EURASIP Journal on Applied Signal Processing 2002:5, 525–531 c 2002 Hindawi Publishing Corporation
Maximum-Likelihood Sequence Detection of Multiple Antenna Systems over Dispersive Channels viaSphereDecoding
Haris Vikalo Information Systems Laboratory, Stanford University, Stanford, CA 94305, USA Email: [email protected]
Babak Hassibi Department of Electrical Engineering, California Institute of Technology, Pasadena, CA 91125, USA Email: [email protected]
Received 6 May 2001 and in revised form 28 March 2002
Multiple antenna systems are capable of providing high data rate transmissions over wireless channels. When the channels are dispersive, the signal at each receive antenna is a combination of both the current and past symbols sent from all transmit anten- nas corrupted by noise. The optimal receiver is a maximum-likelihood sequence detector and is often considered to be practically infeasible due to high computational complexity (exponential in number of antennas and channel memory). Therefore, in prac- tice, one often settles for a less complex suboptimal receiver structure, typically with an equalizer meant to suppress both the intersymbol and interuser interference, followed by the decoder. We propose a sphere decoding for the sequence detection in multiple antenna communication systems over dispersive channels. The sphere decoding provides the maximum-likelihood esti- mate with computational complexity comparable to the standard space-time decision-feedback equalizing (DFE) algorithms. The performance and complexity of the sphere decoding are compared with the DFE algorithm by means of simulations. Keywords and phrases: sphere decoding, maximum-likelihood, multiple antennas, dispersive channels, computational complexity.
1. INTRODUCTION may be linear (zero-forcing or minimum mean square), Multiple antenna wireless communication systems are capa- or nonlinear decision-feedback equalizer (DFE). DFEs es- ble of providing data transmission at potentially very high sentially perform successive interference cancellation: a soft rates [1]. To secure high reliability of the data transmis- symbol estimate is used to cancel the trailing interference, sion, special attention has to be payed to the design of the upon which the hard decision is made to recover the sym- receiver. When transmitting over noisy dispersive channels, bol. (For the analysis of the performance of DFE algorithm in the received signal at each receive antenna is the combi- a dispersive MIMO environment, see [6].) For high enough nation of the transmitted signals perturbed by noise, in- SNR, DFEs obtain better performance than linear equalizers tersymbol interference (ISI), and by interuser interference while still having much lower complexity than the optimal (IUI). In this case, the optimal receiver structure is the multi- MLSE algorithm. However, the performance of the DFE is channel maximum-likelihood sequence estimation (MLSE). highly inferior compared to the performance of the optimal However, the computational complexity of the traditional MLSE algorithm. maximum-likelihood sequence detector often prohibits its In this paper, we propose an algorithm that yields the practical implementation. (For instance, the Viterbi decoder optimal MLSE performance on dispersive multiple-input is exponential in the length of the channel [2].) One way multiple-output (MIMO) channels with finite impulse re- to alleviate the computational burden is to settle for (sub- sponse (FIR). (We should point out that the wireless commu- optimal) reduced complexity MLSE algorithms by reducing nication systems may or may not employ feedback from the the number of states (see, e.g., [3, 4]). In practice, however, receiver to the transmitter. In this paper, we focus on optimal most often a multichannel (space-time) equalizer is used to detector structures for systems where feedback is unavail- suppress ISI and IUI first; then, a hard decision is made to able and the receiver learns the channel based on the training recover the symbol that has been sent [2, 5, 6]. The equalizer information.) 526 EURASIP Journal on Applied Signal Processing
ν(1) We consider the so-called sphere decoding, an algorithm k (1) for solving integer least-squares problems, which, in the s , χ(1) k h(2 1) k communication context, provides the ML estimate of the transmitted data sequence. The algorithm is due to Fincke h(1,2) ν(2) and Pohst [7] and was first proposed in the context of the k s(2) χ(2) closest point searches in lattices (for a review of these, see k k [8] and the references therein). The algorithm was rediscov- ered in [9] in the context of detection in GPS systems. The use of the sphere decoding for lattice codes was first pro- . (N,1) . . h . posed in [10],andfurtherinvestigatedin[11, 12]. In [13], . it has been analytically shown that the average complexity ν(N) of the sphere decoding