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chronous slow frequency-hop spread-spectrum multiple-access. (SFHSS-MA) networks transmitting bits per hop using binary differential phase shift keying ...
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 53, NO. 9, SEPTEMBER 2005

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Uplink Performance of Slow Frequency-Hop Multiple-Access Networks Using Binary DPSK Jooyeol Yang and Kyungwhoon Cheun, Member, IEEE

Abstract—The uplink performance of synchronous and asynchronous slow frequency-hop spread-spectrum multiple-access (SFHSS-MA) networks transmitting bits per hop using binary differential phase shift keying (BDPSK) is analyzed under the additive white Gaussian noise (AWGN) and Rayleigh fading channels. Analytic expressions for the average conditional bit error probabilities given a hop is hit by interfering users are derived. Results show that SFHSS-MA networks using BDPSK achieve nearly twice the maximum normalized network throughput compared to networks using BFSK under both AWGN and Rayleigh fading channels. Index Terms—Differential phase shift keying, error analysis, frequency-hop communication, multiaccess communication, spreadspectrum communication.

I. INTRODUCTION

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N this paper, the uplink performance of slow frequency-hop spread-spectrum multiple-access (SFHSS-MA) networks transmitting bits per hop using binary differential phase shift keying (BDPSK) is investigated. Coherent detection is usually not feasible in frequency-hop (FH) systems due to insufficient hop durations. However, in slow frequency-hop (SFH) systems transmitting multiple symbols per hop, differential detection is applicable if the first symbol of each hop is used as a pilot symbol. One clear advantage of using BDPSK over its noncoherent counterpart, i.e., binary frequency shift keying (BFSK), is that the required bandwidth for BDPSK is approximately half that of BFSK. Thus, for a given available RF bandwidth, twice as many frequency hop slots are available with BDPSK than with BFSK. Hence, if the conditional error probability given a hop is hit by a given number of interfering users is comparable, FH systems employing BDPSK should have the advantage due to the decrease in the hit probability. The derived analytical results indicate that this is indeed the case for sufficiently large values of . The error performance of FHSS-MA networks using FSK has been extensively studied in [10]–[16]. On the other hand, analytical results for the error performance of SFHSS-MA networks employing BDPSK are not yet available. However, the performance of SFH systems in the presence of continuous tone-jamPaper approved by M. Zorzi, the Editor for Multiple Access of the IEEE Communications Society. Manuscript received February 6, 2004; revised November 23, 2004 and February 1, 2005. This work was supported by the Center for Broadband OFDM Mobile Access (BrOMA) at POSTECH supported by the ITRC Program of the Ministry of Information and Communication, Korea, supervised by the Institute of Information Technology Assessment (IITA). The authors are with the Division of Electrical and Computer Engineering, Pohang University of Science and Technology (POSTECH) Pohang 790-784, Korea (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TCOMM.2005.855012

ming has been rather extensively studied in [1]–[6]. Houston in [1] investigated the performance of SFH systems using binary and quaternary DPSK in the presence of partial-band multitone jamming using a geometric approach. In [2], Simon generalized the results of [1] to SFH systems using -ary DPSK in the presence of partial-band multitone jamming. McGuffin in [3] investigated the performance of SFH systems using BDPSK with the jamming tone frequencies randomly located within the hopping bandwidth. Wang et al. in [4] took a different approach and derived the joint probability distribution of the magnitude and the differential phase of the received DPSK signal corrupted by a jamming tone. This result was used to analyze the performance of SFH systems using binary and quaternary DPSK under multitone jamming, and the results were extended up to 32-ary DPSK in [5]. Mason [6] further extended the results to analyze the performance of SFH systems using -ary DPSK under multitone jamming and frequency-flat, time-selective, Rician fading channels. Unfortunately, the analytical approaches taken in [1]–[6] are not directly applicable to the analysis of SFHSS-MA networks using DPSK. In order to overcome the limitation of the approaches taken in [1]–[6], more efficient analytical tools were presented in [7]–[9]. In [7] and [8], the probability distribution of the phase between two vectors perturbed by correlated Gaussian noise was derived using the joint characteristic function of the vectors. Using this result, Zeng and Wang [9] presented an alternate expression for the probability distribution of the differential phase between two consecutively received DPSK symbols corrupted by both a jamming tone and Gaussian noise. This result was then used to analyze the performance of SFH systems using BDPSK under partial-band multitone jamming. In this paper, we utilize the results of [9] to analyze the uplink performance of SFHSS-MA networks using BDPSK. The receiver matched filter output in a multiple-access environment is a vector sum of contributions from three independent sources, namely, the desired user, the interfering users, and AWGN. Hence, the joint characteristic function of two consecutive matched filter outputs is given by the product of the joint characteristic functions of these three sources. Both synchronous and asynchronous hopping are considered under the AWGN and Rayleigh fading channels. We derive analytic expressions for the average conditional bit error probabilities interfering users as a function of the number of bits given transmitted per hop . We find that, for asynchronous hopping, the average conditional bit error probability increases with for under the AWGN channel but shows minimal . For the Rayleigh fading channels, dependence on for the dependence of the average conditional bit error probability

