IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 49, NO. 6, JUNE 2001
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Minimum-Error-Probability Single-User Detection for ISI-Impaired Narrow-Band Multiuser Systems Enzo Baccarelli and Stefano Galli, Member, IEEE
Abstract—The goal of this contribution is to give some insight into the cochannel interference (CCI) suppression capability of novel symbol-by-symbol-type maximum a posteriori probability single-user receivers for nonspread-spectrum multiuser narrow-band systems impaired by intersymbol interference and CCI. The presented multiuser receivers minimize the error probability in the detection of the desired user message on a per-symbol basis. Practical application environments for the developed detectors can be constituted by Ethernet-type LANs and DSL-based high-throughput links connecting central offices to subscribers. Index Terms—Colored noise, MAP receivers, multiuser detection, Wiener filter.
I. SYSTEM-CONSIDERATIONS ABOUT NARROW-BAND MULTIUSER (MU) NETWORKS
T
HE FAST increasing traffic-loads experienced in the last years by MU networks make the available system-band a resource that must be efficiently exploited. Since conventional spread-spectrum code-division multiple-access (SS-CDMA) systems based on orthogonal signature-sequences [5, Ch. 6] are inherently bandwidth-inefficient [3], [8], several competing non-SS-CDMA techniques have recently been proposed [8]. These techniques utilize suitable forms of coding [4] and/or precoding [1], [3] to obtain good performance without wasting the available band. Obviously, the ultimate performance of an MU system also depends on the approach adopted to detect the cochannel interference (CCI)-affected received signal. To this regard, it is well understood that decentralized-type multiuser receivers [2] generally exhibit a good tradeoff between the two contrasting requirements of reliable performance and low implementation complexity ([1], [2], [4] and references therein). In essence, these receivers carefully exploit the statistical features of the CCI but track and detect only the message of the desired user so that, in general, their implementation looks attractive, especially for the subscribers of MU systems [1], [2], [5]. From a practical point of view, the most appealing feature of MU narrow-band systems (MUNSs) is their spectral-effithat grows linearly with the users’ number acciency , (bits/s/Hz).1 cording to the relationship Paper approved by B. L. Hughes, the Editor for Theory and Systems of the IEEE Communications Society. Manuscript received October 9, 1998; revised January 7, 1999 and September 13, 2000. E. Baccarelli is with the INFO-COM Department, University of Rome “La Sapienza,” 00184 Rome, Italy (e-mail:
[email protected]). S. Galli is with Telcordia Technologies, Inc., Morristown, NJ 07960 USA (e-mail:
[email protected]). Publisher Item Identifier S 0090-6778(01)04871-1. 1q
is the size of the employed quadrature amplitude modulation (QAM) constellation.
Since the corresponding spectral-efficiency of a conventional SS-CDMA system which employs orthogonal signature (see [5, Sec. sequences is upper-bounded by 6.7.3]), the design and optimization of MUNSs have received growing interest in the last years (see, for example, [3], [4], [8] and references therein). However, despite its practical relevance, the overall topic about the MU decentralized detection of intersymbol interference (ISI) and CCI impaired data transmitted via MUNSs does not seem until now deeply explored [7], [9, Ch. 1]. Moreover, explicit results about CCI mitigation capability of these bandwidth-efficient systems are not available yet [9, Sec. 1.4 and references therein]. Therefore, motivated by these considerations, the goals of the present contribution are twofold. First, we present new decentralized-type minimum-errorprobability MU receivers for ISI and CCI-impaired MUNSs. In fact, although the reliable performance achieved by fully-centralized minimum-error-probability MU detectors for synchronous and asynchronous transmissions over ISI-free waveform channels is well understood for SS-CDMA systems (see [9, Sec. 4.1–4.3 and references therein]), the resulting centralized receivers look too complex to be implemented at the subscriber’s sides. Moreover, in the above-mentioned contributions the ISI effects of the physical waveform transmission channels are not taken into account. Secondly, we attempt to give some insight into the ISI and CCI mitigation capability of the proposed detectors working in CCI-dominated environments. For this purpose, we present numerical performance comparisons between the proposed MU receivers and some competing conventional ones in the conclusive Section IV. Moreover, the tradeoff between performances and complexity is also stressed. The paper is organized as follows. The modeling of MUNSs as well as the basic relationships characterizing a symbol-by-symbol (SbS) maximum a posteriori probability (MAP) detector are addressed in Section II. In Section III, we describe the proposed SbS-MAP detectors for MUNSs impaired by ISI and CCI; in particular, the three proposed receivers are the optimum SbS-MAP solution and the two suboptimum solutions that arise under the conditions of memoryless and colored CCI. Finally, performance results and comparisons with other competing methods are given in Section IV. II. MODELING OF MUNSS IMPAIRED BY ISI AND CCI The baud-rate sampled low-pass (complex) version of the considered narrow-band ISI-corrupted MU system is sketched
0090–6778/01$10.00 © 2001 IEEE
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Fig. 1. Baud-rate sampled baseband non-SS MU system. As usual [1], [3], the (L + 1) impulse responses combined effects of precoders, transmitting channels and front-end filters.