used for ML detection in flat fading k M s( ) χ(N) multiple-antenna systems is polynomial (often sub-cubic) k k for a wide range of signal-to-noise ratios (SNRs). The paper is organized as follows: in Section 2,wede- scribe the FIR MIMO channel model. In Section 3,wepose Figure 1: FIR MIMO channel model. the detection problem, briefly overview heuristics for solving it, and describe the sphere decoding algorithm. Simulation results are presented in Section 4, where it is shown that the matrix form as sphere decoding provides significant improvement (several dBs) over the MIMO DFE. The computational complexity of C ᐄ = H ᐂ , the sphere decoding turns out to be comparable to that of the k l k−l + k (3) MIMO DFE, thereby suggesting that it can be implemented l=1 in practice. The paper concludes with Section 5. where = s(1) s(2) ··· s(M) 2. FIR MIMO MODEL DESCRIPTION k k k k (4) M We consider a multiple-antenna system with transmit and is the transmit vector, whose entries typically come from a N N× receive antennas. The MIMO channel is modeled as block- QAM constellation, ᐂk ∈ Ꮿ 1 is the additive noise vector fading frequency-selective, where the channel impulse re- defined as sponse is constant for some discrete interval T,afterwhich it changes to another (independent) impulse response that (1) (2) (N) ᐂk = ν ν ··· ν , (5) remains constant for another interval T, and so on. The addi- k k k tive noise is spatially and temporally independent identically H ∈ ᏯN×M l ffi distributed (i.i.d.) circularly-symmetric complex-Gaussian. and l is the th coe cient matrix in the MIMO The MIMO channel model is shown in Figure 1. channel impulse response, The channel is represented by its complex baseband h(1,1) h(1,2) ··· h(1,M) equivalent model. Let the column vector l l l (2,1) (2,2) (2,M) h h ··· h (i,j) = (i,j) (i,j) (i,j) H = l l l . h h h ··· h i,j (1) l (6) 1 2 C( ) . . .. . . . . . denote the single-input single-output (SISO) channel im- h(N,1) h(N,2) ··· h(N,M) pulse response from the jth transmit to the ith receive an- l l l tenna. For convenience, we shall make the following assump- In other words, the z-transform of the MIMO channel tions on the SISO channels h(i,j): impulse response is given by i,j (1) C( ) = C,1 ≤ i ≤ N,1 ≤ j ≤ M, that is, all SISO −1 −(C−1) H(z) = H1 + H2z + ···+ HCz . (7) channels have impulse responses of the same length, ffi h(i,j) ≤ l ≤ C ≤ i ≤ N (2) the channel coe cients l ,1 ,1 , Define the following vectors: 1 ≤ j ≤ M are i.i.d. Ꮿ(0, 1). ᐄ = ᐄ ᐄ ··· ᐄT C− , 1 2 + 1 The received signal at the ith antenna can then be expressed ᐂ = ᐂ ᐂ ··· ᐂT C− , (8) as 1 2 + 1 = ··· . M C 1 2 T i i,j j i χ( ) = h( )s( ) + ν( ), (2) k l k−l k ᐂ ∈ ᏯN(T+C−1) j=1 l=1 (Note that the random vector has unit vari- ∗ ance complex Gaussian i.i.d. entries, E[ᐂᐂ ] = IN(T+C−1).) for k = 1, 2,...,T + C − 1. Equation (2)canbewrittenina Then from (3) we can write the input-output relation for the MIMO MLSD via Sphere Decoding 527
FIR MIMO channel in the matrix form as ᐂ
ᐄ = Ᏼ ᐂ, ᐄ + (9) Ᏼ where Ᏼ ∈ ᏯN(T+C−1)×MT is constructed as Figure 2: Matrix equivalent channel model. H1 H H 2 1 as . . . . . .. x = Hs + v, (14) HC ··· H 1 Ᏼ = .. .. . (10) . . where the signal vectors s are typically obtained upon mod- H ··· H L Ᏸ2MT C 1 ulation of the input bits onto an -PAM constellation L , .. . . . . . H H L − L − L − L − 2MT C C−1 2MT 1 3 3 1 ᏰL = − , − ,..., , . (15) HC 2 2 2 2
Model (9)isillustratedinFigure 2. We assume that symbol (This particular structure of vector s stems from the assump- L × L bursts are uncorrelated (which is an appropriate assumption tion that entries of in (9) are points in QAM constel- L when modeling, for instance, packet transmission in TDMA lation.) Notice that we assumed that is even. (In practice, L systems). is commonly a power of 2, giving rise to 2-PAM, 4-PAM, It will be convenient to define the signal-to-noise ratio ρ 8-PAM, etc., constellations.) Ᏸ2MT for the system in (9), Finally, notice that L is a finite lattice carved from an infinite one, ᐆ2MT. EᏴ2 ρ = 2 Eᐂ2 3. PROBLEM STATEMENT 2 E tr Ᏼ∗Ᏼ∗ With the notation introduced in Section 2, due to the Gaus- = (11) E tr ᐂᐂ∗ sian assumption on the additive noise, we can express the MLSE problem as the optimization problem E tr ∗Ᏼ∗Ᏼ = . N(T + C − 1) min x − Hs2, (16) 2MT 2MT s∈ᏰL ⊂ᐆ Assuming that the entries in are coming from an L×L QAM L where the minimization is over all points in the constellation constellation (where is assumed to be even), and that the 2MT ᏰL . We can interpret problem (16) as follows. minimum distance between constellation points is dmin = 1, we find that Given the “skewed” lattice Hs, find the “closest” lattice point to a given 2NT-dimensional vector x. 2 L − 1 ∗ The closest lattice point search problem in (16) is known ρ = E tr Ᏼ Ᏼ 6N(T + C − 1) to be, in general, of exponential complexity [8]. There are L2 − 1 several reduced complexity heuristic methods that can be = MTCN (12) used to obtain approximate solutions to (16). The most ob- 6N(T + C − 1) vious are the following two. L2 − 1 MTC = . • 6(T + C − 1) Inverting and rounding to the closest integer
