Adaptive Pilot-Symbol Patterns for MIMO OFDM Systems - IEEE Xplore

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 9, SEPTEMBER 2013

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Adaptive Pilot-Symbol Patterns for MIMO OFDM Systems ˇ Michal Simko, Student Member, IEEE, Paulo S. R. Diniz, Fellow, IEEE, Qi Wang, Student Member, IEEE, and Markus Rupp, Senior Member, IEEE

Abstract—Recent standards for cellular transmission systems offer a lot of flexibility, such as the choice of transmission modes, modulation alphabets, coding rates, and precoding matrices. Despite this trend, pilot-symbol patterns in today’s standards remain fixed, although such an approach is suboptimal. In this paper, we show how to design optimal pilot-symbol patterns by maximizing an upper bound of a constrained capacity that takes channel estimation errors and Inter Carrier Interference into account. Furthermore, we propose adaptive pilot-symbol patterns that follow changing channel statistics. As a proof of concept, we present throughput simulation results of two competitive systems, a transmission system compliant with the Long Term Evolution (LTE)-standard and an improved system utilizing the proposed adaptive pilot patterns. The transmission system utilizing adaptive pilot patterns outperforms an LTEstandard compliant system in all considered scenarios. The throughput gain for a single input single output system ranges between 3% and 80%. For a 4 × 4 transmission system, the performance gain is significantly higher and can reach up to 850% compared to a conventional LTE system. Index Terms—Pilot pattern, OFDM, MIMO, LTE, adaptive transmission system.

I. I NTRODUCTION OHERENT detection is utilized in most of the transmission systems for mobile wireless communications. The performance of such systems especially depends on the utilized pilot-symbol patterns. To avoid jeopardizing the performance of the overall system, standardization organizations prefer fixed and therefore robust pilot-symbol patterns, which allow to estimate the transmission channel with sufficient high accuracy under various channel conditions. This overprovisioning approach leads to an advantage in terms of system robustness at the cost of reducing the system efficiency. In this work, we show how to design optimal pilot-symbol patterns under doubly selective channels with an optimal power distribution between pilot- and data-symbols. Furthermore, we propose the usage of adaptive pilot-symbol patterns that adapt to the varying channel statistics.

C

Manuscript received December 18, 2013; revised April 5, 2013; accepted June 30, 2013. The associate editor coordinating the review of this paper and approving it for publication was G. Li. ˇ M. Simko, Q. Wang, and M. Rupp are with the Institute of Telecommunication, Vienna University of Technology, A-1040 Vienna, Austria (e-mail: {msimko, qwang, mrupp}@nt.tuwien.ac.at.). P. S. R. Diniz is with DEL POLI/UFRJ, PEE COPPE/UFRJ, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil (e-mail: [email protected]). Parts of this work have been presented at the IEEE Wireless Communicaˇ tions and Networking Conference 2013 (M. Simko, P. S. R. Diniz, Q. Wang, and M. Rupp, “New insights in optimal pilot symbol patterns for OFDM systems,” in Proc. IEEE WCNC 2013, Shanghai, China, Apr. 2013. ). Digital Object Identifier 10.1109/TWC.2013.081413.121998

A. Related Work In the past, many researchers attempted to find an optimal pilot-symbol pattern by various criteria. In [1], [2], the authors chose the Mean Squared Error (MSE) of a channel estimator as a cost function for the design of the pilot-symbol patterns. They showed that equi-powered and equi-spaced pilot-symbols led to the lowest MSE. The authors of [3], [4] proposed a pattern design that maximized the channel capacity. There are many different approaches for designing pilot-symbol patterns based on the minimization of the Bit Error Ratio (BER) [5] or the Symbol Error Ratio (SER) [6]. A summary of these methods can be found in [7]. The authors of [8]–[11] showed how to distribute the available power among data- and pilot-symbols, given a certain pilot-symbol pattern. The authors established the postequalization Signal-to-Interference-and-Noise Ratio (SINR) under imperfect channel knowledge as a cost function to solve the formulated problem. This relatively simple framework allows to treat the problem analytically and to find a solution independent of the actual channel realization. In spite of these advantages, the achievable gain is limited, since the power distribution modifies only a term inside of the logarithm in the capacity formula. The adaptation of the pilot patterns in Orthogonal Frequency Division Multiplexing (OFDM) systems was first proposed in [12]. Simeone and Spagnolini designed pilot patterns in a way that the effective Signal-to-Noise Ratio (SNR) loss due to the channel estimation error remained limited within a desired bound. Their solution requires a complex Kalman channel estimator and only a greedy recommendation was proposed when designing the pilot patterns. A similar approach was presented in [13], the authors of which designed pilot patterns such that the channel estimation MSE was bounded as desired by the system designer while minimizing the pilot-symbol overhead. The presented solution was limited to a Linear Minimum Mean Squared Error (LMMSE) channel estimator and a Least Squares (LS) channel estimator with a linear interpolation. The authors of [14] considered the flatness of the channel estimation MSE as the cost function for their adaptive pilot design. The proposed solution was applied with an LMMSE channel estimator and with an LMMSE approximation. In [15], the authors proposed an adaptive pilot density depending on the channel variations satisfying a Nyquist sampling theorem in order to preserve channel estimation performance. The presented solutions [12]– [15] for adaptive pilot pattern design focus on the channel