in Fig. 1 where and , , represent the data-streams generated by the desired user and the interfering ones at a common signaling-period . These data-streams are assumed zero-mean, unitary variance, mutually independent, and their equi-distributed outcomes take values on an assigned -ary QAM constellation . After the amplifications introduced by the , , (deterministic) nonnegative transmitting gains the desired and interfering streams cross the corresponding ISI channels2 so that the resulting received sequence can be modeled as
(1)
fh (n); 0 i Lg take into account for the
we can equivalently rewrite the relationships in (1) in a compact form as (4) , with the positions . Each channel-state sequence , , -variate Markovian chain which takes values is an on the set (5) -variate vector , , denotes the th where the . Furthermore, allowable outcome of the channel-state , , is a stationary Markov chain which since , the evolves as the state of a right-shift register of length transition-probability elements of the corresponding are defined according to the usual matrix relationship [6, Sec. II]
(2) is the ISI-corrupted desired sequence, where is the (ISI-impaired) CCI sequence, and is a complex additive white Gaussian noise with variance . Therefore, after channel-state sequences3 introducing the
(3) 2Without loss
of generality, we can assume all the above channel impulse-responses normalized to unitary energy so that the signal-to-noise ratio (SNR) , the signal-to-ith interference ratio (SIR ) , and the signal-to-total interference ratio (SIR) are given by the following relationships: (G ) =N ,
(G ) =(G ) , (G ) = (G(i)) . 3Hereafter, vectors are denoted by underlined letters while matrices are boldface characters. Furthermore, 1 indicates the column vector constituted by m unit elements and diag ; . . . ; denotes a P P diagonal matrix with the elements ; . . . ; disposed along the main diagonal.
f
f
g
g
2
if
is an allowable continuation of
otherwise. (6) The ultimate goal of the minimum-error-probability receiver present in the system of Fig. 1 is to deliver the -delayed4 detected stream for the desired 4On the basis of several numerical results, in [10, pp. 711–712] it is stressed that SbS-MAP detectors give rise to reliable performances for values of the decision-delay D limited up to the memory-length of the transmission channel (see also [10, Sec. VI and references therein]). Also the analytical bounds recently presented in [6, eq. (16) and following text] and [11] have confirmed this conclusion. Thus, from a practical point of view, SbS-MAP detectors with a decision delay D set to (L 1) look very appealing since they typically offer good tradeoffs between complexity and performance [6], [11], [10, Sec. V, VI].