= † , Notice that all quantities in (9) are complex. We will find sˆ H x ᐆ (17) it useful to rewrite (9) in terms of real quantities. To this end, † define where H denotes the pseudo-inverse, and where for a ∈ the notation [a]ᐆ means the closest integer to † x = (ᐄ) (ᐄ) , a.So[H x]ᐆ is simply the vector obtained by this op- † ˆ eration applied to each entry of H x. The above s is v = (ᐂ) (ᐂ) , called the Babai point (estimate). In the communica- (13) tions context, the preceding procedure is nothing but (Ᏼ) −(Ᏼ) H = . simple zero-forcing equalization, followed by a hard (Ᏼ) (Ᏼ) decision. • In nulling and canceling [14], one uses the Babai es- Thus, with the previously defined x ∈ 2N(T+C−1)×1, v ∈ timate for one of the entries of s,says(1); then as- 2N(T+C−1)×1,andH ∈ 2N(T+C−1)×2MT,wecanrewrite(9) sumes that s(1) is known and subtracts out its effect 528 EURASIP Journal on Applied Signal Processing
to obtain a reduced integer least-squares problem with that s lies in a sphere of radius r if 2MT − 1 unknowns. Then the procedure is repeated ∗ to solve similarly for s(2), and so on. (Nulling and can- r2 ≥x − Hs2 = s − sˆ H∗H s − sˆ + x2 − Hsˆ2, (21) celling is fundamentally equivalent to the generalized † decision-feedback equalization discussed in [15].) As where sˆ = H x. To make the notation simpler, denote size of a side note, one can further improve the performance the vector s as of nulling and canceling by introducing optimal order- m = MT. ing: the algorithm starts from the “strongest” and pro- 2 (22) ceeds to the “weakest” entry in s (see, e.g., [14, 16]). (Note that m is the number of unknowns and it will be of The aforementioned heuristics have acceptable polyno- interest in studying the complexity.) mial-time computational complexity for practical imple- Introducing the QR decomposition H = QR (where Q is mentation purposes. However, their performance is inferior unitary and R is upper triangular), and defining r 2 = r2 − in comparison with the exact solution to the MLSE problem. x2 + Hsˆ2,wecanwrite(21)as We proceed by describing an algorithm, the so-called r 2 ≥ − ∗R∗ Q∗Q R − sphere decoding,forefficient closest point search in the lattice. s sˆ s sˆ =I ∗ 3.1. Sphere decoding ≥ s − sˆ R∗R s − sˆ m m The sphere decoding performs the closest-point search in rij 2 2 = rii si − sˆi + sj − sˆj a somewhat more sophisticated manner than doing a full rii i=1 j=i+1 search over the integer lattice, which requires exponential 2 2 complexity. In particular, it performs search only over lat- = rmm sm − sˆm tice points lying in a certain hypersphere of radius r cen- r 2 r2 s − s m−1,m s − s ··· , tered around the received vector x. The closest lattice point is + m−1,m−1 m−1 ˆm−1 + m ˆm + rm−1,m−1 clearly the solution. (23) From a practical point of view, there are two issues that have to be resolved. One is the proper choice of the sphere ra- where ri,j denotes (i, j) entry of the matrix R. A necessary r r dius :if is too large there will be too many lattice points in condition for s to lie inside the sphere is therefore that the sphere and we may still require an exponential search; if r 2 2 2 is too small there will be no points in the sphere. The other rmm sm − sˆm ≤ r . (24) issue concerns determining which lattice points lie within the sphere—if the algorithm were to check all the points in the This condition is easy to check and it leads to lattice, we would be again stuck with an exponential search. We use a statistical criterion to choose radius r.Inpar- r r sˆm − ≤ sm ≤ sˆm + . (25) ticular, the radius of the sphere is chosen so that with high rmm rmm probability we find at least one lattice point in the sphere. To this end, note that However, condition (25)isbynomeanssufficient. For every s r 2 = r 2 − r2 s − s 2 m satisfying (25), upon defining m−1 mm( m ˆm) v2 = x − Hs2 (18) one can state a stronger necessary condition is a chi-square random variable with NT degrees of freedom. 2 r (Recall that each entry on v is an independent N(0,σ2)ran- r2 s − s m−1,m s − s ≤ r 2 , m−1,m−1 m−1 ˆm−1 + r m ˆm m−1 (26) dom variable.) We choose the radius r to be a linear function m−1,m−1 v2 of the variance of , sˆm−1|m