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on is minimal for all . Furthermore, results show that for either synchronous or asynchronous SFHSS-MA networks, BDPSK achieves nearly twice the maximum normalized network throughput compared to BFSK for both AWGN and Rayleigh fading channels. The remainder of the paper is organized as follows. In Section II, the assumed system and channel models are described, and, in Section III, the decision variable at the differential detector output is derived. Analytic expressions for the average are conditional bit error probabilities as functions of and derived in Section IV. In Section V, the dependence of the average conditional bit error probability on is investigated for asynchronous hopping. Also, in Section V, the throughput performance of SFHSS-MA networks using BDPSK is compared to those using BFSK. Finally, conclusions are drawn in Section VI. II. SYSTEM AND CHANNEL MODELS The system model considered is a homogeneous SFHSS-MA identical active users (transnetwork using BDPSK with bits per hop mitter–receiver pairs). The transmitters send using BDPSK in one of the available frequency hop slots. Independent Markov hopping patterns [10], [14] are assumed with the frequency separation between contiguous frequency , where is the symbol duration. hop slots of The complex baseband equivalent of the received signal of the desired user, say user number zero, during hop duration can be written as follows:

(1) is the number of interfering users within the hop where and is the equivalent low-pass and complex white Gaussian noise process with independent real and imaginary parts with identical two-sided power spectral . Then, is the normalized complex densities of white Gaussian noise process with independent real and imaginary parts with identical two-sided power spectral densities . The normalized received signal amplitude of of where the th user, , is defined as is the received symbol energy of the th user. Under perfect power control, ’s are assumed to have a constant value of without fading and are independent, identically distributed under (i.i.d.) with pdf Rayleigh fading. Note that this assumption may be practical only for the uplink channel. Since we assume that the first is equal to symbol of a hop is used as a pilot symbol, , where is the average received energy per information bit. Then, under perfect power control, ’s are equal to 1 without fading and are i.i.d. with pdf

Fig. 1. Examples of m(k; n; i) and I for n = 3. (a) Case when all m(k; 3; i)s are integers between 0 and L. (b) Case when m(k; 3; 0) is 1.

0

, under Rayleigh fading. We also assume that the normalized received signal amplitudes are constant during a hop and independent between hops. The normalized (by ) hop delay of the th user (see Fig. 1) is assumed to be uniformly and independent among difdistributed on is assumed to be indepenferent users. The random phase , and dent among different users, uniformly distributed on constant within a hop. The pulse shape equals 1 for and zero otherwise. The BDPSK encoded symbol coris given by responding to the data bit , where is the message-carrying phase1 given by . The differential phase is where is the th element of the given by denotes a modulo-2 addition. The scrambling sequence and scrambling sequence is used to guarantee that the conditional bit error probability is independent of the transmitted data bit, ensuring that the resulting channel is symmetric [17].2 Finally, we assume that the hopping pattern of a receiver is perfectly synchronized to that of its paired transmitter. The analytical results in the following sections are derived for the case of asynchronous hopping which may be specialized to the case of synfor all . chronous hopping by setting III. DECISION VARIABLE In order to demodulate the th symbol of the desired user, the receiver observes

in the intervals

1The first symbol in a hop a is used as a pilot symbol, and its phase  is assumed to be uniformly distributed on [0; 2 ). 2For asynchronous hopping, the bit error probability is dependent on the specific differential phase used to carry the bit. The channel symmetry property is utilized in the derivation of the normalized network throughput in Section V.