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BACCARELLI AND GALLI: MINIMUM-ERROR-PROBABILITY SINGLE-USER DETECTION FOR ISI-IMPAIRED NARROW-BAND MU SYSTEMS
user by working in accordance with the usual MAP decision rule
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be accomplished by updating, at first, the vector
(9)
(7) gathers the received where the vector samples of (4) until step . Now, an application of the total probability theorem allows us to compute the a posteriori probabilities (APPs) in (7) by linearly combining the elements of the vector of the APPs of the state-chain of the desired channel according to the relationship [6, and references therein]
of the “predicted” APPs on the basis of the vector obtained at the previous step of the recursion and then by from . As far as the updating computing from is concerned, an appliof cation of the total probability theorem and the Bayes’ rule leads to the following relationship:
(10) (8) is the set constituted by the outcomes of with the th component equal to . Therefore, the computation the th constellation symbol can be of the desired detected stream carried out on the basis of the above-defined APP sequence and, in turn, this last task could be accomplished via several algorithms of various complexities. Obviously, the simplest SbS-MAP decentralized-type deas tector we can derive models the CCI sequence an additional (complex) white Gaussian noise so that the recursive computation of the above-introduced APP vector can be directly carried out via the conventional Abend–Fritchman algorithm of [6, and references therein]. The complexity of this decentralized detector (which in the sequel will be referred to as conventional single-user (CSU) receiver) is fully independent of the number of the interfering users. However, the CSU receiver is deeply CCI-limited and for medium to low SIRs its performance is very poor even for high SNRs (see Section IV).
where
follows from the Markovian property of . where Thus, after recognizing that the first conditional probability in of the transition-probability ma(10) is the element (see (6) for ), it is easy to prove that the trix relationships in (10) can be recast in a vector form as below reported (11) For the updating of for the th element of holds:
from , we note that , the following development
(12) stems from a reiterated application of the Bayes’ rule. where Now, since the summation (over the -index) of the probabilities in (12) must be unity, the denominator of (12) can be computed as
III. PROPOSED SBS-MAP DETECTORS FOR MUNSS On the basis of (8), we conclude that the task of the SbS-MAP detector is to compute the above-defined sequence of the APPs of the states of the desired channel. This task can
(13)
(14)
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which, in turn, allows us to rewrite (12) as (14), shown at the bottom of the previous page. For evaluating the conditional probability density functions (pdfs) of the observation present in (14), we exploit the property that and are and are given. independent when the values of So doing, we obtain
A. Optimum SbS-MAP Detector for MUNSs For an exact evaluation of (18), we note that the CCI term is the superposition of the states , , of the interfering channels [see (4)] and, then, that the expectation (18) can be equivalently carried out over the conditional pdfs of , . After some algebra, the random variables we finally obtain that the conditional expectation in (18) can be written as (19), shown at the bottom of the page, where the mutual independence of the states of the interfering channels has also been accounted for. Now, the conditional probabilities present in (19) are the elements of the “predicted” APP vectors , , of the states , , of the interfering channels. Thus, following the same guidelines formerly reported for the derivations of (11), (16), (18), and (19), it can be found that these APP vectors can be updated as [see (11)]
(15) follows from the above-cited conditional indepenwhere and , while for deriving we have exdence of ploited the Gaussian assumption about the channel-noise in (4) (the expectation in (15) is over the pdf of conditioned ). Therefore, by exploiting the on the observed sequence relationships in (14) can be rewritten definition in (9), the in a vector form as
(20) while for the computation of the th APP vector , the following relationship holds [see (16)]:
(21)
(16) Finally, the elements of the
where the elements of the diagonal matrix (17) are defined as the following conditioned expectations [see (15)]:
(18) Now, the computation of (18) can be carried out in several ways depending on the considered application and, where possible, resorting to suitable simplifying assumptions. In the following sections, we present three algorithms for the recursive evaluation of the expectations in (18), which give rise to three corresponding SbS-MAP MU detectors of decreasing complexities.