r2 = α2NTσ2, (19) which is equivalent to r r where the coefficient α is chosen in such a way that with a s − m−1 ≤ s ≤ s m−1 . ˆm−1|m r m−1 ˆm−1|m + r (27) high probability pfp we find a lattice point inside a sphere, m−1,m−1 m−1,m−1 s α2NT λNT−1 In a similar fashion, one proceeds for m−2, and so on, e−λ dλ = p . stating nested necessary conditions for all elements of s. This Γ NT fp (20) 0 ( ) leads us to the sphere decoding algorithm which essentially finds all points that satisfy the previously stated conditions: We find α in (20) by a simple table lookup. Once we have chosen radius r, we need to determine Input: R, x, sˆ, r. 2 2 2 2 which lattice points belong to the sphere of radius r.Anef- (1) Set k = m, rm = r −x + Hsˆ , sˆm|m+1 = sˆm. s z = r /r UB s = z s ficient way to check whether a lattice point belongs to the (2) (Bounds for k)set k kk, ( k) + ˆk|k+1 , sphere is given by the algorithm of Fincke and Pohst [7]. Note sk = −z + sˆk|k+1 −1. MIMO MLSD via Sphere Decoding 529
(3) (Increase sk) sk = sk +1.Ifsk ≤ UB(sk) go to (5), else 100 Sphere decoding to (4). Generalized DFE k k = k k = m (4) (Increase ) +1; if +1, terminate algorithm, 10−1 else go to (3). k k = k = k − s = (5) (Decrease )if 1goto(6).Else 1, ˆk|k−1 −2 m 10 sk rkj/rkk sj − sj r 2 = r 2 − r2 sk − ˆ + j=k+1( )( ˆ ), k k+1 k+1,k+1( +1 s 2 ˆk+1|k+2) , and go to (2). − 10 3 (6) Solution found. Save s and go to (3). BER
In general, the closest point search has both worst-case 10−4 and average complexity that is exponential in the number of unknowns [17]. The same is true for the sphere decoding. 10−5 However, in our application, the vector x in (16)isnotan arbitrary point in space but rather a lattice point perturbed − 10 6 by the noise as expressed by (14). Clearly, the higher the SNR 024 6810 12 14 16 18 20 22 in (12), the less perturbed the lattice point is. Therefore, one SNR (dB) may suspect that the expected complexity of the sphere de- coding algorithm will depend on the SNR. Indeed, this is the Figure 3: BER performance of SD and DFE for M = 2, N = 2, case—the higher the SNR, the lower the complexity. C = 4, T = 4, L = 2. In [13], we have computed in closed-form the expected complexity (averaged over the noise and the lattice) of the sphere decoding for the nondispersive (flat-fading) channels. It is shown that the expected complexity is polynomial-time . over a wide range of SNRs, and is, in fact, often sub-cubic for 3 6 e SNRs that support the data rates being transmitted. c For dispersive channels explicitly computing the ex- 3.4 pected complexity appears to be much more complicated, and we are currently not able to analytically perform all 3.2 the required steps. Nonetheless, simulation suggest the same qualitative performance of polynomial-time complexity as 3 we observe from the examples in Section 4. Complexity exponent Furthermore, the complexity of the sphere decoding can . be improved by exploiting the Toeplitz structure of the chan- 2 8 nel matrix. In particular, note that the channel matrix pre- processing is required only in order to transform H into an 2.6 0246810 12 14 16 18 upper triangular form. Due to the Toeplitz structure of H, SNR (dB) it is in fact sufficient to perform QR factorization of only ffi one coe cient matrix in the MIMO channel impulse re- M = N = C = H H Figure 4: Complexity exponent of the SD for 2, 2, 4, sponse ( C in (10)). Upon QR factorization of C the bot- T = 4, L = 2. tom square submatrix of H becomes upper triangular and thus can be processed by the sphere decoding algorithm to find a lattice point s; then one proceeds by adding the con- (corresponding to 2-PAM, or L = 2, in the real-valued tribution of the top 2(C − 1) rows of H to find the metric set of (14)). The resulting transmission rate is therefore x − Hs2 and by testing whether the lattice point s belongs 4 bits/channel use. The performance comparison of an un- to the sphere. coded transmission in terms of bit error rate (BER) between Further improvement in the complexity of the sphere de- the sphere decoding and nulling and canceling (or, equiva- coding can be obtained by employing the Schnorr-Euchner lently, generalized DFE) is shown in Figure 3. variation of the Fincke-Pohst algorithm (see [8, 18]). Essen- As an indicator of the expected computational complex- tially, by examining points in the hypersphere in a different ity of the sphere decoding, we adopt the complexity expo- order (in particular, by starting from the Babai point), signif- nent, ce,definedas icant computational savings can be obtained [18]. log(expected total flop count) ce = , (28) 4. SIMULATION RESULTS log(m) M = We first consider a communication system with 2 where m is defined in (22). The expected complexity can N = transmit and 2 receive antennas. The channel mem- therefore be expressed as C = ory is assumed to be 4, and the coherence interval time T = 4. Data is modulated onto 4-QAM constellation O mce = O (2MT)ce . (29) 530 EURASIP Journal on Applied Signal Processing
100 100 Sphere decoding Sphere decoding Generalized DFE Generalized DFE 10−1 10−1
10−2 10−2
10−3 10−3 BER BER
10−4 10−4
10−5 10−5
10−6 10−6 12 14 16 18 20 22 24 26 28 32 34 6 8 10 12 14 16 18 20 22 24 SNR (dB) SNR (dB)
Figure 5: BER performance of SD and DFE for M = 2, N = 2, Figure 7: BER performance of SD and GDFE for M = 4, N = 4, C = 4, T = 8, L = 4. C = 4, T = 8, L = 4.