c 2013 IEEE 1536-1276/13$31.00

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estimation performance in various forms as the cost function, with less or no emphasis on the throughput. Additionally, the presented solutions are mostly limited to an LMMSE channel estimator, which in reality cannot be utilized due to its high computational complexity and its a-priori requirements on the channel statistics. In this paper, we propose a framework for the design of adaptive pilot patterns that maximizes the throughput performance of the system. The framework is intended for any linear channel estimation method. Furthermore, the proposed design maximizes the throughput performance rather than the channel estimation performance as proposed in already existing methods [12]–[15]. The channel estimation performance in our work is merely a side constraint while the system performance metric is the system throughput. Additionally, our framework includes power distribution among pilot- and data-symbols, which was not considered as a part of the adaptive pilot pattern design in the state-of-the-art [12]–[15]. B. Contribution The main contributions of this paper are: • By maximizing an upper bound of the constrained capacity (see Equation (22) further ahead), we derive optimal distances between adjacent pilot-symbols under doubly selective channels along with an optimal power distribution between pilot- and data-symbols. With this we take advantage of the potential to increase pre-log terms in the constrained capacity formula which gives much higher gains than by only modifying the pilot power. • The proposed solution can be applied to any linear channel estimator. • We propose adaptive pilot-symbol patterns that adapt to the changing channel statistics. • The proposed adaptive pilot-symbol patterns aim to maximize the throughput in contrast to the already existing methods that are trying to preserve channel estimation performance [12]–[15]. • Our proposed solution can be applied to a LTE system with maximally 4 bits of extra feedback. Since the pilotsymbol pattern is used across the entire transmission bandwidth, the amount of required feedback bits is negligible compared to the amount required by other narrowband feedback indicators (channel quality indicator, rank indicator, precoding matrix indicator). • Simulation results with an LTE compliant simulator [16], [17] validate the presented optimal pilot-symbol design.1 • A comparison of simulated throughput of an LTEstandard compliant system with the same system that utilizes our proposed adaptive pilot-symbol patterns, confirms the superiority of the proposed adaptive pilotsymbol patterns when compared to the fixed pilot patterns. The remainder of the paper is organized as follows. In Section II, we introduce a mathematical model for Multiple Input Multiple Output (MIMO) OFDM transmissions. In 1 As with our previous work, all data, tools, as well implementations needed to reproduce the results of this paper can be downloaded from our homepage [18].

Section III, we briefly summarize important knowledge about the post-equalization SINR for Zero Forcing (ZF) equalizers under imperfect channel knowledge, and about state-of-the-art channel estimators. Furthermore, in the same section we show how to design optimal pilot-symbol patterns under doubly selective channels, and how to use adaptive pilot-symbol patterns that adjust to the varying channel statistics. Finally, we present throughput simulation results in Section IV and conclude our paper in Section V. II. T RANSMISSION M ODEL In this section, we introduce a transmission model suitable for our further derivation. The most important variables of this paper and their description are summarized in Table I. A received OFDM symbol in the frequency domain at the nr -th receive antenna can be represented as ˜ nr = y