,
diagonal matrices
(22) present in (21) are given by [see (19)] (23), shown at the bottom of the next page. Therefore, as also summarized in the first row of Table I, the optimum SbS-MAP MU detector recursively updates the orderly set of relationships reported in (11), (20), (19), (16), (23), and (21), and then on the basis of the computed APP delivers the detected stream of the desired user vector according to the decision rule in (7). Remark (Computational Aspects and Implementation Considerations): The computational complexity (per -ary transmitted symbol) of the presented algorithm is (at most) , where . However, the state-reducing techniques recently presented in [15] may be effectively exploited to “shorten” the impulse responses of the
(19)
BACCARELLI AND GALLI: MINIMUM-ERROR-PROBABILITY SINGLE-USER DETECTION FOR ISI-IMPAIRED NARROW-BAND MU SYSTEMS
TABLE I SUMMARY OF THE RECURSIONS REQUESTED FOR THE IMPLEMENTATIONS OF THE PROPOSED SbS-MAP MU DETECTORS OF SECTIONS III-A–III-C
for
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, (19) can be rewritten as
(24)
transmitted channels and then lower the complexity of the presented MU detector. Furthermore, since the relationships APP vectors (16), (21) for the updating of the , , share the same structure and perform the same basic operations, a practical implementation of the proposed detector may actually exploit this modular structure by splitting the above-mentioned overall computational load similar processing units (based, for example, among on systolic architectures) which run in parallel and separately APP streams. Lastly, it could also be pointed deliver the out that the modular structure of the proposed detector makes its utilization appealing even at the central offices of LANs where also the detection of the interfering users’ messages of Fig. 1 is, indeed, requested [7]. In fact, the recursive generation , , of the detected messages can be accomplished by directly exploiting the APP vectors in (21) via separate applications of the above-mentioned MAP decision rule. B. SbS-MAP MU Detector for MUNSs with Memoryless CCI In application scenarios where the CCI is essentially memoryless and the resulting CCI power density spectrum is virtually flat over the system band,5 the conditional expectation in (18) can be replaced by the corresponding unconditional one so that,
5The operating conditions of some emerging non-SS-CDMA systems [3], [4] well meet this assumption. To this regard, it should be also pointed out that, in principle, in non-Gaussian environments the flatness of the CCI spectrum does not imply the memoryless property for the corresponding CCI process. However, in practice, it is generally experienced that a “white” noise is almost memoryless and the simulation results of Section IV confirm that the performance of the MU detector presented in this subsection approaches that of the optimum one when the spectrum of the CCI process is essentially flat over the system band.
For CCI-dominated MUNSs operating at sufficiently high SNRs, the computational burden requested for the evaluation the of (24) can be further reduced by noting that for low summation in (24) is typically dominated by the exponential term with the minimum argument [4, Sec. IV]; therefore, for , we can use the asymptotically tight approximavanishing tion
(25) is the minimum squared Euclidean distance dewhere fined as [see (24)]
(26) In summary, for MUNSs affected by memoryless CCI and operating at sufficiently high SNRs, the corresponding SbS-MAP MU detector performs the recursive updating of the set of relationships (11), (26), (25), (17), (16) (as also reported in the second row of Table I). Therefore, this detection procedure does not require the updating of the APP vectors of the states of the interfering channels so that its computational complexity depends on the number of interfering users only via the -fold min-operations in (26). C. Simple MAP MU Detector for MUNSs Impaired by Colored CCI Unfortunately, the numerical results of Section IV unveil that the performance of the simplified detector of Section III-B is poor when the memoryless assumption on the CCI falls short.