YANG AND CHEUN: UPLINK PERFORMANCE OF SLOW FREQUENCY-HOP MULTIPLE-ACCESS NETWORKS USING BINARY DPSK

tributed on are given as follows:

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, the probabilities of the hit patterns

or or

(3)

Since we assume that the users employ independent hopping patterns, s are independent for different values of . Finally, and are i.i.d. complex Gaussian random variables repand , reresenting the contribution of the AWGN on spectively, with independent real and imaginary parts each following the Gaussian distribution with zero mean and variance . The decision variable given by the differential phase between and is given by Arg

Fig. 2.

function has a main value in the range where the Arg and denotes the complex conjugate of . Then, the estimate of the transmitted differential phase of the desired user and for is 0 for .

Classification of hit patterns for asynchronous hopping.

and Fig. 2) and computes the statistics

(4)

(see and

IV. AVERAGE CONDITIONAL BIT ERROR PROBABILITY

given by

In this section, we derive the analytic expressions for the avand erage conditional bit error probabilities as functions of given as (2) (5)

where and for , and . Here, the normalized (by ) symbol delay of the th user (see Fig. 1) is defined as where is the largest integer not greater than and is also assumed to and independent among difbe uniformly distributed on ferent users. Also, where is the smallest integer greater than and is the index of the three possible interfering symbols of the th user occupying the interval when . Fig. 1 illustrates an example of for . The random vector is used to distinguish the six possible symbol hit patterns by the th interfering user in the in(see Fig. 2). The terval random variable equals 1 for and 0 otherwise.3 Using the fact that is uniformly dis-

3If m(k; n; i) is not an integer between 0 and L, the desired user’s signal in the interval I is not hit by the k th user, as depicted in Fig. 1, and h equals zero.

is the probability of a hop being hit by an interfering where available frequency-hop slots and Markov hopuser. With equals for asynchronous hopping and ping, for synchronous hopping [14]. Also, , the average conditional bit error probability given and , is given as (6) where and for equally likely data, we have

. Since we assume

(7) where

(8)

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with

and . To evaluate (8), probabilities of the form must be computed. Applying the results of [7]–[9], this can be expressed in terms of an auxiliary function as

where and . Also

(9) where [7]

(10) Here, tion of

and

is the joint characteristic funcgiven as [7] (16)

(11) where is the Bessel function of the first kind of order zero and consist of sums of independent random [19]. Since variables, (11) can be written as the product of the characteristic functions of the corresponding sources as follows:

where and . We will simply and in place of and write to simplify notation when there is no concern for ambiguity. Finally, differentiating the joint characteristic function with respect to results in

(12) Here

(17)

(13) represent the contribution from the desired signal, MAI, and background noise, where for and . Transforming to polar coordinates by setting and setting , the auxiliary function can be expressed as

Here

(18) (14)

with

From now on, we will simply denote the joint characteristic as for a given random vector in function order to simply notation. Then

(15)

(19)

YANG AND CHEUN: UPLINK PERFORMANCE OF SLOW FREQUENCY-HOP MULTIPLE-ACCESS NETWORKS USING BINARY DPSK

and is the Bessel function of the first kind of order one and simply as [19]. We again denote and when there is no concern for ambiguity.

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Also, it may be easily verified that the following relations are true:

A. AWGN Channel under the AWGN Note that channel. Hence, from (6) and (7), we have

(20) (25)

Also, from (8) and (9), we have and thus

(26) Substituting (25) and (26) into (23), expressions in (21) may further be simplified as

(21) To evaluate (21), we need to compute expectations of the form . Substituting (15)–(19) into (14), we have

(27) The explicit expressions for and are quite complicated and are given in Appendix A. With these results in may be computed by substituting (27) into hand, (20). B. Rayleigh Fading Channel (22) Since fied as

Recall that ’s are i.i.d. with pdf in this case. Hence, from (6) and (7), we have

are i.i.d. for different , this may further be simpli(28) Also, from (8) and (9), we have

(23) where

(24)

(29)

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To evaluate (29), we need to compute expectations of the form . Again, substituting (15)–(19) into (14), we have

Here, invoking the relation for [18], and are given as and . The expressions and are again quite complicated and are for derived in Appendix B. With these results in hand, can be computed by substituting (34) into (28).

