymptotic parameters defined as follows: (23) (24)

where denotes the optimal bandwidth expansion. Since these values cannot be computed, and previous results show and are sufficiently stable at that optimum values of , for the numerical results, we approximate by . In Table II, , along with the -triples, are listed. We note that is consistently four or eight for asynchronous hopping systems, and four for synchronous hopping. From these results, we may conclude for FHSS-MA networks using MFSK that the optimal modulation is always four or eight, and is insensitive to other , SNR, , and whether the system parameters, including received signal fades or not. It is also found from Fig. 5 and Table II that the optimum code rate is determined mainly based on the SNR and whether the received signal fades or not, and or . From Table II, does not show much dependence on some important comparisons can be also made between different systems based on the maximum achievable throughputs. For the case of synchronous hopping, it is observed that a receiver erasing hit symbols with perfect side information offers significantly higher maximum throughput than a hard decisions receiver. Although Table II does not include the case of asynchronous hopping with a receiver erasing hit symbols, we know that as increases, the hit probability converges to , and thus, the maximum throughput converges to that of the synchronous hopping system with a receiver erasing hit symbols. Also, comparing the maximum throughand puts for the case of asynchronous hopping with hard decisions decoding with those of synchronous hopping erasing all hit symbols, we find that the synchronous hopping system offers higher maximum throughput, except for the no-fading case with high SNRs. For the case when the receiver makes hard decisions, there is only a small difference in the maximum achievable throughputs between asynchronous and synchronous hopping systems under Rayleigh fading. On the

CHOI AND CHEUN: MAXIMUM THROUGHPUT OF FHSS MULTIPLE-ACCESS NETWORKS USING MFSK MODULATION

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TABLE II MAXIMUM THROUGHPUTS AND OPTIMUM PARAMETERS FOR VARIOUS SYSTEMS

other hand, without fading, the maximum throughputs of the asynchronous hopping system is significantly larger than those of the synchronous hopping system. As can be expected from results given in Table I, we find that for the case of synchronous hopping, significantly increased performance can be expected for Rayleigh fading channel at high SNRs, compared with nonfading channels. Also, for the case of asynchronous hopping, is it is observed that the maximum throughput for higher than that for , especially under Rayleigh fading and high SNRs, due to the improvement in the uncoded error performance previously observed in Figs. 3 and 4. From Table II, we note that the significant differences are among -triples between the cases found only in and . This implies that the improvement of in the uncoded error performance with increasing affects the optimization in the form of the reduction of the number of FH slots. V. CONCLUSION In this paper, optimum system parameters maximizing the network throughput are obtained for an FHSS-MA system employing RS codes with MFSK modulation based on simulated error probabilities. We found that optimum modulation alphabet size is consistently four or eight, regardless of other system parameters, including code symbol size, the number of symbols per hop, SNR, the number of active users, and whether the received signal fades or not. Optimum code rate is shown to be determined primarily based on channel environment, and does not show much dependence on modulation alphabet size, code symbol size, or the number of symbols per hop. It was also shown that for the case of synchronous hopping under Rayleigh fading and high SNRs, the difference in instantaneous power

among the interfering users significantly improves the performance, compared with the case when there is no fading. For the case of synchronous hopping, a receiver erasing hit symbols results in higher maximum throughput than the simple hard decisions receiver, and independent Rayleigh fading improves the performance of hard decisions receiver at high SNRs. REFERENCES [1] K. Cheun and W. E. Stark, “Optimal selection of Reed–Solomon code rate and the number of frequency slots in asynchronous FHSS-MA networks,” IEEE Trans. Commun., vol. 41, pp. 307–311, Feb. 1993. [2] 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. [3] K. Choi and K. Cheun, “Performance of asynchronous slow frequency-hop multiple-access networks with MFSK modulation,” IEEE Trans. Commun., vol. 48, pp. 298–307, Feb. 2000. [4] K. Cheun and K. Choi, “Performance of FHSS multiple-access networks using MFSK modulation,” IEEE Trans. Commun., vol. 44, pp. 1514–1526, Nov. 1996. [5] S. W. Kim and S. Kim, “Optimal MFSK signaling for Reed–Solomon coded frequency-hopped multiple-access communications,” Electron. Lett., vol. 30, pp. 1921–1923, Nov. 1994. [6] S. W. Kim, Y. H. Lee, and S. M. Kim, “Bandwidth tradeoffs among coding, processing gain and modulation in frequency hopped multiple access communications,” IEE Proc. Commun., vol. 141, pp. 63–69, Apr. 1994. [7] K. Yang and G. L. Stuber, “Throughput analysis of a slotted frequency-hop multiple-access network,” IEEE J. Select. Areas Commun., vol. 84, pp. 588–602, May 1990. [8] C. P. Hung and Y. T. Su, “Diversity combining considerations for incoherent frequency hopping multiple access systems,” IEEE J. Select. Areas Commun., vol. 13, pp. 333–344, Feb. 1995. [9] K. Choi, “Error probability of -ary symbol consisting of multiple channel symbols under Rayleigh fading,” IEEE Commun. Lett., vol. 8, pp. 48–50, Jan. 2004. [10] 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.

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[11] M. P. Fitton, D. J. Purle, M. A. Beach, and J. P. McGeehan, “Implementation issues of a frequency-hopped modem,” in Proc. Vehicular Technology Conf., vol. 1, July 1995, pp. 125–129. [12] R. C. Dixon, Spread Spectrum Systems with Commercial Applications. New York: Wiley, 1994. [13] M. K. Simon et al., Spread Spectrum Communications. Rockville, MD: Computer Science, 1989. [14] J. G. Proakis, Digital Communications. New York: McGraw-Hill, 1983. [15] A. M. Michelson and A. H. Levesque, Error-Control Techniques for Digital Communication. New York: Wiley, 1985.

Kwonhue Choi (S’94–A’99) received the B.S., M.S., and Ph.D. degrees in electronic and electrical engineering from Pohang University of Science and Technology (POSTECH), Pohang, Korea, in 1994, 1996, and 2000, respectively. From 2000 to 2003, he was with ETRI, Korea as a Senior Research Staff Member and worked on the development of efficient transmission algorithms for satellite communications. In 2003, he joined Yeungnam University, Gyeongsangbuk-do, Korea. His research interests are performance analysis of CDMA networks and adaptive transmission algorithms for broadband wireless communications systems in a fading environment, and efficient modulation/demodulation schemes for multicarrier CDMA systems, OFDM, and DTV systems.

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Kyungwhoon Cheun (S’88–M’90) 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, University of Michigan, and from 1989 to 1991, he was with the Electrical Engineering Department, University of Delaware, Newark, as an Assistant Professor. In 1991, he joined the Division of Electrical and Computer Engineering, Pohang University of Science and Technology (POSTECH), Pohang, Korea, where he is currently a 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 turbo codes, RA codes, space–time codes, MIMO systems, UWB communications, cellular and packet radio networks, and OFDM systems.