Nt

˜ nt ,nr xnt + n ˜ nr , H

(1)

nt =1

˜ n ,n ∈ CNsub ×Nsub represents the channel matrix where H t r in the frequency domain between the nt -th transmit and nr -th receive antennas. The transmitted signal vector is referred to as ˜ nr ∈ CNsub ×1 . xnt ∈ CNsub ×1 , the received signal vector as y Nsub ×1 ˜ Each entry of vector nnr ∈ C represents an additive white Gaussian zero-mean noise with variance σn2 on the nr -th receive antenna. In case of time-invariant channels, ˜ nt ,nr appears as a diagonal matrix, whereas a channel matrix H ˜ nt ,nr to become time-variant channel forces channel matrix H non-diagonal. The non-diagonal elements indicate that the orthogonality between subcarriers is distorted, leading to the so-called Inter Carrier Interference (ICI). Specifically, vector xnt ∈ CNsub ×1 in Equation (1) comprises precoded datasymbols xd,nt ∈ CNd ×1 and pilot-symbols xp,nt ∈ PNp ×1 from the set of all possible pilot-symbols P, at the nt -th transmit antenna placed by a suitable permutation matrix P T T xnt = P xT . (2) p,nt xd,nt Vector xnt has Nsub entries, corresponding to the number of non-zero subcarriers. The variables Np and Nd denote the number of the pilot-symbols and the number of the precoded data-symbols, respectively. The precoding process on a subcarrier k can be described as [xd,1,k · · · xd,Nt ,k ]T = Wk [s1,k s2,k · · · sNl ,k ]T ,

(3)

where xd,nt ,k is a precoded data-symbol at the nt -th transmit antenna port and the k-th subcarrier, Wk ∈ CNt ×Nl is a unitary precoding matrix at the k-th subcarrier and snl ,k ∈ D1×1 is the data-symbol of the nl -th layer [19] at the k-th subcarrier. Here, D denotes the set of available modulation alphabets. Data-symbol vectors xd,nt are obtained by stacking datasymbols xd,nt ,k from Equation (3) at a specific antenna nt into a vector. Note that we do not assume anything about the choice of the precoding matrix Wk . In a typical transmission system, it is chosen from a given set of precoding matrices either based on the feedback from the user (closed-loop operational mode), or it is circularly varied (open-loop operational mode).

ˇ SIMKO et al.: ADAPTIVE PILOT-SYMBOL PATTERNS FOR MIMO OFDM SYSTEMS

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TABLE I M OST IMPORTANT VARIABLES Variable ˜ nr y ˜ nr ,nt H xnt xp,nt xd,nt ˜ nr n yk Hk,l Wk Gk sk nk Ek σs2 σp2 σd2 2 σICI 2 σn σe2 d fc Np Nd Nl Nt Nr Nsub poff γl

Dimension CNsub ×1 CNsub ×Nsub

Description received symbol vector at antenna nr channel matrix between antennas nt and nr in frequency domain transmit symbol vector at antenna nt pilot-symbols vector at antenna nt transmit data vector at antenna nt additive noise at antenna nr received symbol vector at subcarrier k MIMO channel matrix between subcarriers k and l precoding matrix at subcarrier k effective channel matrix Hk,k Wk transmit data at subcarrier k additive noise at subcarrier k channel estimation error at subcarrier k transmit power of one layer transmit pilot-symbol power transmit data power Inter Carrier Interference power noise power channel estimation error variance interpolation error carrier frequency number of pilot-symbols number of data-symbols number of layers number of transmit antennas number of receive antennas number of subcarriers offset between power of pilot-symbols and data-symbols post-equalization SINR at layer l

CNsub ×1 PNp ×1 CNd ×1 CNsub ×1 CNr ×1 CNr ×Nt CNt ×Nl CNr ×Nl DNl ×1 CNr ×1 CNr ×Nt R R R R R R R R N N N N N N R R

For the derivation of the post-equalization SINR, we use an MIMO input-output relation at the subcarrier level, given as: yk = Hk,k Wk sk + nk + Hk,m Wm sm . (4) m=k

ICI

A. Channel Estimation

Matrix Hk,m ∈ CNr ×Nt denotes an MIMO channel matrix between the k-th and m-th subcarrier. MIMO channel matrix Hk,m contains appropriately ordered elements of matrices ˜ nt ,nr located in the k-th row and the m-th column. Vector sk H consists of the data-symbols of all layers at the k-th subcarrier. Vector nk represents additive white Gaussian zero-mean noise with variance σn2 at subcarrier k. We denote the effective channel matrix including precoding by Gk,k = Hk,k Wk .

the post-equalization SINR under channel estimation error. At the end of this section, we explain the actual design of the optimal pilot-symbol patterns under doubly selective channels.