4.2 4.4 4 4.2 3.8
e 4 e c c 3.6 3.8 3.4 3.6 . 3.4 3 2 3.2 3 3 2.8 Complexity exponent Complexity exponent 2.8 2.6 2.6 2.4 2.4 2.2 12 14 16 18 20 22 24 26 28 6 8 10 12 14 16 18 20 SNR (dB) SNR (dB)
Figure 6: Complexity exponent of the SD for M = 2, N = 2, C = 4, Figure 8: Complexity exponent of the SD for M = 4, N = 4, C = 4, T = 8, L = 4. T = 8, L = 4.
The complexity exponent as the function of SNR for the corresponding complexity exponent of the sphere decoding previous example with m = 16 is shown in Figure 4.Note is shown in Figure 8 and is sub-cubic for SNRs above 12 dB. that for SNRs above 7 dB we obtain sub-cubic complexity. As another example, we consider the same 2 × 2system 5. DISCUSSION AND CONCLUSION (M = 2, N = 2), with C = 4, but now increase the block length to T = 8, and the constellation to 16-QAM, corre- We have proposed sphere decoding for maximum-likelihood sponding to L = 4 and a transmission rate of 8 bits/channel sequence detection of multiple antenna systems over use. The performance comparison between the sphere de- frequency-selective channels. To employ the sphere decod- coding and generalized DFE is shown in Figure 5.Thecom- ing, the detection problem was posed as an integer least- plexity exponent as the function of SNR for this example squares problem. As illustrated by simulations, the sphere (where m = 32) is shown in Figure 6. decoding provides several dBs improvement over the MIMO As a final example, consider the 4×4 communication sys- decision-feedback equalization. We have shown empirically tem (M = 4, N = 4), with C = 4andblocklengthT = 8(and that the expected computational complexity of the sphere thus m = 64). The constellation used is 4-QAM (hence L = 2, decoding is polynomial (often sub-cubic) for a wide range and the corresponding transmission rate is 8 bits/channel of SNRs. Both the sphere decoding and MIMO DFE re- use). The performance comparison between sphere decoding quire some preprocessing of the channel matrix (usually in and generalized DFE for this system is shown in Figure 7.The aformofQRfactorization)which,ingeneral,hascubic MIMO MLSD via Sphere Decoding 531 complexity. Therefore, the maximum-likelihood detection [18] C. P. Schnorr and M. Euchner, “Lattice basis reduction: im- on MIMO channels with memory can be implemented with proved practical algorithms and solving subset sum prob- complexity similar to that of heuristic methods, but with sig- lems,” Mathematical Programming, vol. 66, pp. 181–191, 1994. nificant performance gains. Haris Vikalo was born in Tuzla, Bosnia and Herzegovina. He re- REFERENCES ceived his B.S. degree from University of Zagreb, Croatia, in 1994, his M.S. degree from Lehigh University, Bethlehem, PA, in 1997, [1] I. E. Telatar, “Capacity of multi-antenna Gaussian channels,” and Ph.D. degree from Stanford University, Stanford, Calif, USA, European Transactions on Telecommunications,vol.6,no.10, in 2002, all in electrical engineering. He held short-term positions pp. 585–595, 1999. at Siemens (Croatia), Bell Laboratories (Murray Hill, NJ, USA), and [2] C. Tidestav, A. Ahlen,´ and M. Sternad, “Realizable MIMO California Institute of Technology (Pasadena, Calif, USA). His re- decision feedback equalizers: structure and design,” IEEE search interests include wireless communications, signal process- Trans. Signal Processing, vol. 49, no. 1, pp. 121–133, 2001. [3] M.V.Eyuboglu´ and S. U. H. Qureshi, “Reduced state sequence ing, and algorithm complexity. estimation for coded modulation on intersymbol interference Babak Hassibi was born in Tehran, Iran, in 1967. He received his channels,” IEEE Journal on Selected Areas in Communications, vol. 7, no. 6, pp. 989–995, 1989. B.S. degree from University of Tehran in 1989 and the M.S. and [4] R. Raheli, A. Polydoros, and C.-K. Tzou, “The principle of Ph.D. degrees from Stanford University, Stanford, Calif, USA, in per-survivor processing: a general approach to approximate 1993 and 1996, respectively, all in electrical engineering. From Oc- and adaptive MLSE,” in Proc. Global Telecommunications Con- tober 1996 to October 1998, he was a Research Associate with the ference, vol. 2, pp. 1170–1175, Phoenix, Ariz, USA, 1991. Information Systems Laboratory, Stanford University, and from [5]A.M.Tehrani,B.Hassibi,andJ.Cioffi, “Adaptive equalization November 1998 to January 2001, he was Member of Technical Staff of multiple-input multiple-output frequency selective chan- at Bell Laboratories, Murray Hill, NJ, USA. Since January 2001, he nels,” in Proc. 33rd Asilomar Conference on Signals, Systems, has been an Assistant Professor of electrical engineering at the Cal- and Computers, October 1999. ifornia Institute of Technology, Pasadena, USA. He has also held [6] N. Al-Dhahir and A. H. Sayed, “The finite-length multi-input short-term appointments at Ricoh California Research Center, the multi-output MMSE-DFE,” IEEE Trans. Signal Processing,vol. Indian Institute of Science, and Linkoping¨ University, Linkoping,¨ 48, no. 10, pp. 2921–2936, 2000. Sweden. 