(23)
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Therefore, as in [12] and [13], and references therein, we focus now on MUNSs impaired by colored CCI which support a large ). Since in these apnumber of interfering users (e.g., plication scenarios, the optimum detector of Section III-A may be too complex to be implemented, it could be appealing to develop simple decentralized MU detectors that both exploit the CCI coloration and present a complexity fully independent of the number of interfering users [2, Sec. IV], [12], [13]. This goal may be pursued by resorting to the Central Limit Theorem and, then, considering a Gaussian approximation for conditioned on .6 Under this assumption, the pdf of the expectation in (18) can be evaluated by resorting to known formulas for the computation of Gaussian-type integrals [14, eq. (4.118)] which, for PAM transmissions over real baseband ISI channels,7 leads to
=
Fig. 2. Performance plots at SIR 10 dB of the proposed detectors of Sections III-A–III-C and the standard CSU, L-MMSE, and V-MLSE ones for a BPSK-modulated MU system with only one interfering user (L = 1). The impulse responses of the desired and interfering channels are given by h [0:774; 0:627; 0:0854] , respectively. [0:447; 0:775; 0:447] h
(27) and denote the first two moments of the where . Now, according to the system conditional pdf of considerations presented in [9, Sec. 6.1–6.2], we can keep limited the complexity of the resulting detector by resorting to a simple Wiener-like sliding window linear minimum mean-square-error (L-MMSE) estimator for a reasonably good evaluation of the conditional moments present in (27). So doing, a suitable application of the orthogonal projection principle [14, p. 497] to the observation model in (4) leads to the following Wiener-type relationships: (28) (29) where the right-hand side of (28) and (29) are, respectively, the above-mentioned Wiener-type sliding-window L-MMSE estiand the corresponding mean square error (MSE) mate of computed on the basis of the -windowed observed sequence . Furthermore, the -variate in (28) and (29) gathers the cross-covariances bevector and , and it is composed by the lags of the tween of the CCI process autocorrelation sequence (acs) to . Finally, in (28) and (29) is the from Toeplitz-type covariance matrix built up with usual 6The validity of this assumption is well debated in [12] and [13], where it is concluded that the CCI caused in CDMA MU systems by a large number of interfering users can be adequately modeled as a Gaussian noise whose coloration may be effectively exploited for improving the system performance without substantial increment of the system complexity (see, in particular, [12, Sec. IV]). Such a kind of approximation is also exploited in [2, Sec. IV] for deriving locally optimum MU receivers. 7The generalization of the presented algorithm to QAM transmissions over complex channels is straightforward but it requires the introduction of a lot of positions about the second order statistics of the processes involved by (4). Due to space limitations, the explicit derivation of the QAM version of the algorithm will be omitted.
the lags of the acs of the observations from to . In summary, the presented SbS-MAP MU detector for MUNSs impaired by colored CCI computes off-line the covariance in (29) and then updates the orderly set of relationships in (11), (29), (27), (17), and (16) (see the third row of Table I). Remark (Computational Aspects and Comparisons with Competing Algorithms): The most appealing feature of the detector here presented is that its computational complexity is and, therefore, it is fully independent of the number of of the interfering users. Furthermore, simplified versions of this detector for application scenarios with large have been presented in [15]. To this regard, it should be pointed out that in Gaussian-dominated environments, it is a common practice to achieve CCI mitigation by performing an L-MMSE cascaded sliding window filtering on the desired steam to a slicer [1, eq. (25) and Fig. 1], [7], [9, Ch. 6]. However, since this detector (thereinafter referred to as L-MMSE) treats ISI as an additional Gaussian noise, its performance suffers severe degradation when the ISI effects are not negligible (see the numerical plots of Section IV, curves labeled “L-MMSE”). IV. NUMERICAL RESULTS AND PERFORMANCE COMPARISONS In this section, we present some performance results on the CCI suppression capability of the proposed detectors obtained on the basis of computer simulations. To better evaluate the actual CCI suppression capability of the proposed MU detectors, we have also reported the performances of a conventional Viterbi-type maximum-likelihood sequence estimator (curves labeled “V-MLSE”). The latter equalizes the desired channel and treats the CCI as with a decision delay . an additional Gaussian noise so that its complexity is As a benchmark, the performance of an SbS-MAP equalizer [6] at an SIR is also reacting on the desired channel ported (curves labeled “SbS-MAP—No CCI”). Figs. 2–5 refer to MUNS with a spectral efficiency that ranges from 1 bit/s/Hz to 6 bits/s/Hz and characterized by ISI
BACCARELLI AND GALLI: MINIMUM-ERROR-PROBABILITY SINGLE-USER DETECTION FOR ISI-IMPAIRED NARROW-BAND MU SYSTEMS
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0
Fig. 3. As in Fig. 2 at an SIR
Fig. 5. Performance plots at SIR = 7 dB ( = = = = = 0 dB) of the proposed detectors of Sections III-A–III-C and the standard CSU, L-MMSE, and V-MLSE ones for a BPSK-modulated MU system with five interfering user (L = 5). The impulse responses of the desired and interfering [0:38; 0:6; 0:6; 0:38] , channels are given, respectively, by h h [0:447; 0:775; 0:447; 0:0] , h 0:5[1; 1; 1 1] , h 0:5[1; 1; 1; 1] , h 0:5[1; 1; 1; 1] , h 0:5[1; 1; 1; 1] .