(5)

Furthermore, the average power transmitted at each of the Nl layers is denoted by σs2 . The total power transmitted on each data position is σd2 , while that on each pilot position is denoted by σp2 . III. O PTIMAL P ILOT PATTERN D ESIGN In this section, we show how to design optimal pilot-symbol patterns for doubly selective channels. As the cost function for the measure of optimality, we choose an upper bound of the constrained capacity based on the post-equalization SINR that includes channel estimation errors. We begin with a brief summary of the state-of-the-art about linear channel estimation. Subsequently, we proceed with an explanation of

The introduced concept is presented for a general linear estimator and interpolator, exemplarily we present results for LS and LMMMSE estimators in combination with linear and LMMSE interpolators [20]. The authors of [3] showed that optimal performance of an MIMO channel estimator was obtained with pilot patterns that are orthogonal over individual transmit antennas. Such pilot patterns allow to estimate an MIMO channel as Nt Nr individual Single Input Single Output (SISO) channels. Due to optimal performance of such MIMO patterns, we restrict our discussion to pilot-symbol patterns that are orthogonal over individual antennas. Note that the LTE-standard utilizes such orthogonal pilot pattern. In a pilot-aided linear channel estimation, an interpolated channel estimate at data position j is obtained as a weighted sum of a set of channel estimates from the pilot positions in the neighborhood Pj of the data positions j ˆ p,i , ˆ d,j = wj,i h (6) h i∈Pj

where ˆhd,j and ˆhp,i are channel estimates at the j-th data position and at the i-th pilot position, respectively.2 In [10], it 2 Note, the indexes j and i represent some positions within the timefrequency grid.

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was shown that the MSE of a linear channel estimator defined in Equation (6) can be stated as follows σe2 = ce

2 σn2 + σICI + d, 2 σp

(7)

where the variables ce and d are real constants that determine the performance of the considered linear channel estimator. The value of the constant ce can be obtained as [10] ce =

Nd 1 2 wj,i , Nd j=1

(8)

i∈Pj

and the value of the interpolation error d as in [10] d= Nd

(9) ⎞

⎛

1 ⎝ wj,i {Rj,i } + wj,i wj,i Ri,i ⎠ , 1−2 Nd j=1 i∈P i∈P j

j

i ∈Pj

where Rj,i is a channel correlation coefficient between the j-th and the i-th channel positions. The choice of the interpolation weights wj,i follows an interpolation scheme.

γ¯l =

σd2

−1 . 2 + σ 2 σ 2 ) eH GH G Nl (σn2 + σICI el k,k e d l k,k

In this subsection, we briefly summarize knowledge related to the post-equalization SINR of a ZF equalizer under channel estimation errors, for more details consult [8], [10]. The key step towards the derivation is to replace the channel matrix Hk,k in the MIMO input-output relation Equation (4) by an ˆ k,k expanded by an estimation estimated channel matrix H error, which we denote by Ek,k

ˆ k,k + Ek,k Wk sk + nk + yk = H Hk,m Wm sm . m=k Hk,k

(10) Since the channel estimation error matrix Ek,k is unknown at ˆ k,k = H ˆ k,k Wk the receiver, the ZF solution is based on G and given by

−1 ˆ ˆH ˆH ˆsk = G G (11) k,k Gk,k k,k yk . With the equalized data-symbol vector, we obtain the expression for the estimated average post-equalization SINR at the l-th transmission layer [8] for a given estimated effective ˆ k,k channel matrix G σd2

−1 , 2 + σ 2 σ 2 ) eH G H G ˆ ˆ Nl (σn2 + σICI el e d l k,k k,k

(12)

where the variable σe2 represents the variance of the elements of the channel estimation matrix Ek,k . In Equation (13), we assumed that the available data power σd2 is evenly distributed σ2 between individual layers, i.e., σs2 = Ndl . For small estimation ˆ k,k in errors Ek,k , the estimated effective channel matrix G Equation (12) can be replaced by its true value Gk,k . By doing so, we can directly obtain the average post-equalization SINR

(13)

Simulations have validated that in the typical operational range of LTE, the expressions in Equation (12) and in Equation (13) do not differ significantly. Furthermore, we include a-priori knowledge about the channel estimation performance into the average SINR expression of a ZF equalizer by inserting Equation (7) in Equation (13) and decompose the expression into two parts γ¯l = fh (Gk,k ) fpow ce , d, σd2 , σp2 , σn2 , (14) with the so-called power fpow ce , d, σd2 , σp2 , σn2 being fpow ce , d, σd2 , σp2 , σn2 =

allocation

σd2

2 σn2 + σICI + ce

2 +σ 2 σn ICI 2 σp

function

+ d σd2 (15)

and the equalizer allocation function fh (Gk,k ) =

B. Post-equalization SINR

γˆ¯l =

of a ZF equalizer at the l-th transmission layer for a given effective channel matrix Gk,k as

1 .