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Forney, “Generalized decision-feedback equalization for packet transmission with ISI and Gaussian noise,” in Communications, Computation, Control, and Sig- nal Processing: a tribute to Thomas Kailath, Kluwer Academic, Boston, Mass, USA, 1997. [16] B. Hassibi, “An efficient square-root algorithm for BLAST,” in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing,vol.2, pp. 737–740, 2000. [17] M. Ajtai, “Generating hard instances of lattice problems,” in Proc. 28th Annual ACS Symposium on the Theory of Comput- ing, pp. 99–108, Philadelphia, Pa, USA, May 1996. EURASIP JOURNAL ON WIRELESS COMMUNICATIONS AND NETWORKING
Special Issue on Advances in Error Control Coding Techniques
Call for Papers
In the past decade, a significant progress has been reported Authors should follow the EURASIP Journal on Wireless in the field of error control coding. In particular, the innova- Communications and Networking manuscript format de- tion of turbo codes and rediscovery of LDPC codes have been scribed at the journal site http://www.hindawi.com/journals/ recognized as two significant breakthroughs in this field. The wcn/. Prospective authors should submit an electronic copy distinct features of these capacity approaching codes have en- of their complete manuscript through the EURASIP Journal abled them to be widely proposed and/or adopted in existing on Wireless Communications and Networking’s manuscript wireless standards, such as CDMA, Wireless LAN, WiMax, tracking system at http://mts.hindawi.com/, according to the Inmarsat, and so forth. Furthermore, the invention of space following timetable. time coding significantly increased the capacity of a wireless system and has been widely applied in the broadband com- munication systems. Recently, new coding concepts employ- Manuscript Due November 1, 2007 ing the distributed nature of networks have been developed, such as network coding and distributed coding techniques. First Round of Reviews February 1, 2008 They have great potential applications in wireless networks, Publication Date May 1, 2008 sensor networks and ad hoc networks. Despite the recent progress, many challenging problems still remain, such as de- velopment of effective analysis tools, novel design criteria for capacity achieving codes over various channel models (e.g., GUEST EDITORS: ergodic, nonergodic, frequency nonselective, frequency se- lective, SISO, and MIMO), and design of efficient distributed Yonghui Li, School of Electrical and Information codes, and so forth. Engineering, The University of Sydney, Sydney NSW 2006, This special issue is devoted to present the state-of-the- Australia; [email protected] art results in theory and applications of coding techniques. Jinhong Yuan, School of Electrical Engineering and Original contributions are solicited in all aspects of this field, Telecommunications, The University of New South Wales, with the emphasis on new coding concepts, coding/decoding Sydney NSW 2052, Australia; [email protected] structures, codec design, theoretical analysis, new applica- Andrej Stefanov, Department of Electrical and Computer tions, and implementation issues. Topics of interests include, Engineering, Polytechnic University, Six Metrotech Center, but are not limited to, the following: Brooklyn, NY 11201, USA; [email protected] • New coding structures, concepts, and applications Branka Vucetic, School of Electrical and Information • Performance analysis Engineering, The University of Sydney, Sydney NSW 2006, • Turbo codes Australia; [email protected] • LDPC codes • Algebraic coding techniques • Space time (frequency) coding • Adaptive modulation and coding, hybrid ARQ • Distributed coding/decoding • Efficient decoder design
Hindawi Publishing Corporation http://www.hindawi.com 6th International Symposium on COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING (CSNDSP’08) 23-25 July 2008, Graz University of Technology, Graz, Austria www.csndsp.com Hosted by: Institute of Broadband Communications, Department of Communications and Wave Propagation Sponsored by: The Mediterranean Journals: - Computer & Networks IEEE Communications - Electronics & Communications Chapter - UK/RI