= 0 dB.
0 0
0
0
0 0
0
Fig. 4. Performance plots at SIR = 4:8 dB ( = = = 0 dB) of the proposed detectors of Sections III-A–III-C and the standard CSU, L-MMSE, and V-MLSE ones for a BPSK-modulated MU system with three interfering user (L = 3). The impulse responses of the desired and interfering channels are given, respectively, by h [0:447; 0:775; 0:447] , h 0:5[1; 1; 1; 1] , h 0:5[1; 1; 1; 1] , h 0:5[1; 1; 1; 1] .
0 0
0 0
0
0
and CCI. The performance of the nonlinear optimum detector of Section III-A (curves labeled “SbS-MAP Optimum”) clearly outperforms the other conventional receivers. In particular, the BERs achieved by the proposed detectors of Section III-A and Section III-B tend to go to zero for high SNR, whereas the other conventional solutions exhibit very high BER floors even at high SNR. Furthermore, Fig. 4 confirms that the performance of the simplified detector of Section III-B (curves labeled “SbS-MAP Memoryless”) closely approaches that of the optimum one of Section III-A when the CCI sequence is essentially white, whereas the conventional CSU and L-MMSE detectors still fall short in such environments. Also, the V-MLSE performance is very poor on CCI-impaired environments, and the performance gaps between the V-MLSE and the proposed SbS-MU detectors can be considered as representative of the CCI suppression capability of these last.
Fig. 6. Performance plots at SIR = 0 dB of the proposed detector of Section III-C for W = 6 and W = 10, of the conventional L-MMSE for W = 10 and the V-MLSE one for the colored Gaussian-shaped CCI sequence of (30) with = 10 . The impulse response of the desired channel is h [0:89; 0; 0:45] .
0
Finally, to obtain insight about the performance gap on Gaussian-dominated environments between the proposed MU detector of Section III-C (curves labeled “SbS-MAP Colored”) and the conventional V-MLSE and L-MMSE competing ones, we have carried out a final set of trials by directly generating a with Gaussian-shaped power Gaussian CCI sequence given by the usual relationship [12], density spectrum [13] (30) where cient of
and .
is the correlation coeffi-
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[9] S. Verdu, Multiuser Detection. Cambridge, U.K.: Cambridge Univ. Press, 1998. [10] Y. Li, B. Vucetic, and Y. Sato, “Optimum soft-output detection for channels with intersymbol interference,” IEEE Trans. Inform. Theory, vol. 41, pp. 704–713, May 1995. [11] E. Baccarelli and S. Galli, “New results about analysis and design of TCM for ISI channels and combined equalization/decoding,” IEEE Trans. Commun., vol. 46, Apr. 1998. [12] A. Monk, M. Davis, L. B. Milstein, and C. W. Helstrom, “A noisewhitening approach to multiple access noise rejection—Part I: Theory and background,” IEEE J. Select. Areas Commun., vol. 12, pp. 817–826, June 1994. [13] Y. Noon and H. Leib, “Matched filters with interference suppression capabilities for DS-CDMA,” IEEE J. Select. Areas Commun., vol. 14, pp. 1410–1421, Oct. 1996. [14] C. W. Helstrom, Probability and Stochastic Processes for Engineers. New York: Macmillan, 1991. [15] E. Baccarelli, S. Galli, A. Fasano, and A Zucchi, “A novel reduced-complexity MAP equalizer using soft-statistics for decision-feedback ISI cancellation,” in Proc. IEEE Globecom Conf., Rio de Janeiro, Brazil, Dec. 5–12, 1999. Fig. 7.
0:5[1;
As in Fig. 6, for a desired channel with impulse response .