V. NUMERICAL RESULTS

(30) , and are independent and ’s and are i.i.d. Since for different values of , this may further be simplified as

(31) with (32) Also, it may be easily verified from the relations given in (25) that the following relations are also true: (33) Substituting (25) and (33) into (31), expressions in (29) may further be simplified as

(34)

For all of the numerical results presented in this section, is assumed to be 30 dB and the frequency separation . First, the average between contiguous FH slots to be and denoted conditional bit error probabilities given , and predicted by the derived analytic expressions are compared to those obtained via computer simulations. The computer simulation results were based on the variables given (and thus and by (2) and (4) where a decision variable ) is generated for each transmitted data bit. The analytical results are computed using (20) for the AWGN channel and (28) for the Rayleigh fading channel. Fig. 3 shows the results and various values of with asynchronous for hopping. We observe that the analytical results very accurately predict the simulation results for all cases considered. Comparisons performed for various other system parameters and with synchronous hopping showed similar results. versus for , In Fig. 4, we plot and under the AWGN channel with asynchronous hopping. as a function of is Note that the behavior of highly dependent on whether or not is equal to 1. For initially increases with and quickly saturates, the error probabilities are insensitive to . whereas for This is mainly due to the large difference in the error probability of a modulation symbol under full and partial hits. We say that th and the th symbol pair suffers a full hit from the the th interfering user if the interference from the th user is . Also, the present for the entire duration pair is said to have suffered a partial hit from the th interfering user if the interference from the th user is present for only a . It is easily verified fraction of the interval that full hits are much more detrimental than partial hits [13]. Since the probability of a full hit monotonically increases with and quickly saturates, so does for . On , the probability that the aggregate the other hand, for interfering users resulting in a full hit interference from all for a consecutive symbol pair is high for all values of . This explains the fact that the conditional error probabilities for are insensitive to . Also, observe that there is a slight decrease . This can in the error probability with increasing for be explained by the fact that the probability that a symbol pair [see (3)], is not hit at all is given by . which monotonically increases with and saturates to versus under Rayleigh In Fig. 4, we also plot fading and asynchronous hopping. We observe that the error probabilities show only a minor dependence on for all values of . The reason is that, under Rayleigh fading, the effect of fading dominates the differential phase of two consecutive

YANG AND CHEUN: UPLINK PERFORMANCE OF SLOW FREQUENCY-HOP MULTIPLE-ACCESS NETWORKS USING BINARY DPSK

Fig. 3. Comparison of analysis and simulation results for P (e j K ; L) with asynchronous hopping E channel, L = 128. (c) Rayleigh fading channel, L = 1. (d) Rayleigh fading channel, L = 128.

Fig. 4. Average conditional bit error probability P (e j K ; L) versus L for K = 1; 2; 3; 4; 5 under AWGN and Rayleigh fading channels with asynchronous hopping, E =N = 30 dB.

matched filter outputs which makes factors.

blind to other

=N

= 30 dB. (a) AWGN channel,

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L

= 1. (b) AWGN

Fig. 5. Average conditional bit error probability P (e j K ; L) versus K for BDPSK and BFSK under AWGN and Rayleigh fading channels with asynchronous hopping L = 1; 128; E =N = 30 dB.

Next, we compare the performance of SFHSS-MA networks using BDPSK to those using BFSK. Fig. 5 shows versus for the two modulation schemes with and

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Fig. 6. Normalized network throughput w (K; L) versus K for BDPSK and BFSK under AWGN and Rayleigh fading channels with asynchronous hopping, q = 50; L = 1; 128; E =N = 30 dB.