First Call for Papers Following the success of the last event, and after 10 years, the CSNDSP steering Steering Committee: Prof. Z Ghassemlooy (Northumbria Univ., UK) – committee decided to hold the next event at the Graz University, Austria. Graz was Chairman the 2003 cultural capital of Europe. CSNDSP, a biannual conference, started in Prof. A C Boucouvalas (Univ. of Peloponnese, Greece) – UK ten years ago and in 2006 it was hold for the first time outside UK in Symp. Secr. Patras/Greece. CSNDSP has now been recognised as a forum for the exchange Prof. R A Carrasco (Newcastle Univ. UK) of ideas among engineers, scientists and young researchers from all over the Dr. Erich Leitgeb (Graz Univ. Austria) – Local Organiser world on advances in communication systems, communications networks, digital signal processing and other related areas and to provide a focus for future Local Organising Committee: Dr. Erich Leitgeb (Local Organising Committee Chair) research and developments. The organising committee invites you to submit Prof. O. Koudelka (Professor) original high quality papers addressing research topics of interest for presentation Dr U. Birnbacher at the conference and inclusion in the symposium proceedings. J. Ritsch and P. Reichel (OVE) Dr J. Wolkerstorfer Papers are solicited from, but not limited to the following topics: P. Schrotter � Adaptive signal processing � New techniques in RF-design and � ATM systems and networks modelling National/International Technical Committee: � Chip design for Communications � Network management & Dr M Ali (Oxford Brookes Univ. UK) � Communication theory operation Prof. E Babulak (American Univ. Girne, North Cyprus) � Coding and error control � Optical communications Prof. P Ball (Oxford Brookes Univ. UK) � Communication protocols � Optical MEMS for lightwave Dr D Benhaddou (University of Houston, USA) � Prof. J L Bihan (Ecole Nation. d'Ingen. de Brest, France) Communications for disaster networks Dr K E Brown (Heriot-Watt Univ. UK) management � RF/Optical wireless Prof. R A Carrasco (Newcastle Univ. UK) � Crosslayer design communications Dr J B Carruthers (Boston University, USA) � DSP algorithms and applications � Photonic Network Prof. F Castanie (INPT, France) � E-commerce and e-learning � Quality of service, reliability and Dr H Castel (Inst. Natio. D. Télécommun., France) applications performance modelling Dr L Chao (Nanyang Tech. Univ. Singapore) � Intelligent systems/networks � Radio, satellite and space Prof. R J Clarke (Heriot-Watt Univ. UK) � Internet communications communications Dr M Connelly (Univ. of Limerick, Ireland) � � Prof. A Constantinides (Imperial College, UK) High performance networks RFID & near field Prof. D Dietrich, (Vienna Univ. of Tech., Austria) IEEE � Mobile communications, communications Austria Section Chair networks, mobile computing for e- � Satellite & space communications Dr D Dimitrov (Tech. Univ. of Sofia, Bulgaria) commerce � Speech technology Dr S Dlay (Newcastle Univ. UK) � Mobility management � Signal processing for storage Prof. Fu, Shan (Shanghai Jiaotong Univ., China) � Modulation and synchronisation � Teletraffic models and traffic Dr. M Gebhart, (NXP, Gratkorn Austria) � Modelling and simulation engineering Dr M Giurgiu (Univ. of Cluj-Napoca, Romania) techniques � VLSI for communications and Dr. M Glabowski, (Poznan Univ. of Tech., Poland) � Prof. Ch Grimm, (Vienna Univ. of Tech., Austria) Multimedia communications and DSP Dr A. Inoue (NTT, Japan) broadband services � Wireless LANs and ad hoc Prof. L Izzo (Univ. of Napoli, Italy) � Microwave Communications networks Prof. G Kandus (IJS Ljubljana, Slovenia) � 3G/4G network evolution Prof. K Kawashima (Tokyo Univ. TUAT, Japan) � Any other related topics Prof. C Knutson (Brigham Young Univ., USA) � Papers may be presented in the form of Oral presentation and/or Poster Prof. G Kubin, (Graz Univ. of Tech., Austria � Contributions by MPhil/PhD research students are particularly encouraged. Prof. K Liu (Reading Univ. UK) Submission Dates: Dr M D Logothetis (Univ. of Patras, Greece) th Prof. E Lutz, (DLR, Oberpfaffenhofen, Germany) � Full Paper due: 27 Jan. 2008 Prof. M Matijasevic (FER Zagreb, Croatia) � Notification of acceptance by: 1st April 2008 Prof. B Mikac (FER Zagreb, Croatia) � Camera ready paper due: 5th May 2008 Dr. W P Ng (Northumbria University, UK) Dr T Ohtsuki (Tokyo Univ. of Sci., Japan) � Electronic submission by e-mail to: [email protected] Prof. F Ozek (Ankara Univ., Turkey) � Prof. R Penty (Cambridge Univ. UK) All papers will be refereed and published in the symposium Prof. W Pribyl, (Graz Univ. of Tech. Austria) proceeding. Selected papers will be published in: The Mediterranean Prof. J A Robinson (Univ. of York, UK) Journals of Computers and Networks and Electronics and Dr D Roviras (INPT, France) Communications, and possibly IET proceedings. Prof. M Rupp, (Vienna Univ. of Tech., Austria) � Dr. S. Sheikh Muhammad (Univ. of Eng. & Tech., A number of travel grants and registration fee waivers will be Pakistan) offered to the delegates. Dr S Shioda (Chiba Univ. Japan) Fees: 360.00 EURO, (Group Delegates of 3 persons: 760.00 Euro) Dr J Sodha (Univ. of West Indies, Barbados, W. Indies) Includes: A copy of the Symposium Proceedings, Lunches, and Symposium Dr I Soto (Santiago Univ. Chile) Dinner on the 24th July. Dr U Speidel (Univ. of Auckland, Newzeland) Prof. M Stasiak (Poznan Univ. Poland) Dr L Stergioulas (Brunel Uni. UK) CSNDSP’08 General Information Prof. M Theologou (Nation. Tech. Univ. Athens, Greece) Contact: Dr. Erich Leitgeb - Local Organising Committee Chair Prof. R. Vijaya (Indian Inst. of Tech., Bombay, India) Dr I Viniotis (N.Caroline State Univ.USA) - Institute of Broadband Communications, Graz University of Technology, A- Dr V Vitsas (TEI of Thessaloniki, Greece) 8010 Graz, Inffeldg. 