01; 1; 01]
h
Fig. 6 shows that, when the ISI affecting the received desired of (2) is light, the performance gap between message the proposed detector of Section III-C and the L-MMSE conventional one of [1, eq. (25)] is quite large but limited. However, from Fig. 7, we conclude that, when the ISI effects are not negligible, the conventional L-MMSE receiver is outperformed by the one proposed in Section III-C. The plots of Figs. 6 and 7 also confirm the poor performance achieved by the V-MLSE receiver in CCI-dominated environments. REFERENCES [1] M. Rupf, F. Tarkoy, and J. L. Massey, “User-separating demodulation for code-division multiple-access systems,” IEEE J. Select. Areas Commun., vol. 12, pp. 786–795, June 1994. [2] H. V. Poor and S. Verdù, “Single-user detectors for multiuser channels,” IEEE Trans. Commun., vol. 36, pp. 50–60, Jan. 1988. [3] G. W. Wornell, “Spread-signature CDMA: Efficient multiuser communication in the presence of fading,” IEEE Trans. Inform. Theory, vol. 41, pp. 1418–1438, Sept. 1995. [4] G. Caire, G. Taricco, J. V. Traveset, and E. Biglieri, “A multiuser approach to narrowband cellular communications,” IEEE Trans. Inform. Theory, vol. 43, pp. 1503–1517, Sept. 1997. [5] A. Vertbi, CDMA-Principles of Spread Spectrum Communication. Reading, MA: Addison-Wesley, 1994. [6] E. Baccarelli, R. Cusani, and S. Galli, “Novel analytical performance bounds for symbol-by-symbol MAP decoding of digital data impaired by ISI and AWGN,” IEEE Trans. Inform. Theory, vol. 43, pp. 744–750, Mar. 1997. [7] S. Glisic and B. Vucetic, Spread Spectrum CDMA Systems for Wireless Communications. Norwood, MA: Artech House, 1997, ch. 6. [8] J. L. Massey, “Toward and information theory of spread-spectrum systems,” in Code Division Multiple Access Communications, S. G. Glisic, Ed: Kluwere, 1995, pp. 29–46.
Enzo Baccarelli was born in Todi, Italy, in 1962. He received the Laurea degree in electronic engineering and the Ph.D. degree in communication theory from the University of Roma, “La Sapienza,” Rome, Italy, in 1989 and 1993, respectively. In 1995, he was in the postdoctorate course at the INFO-COM Department, the University of Roma, Rome, Italy, where he has been a Researcher since 1996 and currently an Associate Professor in signal theory and wireless communications. His main research interests include the areas of random processes and information theory, with applications to radio-mobile digital communications and coding. He is author of about 30 contributions on international journals and 40 conferences’ proceedings on these topics. He holds a U.S. patent in adaptive equalization of radio channels.
Stefano Galli (M’97) was born in Florence, Italy, in 1966. He received the Masters (Laurea) degree in electronic engineering and the Ph.D. (Dottorato di Ricerca) degree in information theory and communications from the University of Rome, “La Sapienza,” Rome, Italy, in 1994 and 1998, respectively. His first research studies were on coherent optical communications; however, during his Ph.D. studies, his interests moved to digital communications in time-variant environments, with particular emphasis on adaptive channel equalization. After completing the Ph.D. degree, he continued as a Teacher Assistant in Signal Theory at the Info-Com Department with the University of Rome. At the same time, he began to work as a free consultant for Italian telecommunications companies. He also worked on the Trans-European Trunked Radio (TETRA) project, in particular on the definition of the line dispatcher functionalities. In October 1998, Stefano joined Bellcore (now Telcordia Technologies, an SAIC company), Morristown, NJ, as a Research Scientist in the Broadband Access and Premises Internetworking Department. His main research efforts are devoted to the problem of automatic loop qualification and, more recently, to the analysis and performance assessment of wireless home networks and power line carriers. His research interests also include detection and estimation, channel equalization, personal wireless communications, xDSL systems, and crosstalk modeling.