under the AWGN channel with asynchronous hopping. For BFSK, was computed using the results derived in shows [10] and [13]. Observe that, for only a minor dependence on and on which modulation scheme increases quite signifiis employed. For cantly with but still shows only a minor dependence on which modulation scheme is employed. Fig. 5 also shows similar plots under Rayleigh fading with asynchronous hopping. Note that, is quite insensitive to and the emin this case, ployed modulation scheme for all values of . The required bandwidth for BDPSK is approximately identical to that of BFSK for but approaches only half that of BFSK as increases. Hence, for a given available RF bandwidth and sufficiently large , nearly twice as many frequency hop slots are available with BDPSK than with BFSK. Hence, the probability of a hop being hit by an interfering user for networks based on BDPSK is approximately half that compared to networks using BFSK. Hence, for a given available RF bandwidth and sufficiently large , SFHSS-MA networks using BDPSK have the advantage due to the decrease in the hit probability. In Fig. 6, the normalized network throughput of SFHSS-MA networks using BDPSK is compared to that of the networks using BFSK. The normalized is defined as network throughput denoted [10], [11], where is the channel capacity [19] with binary coding. The total RF is assumed bandwidth allotted to the network denoted to be fixed. The number of available frequency hop slots for SFHSS-MA networks using BFSK denoted is approximately , and that for networks using BDPSK given by by which denoted approaches for large . We assume for Figs. 6–7. Fig. 6 verifies that SFHSS-MA networks using BDPSK show significantly improved normalized network throughput performance compared to those using BFSK for large values of . For both AWGN and Rayleigh fading channels, SFHSS-MA networks using BDPSK achieve nearly twice the maximum

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 53, NO. 9, SEPTEMBER 2005

Fig. 7. Normalized network throughput w (K; L) versus K for BDPSK under the AWGN channel for various values of L with asynchronous hopping, q = 50; E =N = 30 dB.

normalized network throughput compared to networks using BFSK. Finally, Fig. 7 shows the normalized network throughput curves for BDPSK under the AWGN channel for various is sufficient to realize various values of . Note that the gains provided by slow-hopping for BDPSK modulation is also over BFSK modulation. Though not shown, sufficient under Rayleigh fading. VI. CONCLUSION The uplink performance of synchronous and asynchronous SFHSS-MA networks transmitting bits per hop using BDPSK was analyzed under the AWGN and Rayleigh fading channels. Analytic expressions for the average conditional bit error probinterfering users were deabilities given a hop is hit by rived. For a given RF bandwidth, nearly twice as many FH slots are available with BDPSK than with BFSK for sufficiently large values of . Meanwhile, the derived results show that the average conditional bit error probabilities given a hop is hit by a given number of interfering users are comparable for both BDPSK and BFSK. Hence, SFHSS-MA networks using BDPSK have the advantage due to the decrease in the hit probability. It turns out that SFHSS-MA networks using BDPSK with sufficiently large achieve nearly twice the maximum normalized network throughput compared to networks using BFSK under both AWGN and Rayleigh fading channels. APPENDIX A AND DERIVATION OF After some tedious but straightforward computations, it may be shown from their corresponding definitions given in (26) that and are given as

YANG AND CHEUN: UPLINK PERFORMANCE OF SLOW FREQUENCY-HOP MULTIPLE-ACCESS NETWORKS USING BINARY DPSK

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(A2) where the values of

and

may be either 0 or .

APPENDIX B AND DERIVATION OF Again, after straightforward but quite tedious computations, it may be shown from their corresponding definitions given in (33) that and are given as

(A1) Here

(B1) Here

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YANG AND CHEUN: UPLINK PERFORMANCE OF SLOW FREQUENCY-HOP MULTIPLE-ACCESS NETWORKS USING BINARY DPSK

(B2)

.

where

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[13] K. Choi and K. Cheun, “Performance of asynchronous slow frequency-hop multiple-access networks with MFSK modulation,” IEEE Trans. Commun., vol. 48, no. 2, pp. 298–307, Feb. 2000. [14] E. A. Geraniotis and M. B. Pursley, “Error probabilities for slow-frequency-hop spread-spectrum multiple-access communications over fading channels,” IEEE Trans. Commun., vol. COM-30, no. 5, pp. 996–1009, May 1982. [15] M. V. Hedge and W. E. Stark, “On the error probability of coded frequency-hopped spread-spectrum multiple access sysmtes,” IEEE Trans. Commun., vol. 38, no. 5, pp. 571–573, May 1990. [16] 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, no. 2, pp. 307–311, Feb. 1993. [17] J. Hou, P. H. Siegel, L. B. Milstein, and H. D. Pfister, “Multilevel coding with low-density parity-check component codes,” in Proc. IEEE GLOBECOM, vol. 2, Nov. 2001, pp. 1016–1020. [18] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products. New York: Academic, 1980, p. 717. [19] J. G. Proakis, Digital Communications, 3rd ed. New York: McGrawHill, 1995.