12, Tel.: ++43-316-873-7442, Fax.: ++43-316-463697. Prof. R Weiß, (Graz Univ. of Tech., Austria) Email: [email protected], Web-site: http://www.inw.tugraz.at/ibk Dr P. Xiao (Queens Univ. UK) Prof. M N Zervas (Southampton Univ. UK) CALL FOR PAPERS 3DTV CONFERENCE 2008 THE TRUE VISION CAPTURE, TRANSMISSION AND DISPLAY OF VIDEO 28-30 MAY 2008, HOTEL DEDEMAN, �STANBUL, TURKEY
General Co-Chairs: Following the conference of 2007, the second 3DTV Conference will be held in Istanbul, Turkey U�ur Güdükbay, Bilkent University, TR in May, 2008. The aim of 3DTV-Con is to bring researchers from different locations together A. Aydn Alatan, and provide an opportunity for them to share research results, discuss the current problems Middle East Technical University, TR and exchange ideas. Advisory Board: The conference involves a wide range of research fields such as capturing 3D scenery, 3D image processing, data transmission and 3D displays. You are cordially invited to attend 3DTV-Con Jörn Ostermann, 2008 and submit papers reporting your work related to the conference themes listed below. Leibniz University of Hannover, DE Aljoscha Smolic, Conference Topics Fraunhofer Gesellschaft, DE
A. Murat Tekalp, Koç University, TR 3D Capture and Processing: 3D Visualization: - 3D time-varying scene capture technology - 3D mesh representation Levent Onural, Bilkent University, TR - Multi-camera recording - Texture and point representation - 3D photography algorithms - Object-based representation and segmentation John Watson, University of Aberdeen, UK - Dense stereo and 3D reconstruction - Volume representation Thomas Sikora, - Synchronization and calibration of camera arrays - 3D motion animation Technische Universitaet Berlin, DE - 3D view registration - Stereoscopic display techniques - Multi-view geometry and calibration - Holographic display technology Finance Chair: - Holographic camera techniques - Reduced parallax systems - 3D motion analysis and tracking - Underlying optics and VLSI technology Tark Reyhan, Bilkent University, TR - Surface modeling for 3D scenes - Projection and display technology for 3D videos Publication Chair: - Multi-view image and 3D data processing - Integral imaging techniques - Integral imaging techniques - Human factors Tolga K. Çapn, Bilkent University, TR 3D Transmission: 3D Applications: Publicity Chairs: - Systems, architecture and transmission in 3D - 3D imaging in virtual heritage and virtual archaeology - 3D streaming - 3D teleimmersion and remote collaboration Georgios Triantafyllidis, - Error-related issues and handling of 3D video - Augmented reality and virtual environments Centre for Research & Technology, GR - Hologram compression - 3D television, cinema, games and entertainment - Multi-view video coding - Underlying Technologies for 3DTV Gözde Bozda� Akar, - 3D mesh compression - Medical and biomedical applications Middle East Technical University, TR - Multiple description coding for 3D - 3D content-based retrieval and recognition Industry Liaison: - Signal processing for diffraction and holographic - 3D watermarking 3DTV Ismo Rakkolainen, FogScreen, FI Paper Submission Matt Cowan, RealD, USA Contributors are invited to submit full papers electronically using the online submission American Liaison: interface, following the instructions at http://www.3dtv-con.org. Papers should be in Adobe Kostas Danilidis, PDF format, written in English, with no more than four pages including figures, with a font size of 11. Conference proceedings will be published online by IEEE Xplore. University of Pennsylvania, USA Far East Liaison: Important Dates Kiyoharu Aizawa, University of Tokyo, JP Special sessions and tutorials proposals deadline: 14 December 2007 Special Sessions and Regular paper submission deadline: 11 January 2008 Tutorials Chairs: Notification of paper acceptance: 29 February 2008 Camera-ready paper submission deadline: 21 March 2008 Philip Benzie, University of Aberdeen, UK Conference: 28-30 May 2008 Atanas Gotchev, Tampere University of Technology, FI Sponsors Webmasters: Engin Türetken, Middle East Technical University, TR
Ay�e Küçükylmaz, 3DTV Network Bilkent Middle East Institute of Electrical European MPEG Industry Bilkent University, TR of Excellence University Technical and Electronics Association for Forum University Engineers Signal and Image Processing