REFERENCES

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[1] S. W. Houston, “Modulation techniques for communication, part I: Tone and noise jamming performance of spread spectrum -ary FSK and 2, 4-ary DPSK waveforms,” in NAECON Rec., pp. 51–58. [2] M. K. Simon, “The performance of -ary FH-DPSK in the presence of partial-band multitone jamming,” IEEE Trans. Commun., vol. COM-30, no. 5, pp. 953–958, May 1982. [3] B. F. McGuffin, “Effect of tone interference with unknown frequency on frequency hopped DPSK,” in Proc. Conf. Inform. Science Syst., vol. 2, 1990, pp. 894–899. [4] Q. Wang, T. A. Gulliver, and V. K. Bhargava, “Probability distribution of DPSK in tone interference and applications to SFH/DPSK,” IEEE J. Sel. Areas Commun., vol. 8, no. 6, pp. 895–906, Jun. 1990. [5] Q. Wang, T. A. Gulliver, L. J. Mason, and V. K. Bhargava, “Performance of SFH/ DPSK in tone interference and Gaussian noise,” IEEE Trans. Commun., vol. 42, no. 2/3/4, pp. 1450–1454, Feb./Mar./Apr. 1994. [6] L. J. Mason, “Error probability for FH/MDPSK in multitone jamming, fast Rician fading, and Gaussian noise,” IEEE Trans. Commun., vol. 43, no. 2/3/4, pp. 545–553, Feb./Mar./Apr. 1995. [7] R. F. Pawula, S. O. Rice, and J. H. Roberts, “Distribution of the phase angle between two vectors perturbed by Gaussian noise,” IEEE Trans. Commun., vol. COM-30, no. 8, pp. 1828–1841, Aug. 1982. [8] R. F. Pawula, “Distribution of the phase angle between two vector perturbed by Gaussian noise II,” IEEE Trans. Veh. Technol., vol. 50, no. 3, pp. 576–583, Mar. 2001. [9] M. Zeng and Q. Wang, “On the probability distribution of differential phase perturbed by tone interference and Gaussian noise,” IEEE Trans. Commun., vol. 47, no. 4, pp. 508–510, Apr. 1999. [10] 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, no. 9, pp. 1400–1410, Sep. 1991. [11] K. Cheun and K. Choi, “Performance of FHSS multiple-access networks using MFSK modulation,” IEEE Trans. Commun., vol. 44, no. 11, pp. 1514–1526, Nov. 1996. [12] E. A. Geraniotis, “Multiple-access capability of frequency-hopped spread-spectrum revisited: An analysis of the effect of unequal power levels,” IEEE Trans. Commun., vol. 38, no. 7, pp. 1066–1077, Jul. 1990.

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Jooyeol Yang was born in Daegu, Korea, on July 7, 1975. He received the B.S. and M.S. degrees in electronic and electrical engineering from Pohang University of Science and Technology (POSTECH), Pohang, Korea, in 1998 and 2000, respectively, where he is currently working toward the Ph.D. degree in electronic and electrical engineering. Since 1998, he has been a Research Assistant with the Division of Electrical and Computer Engineering, POSTECH. His current research interests include OFDM, MIMO systems, and space–time codes.

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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, 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 with the Electrical Engineering and Computer Science 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 and the Director of the Center for Broad-band OFDM Multiple Access (BrOMA) supported by the Korean Ministry of Information and Communication (MIC). He has also served as an engineering consultant to various industries in the area of mobile communications and modem design and currently holds the CTO position at Pulsus Technologies, a fabless SOC company specializing in digital amplifiers. His current research interests include OFDM, turbo and turbo-like codes, space–time codes, MIMO systems, software-defined radio structure, and sound processing.