−1 H G G N l eH e k,k m m k,k

(16)

It was shown in [21] that the post-equalization SINR of a ZF equalizer is a random variable following a Gamma distribution for a stationary channel. Therefore, when assuming a stationary channel, the mean value of the equalizer allocation function can be obtained analytically σZF,G = E {fh (Gk,k )} .

(17)

The value of σZF,G is equal to Nr − Nt + 1 if neglecting antenna correlation [21], [22]. Inserting Equation (17) in Equation (14), the average post-equalization SINR for a ZF equalizer under imperfect channel knowledge is obtained as γ¯ = E {¯ γl } =

(σn2 +

(18) σd2 2 σICI +

σe2 σd2 )

σZF,G .

C. Optimal Pilot-Symbol Pattern In [23], it was shown that for channel estimation of doubly selective channels with a given pilot-symbol overhead, diamond-shaped pilot-symbol patterns were optimal in terms of channel estimation MSE. It is, however, not shown how to choose distance parameters of the diamond-shaped pilotsymbol pattern. Figure 1 shows an example of such a diamondshaped pilot-symbol pattern. Diamond-shaped pilot-symbol patterns can be decomposed into two patterns with pilotsymbols equi-spaced in time and in frequency directions with distances Dt and Df , respectively. These two patterns with equi-spaced pilots are separated from each other by D2t in the time direction and by D2f in the frequency direction. Therefore, a diamond-shaped pattern is fully described by two variables Df and Dt . Figure 1 shows an example of a diamond-shaped pilot-symbol pattern with Df = 10 and Dt = 4.


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Dt

1.2

Df/2

Df

Df Dt

1.1 1.0

ce

0.9 0.8 0.7

Dt/2

pilot symbol Fig. 1.

0.6

data symbol

Example of a diamond-shaped pilot-symbol pattern.

Considering only diamond-shaped pilot-symbol patterns, we continue our investigation and show which diamond patterns in combination with power distribution among the pilot- and the data-symbols are optimal. The provided framework is not limited solely to this pilot-pattern family. We consider only the diamond-shaped patterns in order to limit the number of possible pilot patterns. The coefficient ce from Equation (7) is purely determined by the pilot-symbol pattern and interpolation error d additionally depends on the channel autocorrelation function. Therefore, from this point on, we use the following notation ce (Df , Dt ) and d (Df , Dt , Rh ), in which the variable Rh represents the channel autocorrelation matrix. Figure 2 shows an exemplarily behavior of the coefficient ce (Df , Dt ) versus the distance between two adjacent pilotsymbols in one dimension while the distance in the second dimension is fixed. Let us first consider a case, in which the distance in the time direction between adjacent pilot-symbols Dt is fixed and the distance in the frequency direction is varied. This case corresponds to the dashed blue curve in Figure 2. The behavior is intuitive to understand up to a certain distance. With an increasing distance between pilot-symbols Df , the variable ce (Df , Dt ) is also increasing. The curve is not perfectly smooth due to the required extrapolation for points outside the diamond shape. The pilot pattern is always located in a symmetric position with respect to the center of the timefrequency grid. Due to the centralization of the pilot pattern, the number of the points outside of the diamond shape can vary depending on the distance parameters of the diamond pattern. Consider a case, in which increasing the distance between pilot-symbols in the frequency direction does not decrease the amount of pilot-symbols in a given bandwidth. In such a case, there are less data positions to extrapolate and therefore the value of ce (Df , Dt ) slightly decreases even though the distance between the pilot-symbols is increased. This effect is even more identifiable when the variable Df becomes larger and the amount of the data positions to extrapolate becomes significant compared to the number of the total data-symbols. Therefore, at higher values of Df , we observe a sawtooth curve behavior of the variable ce (Df , Dt ). If Df is increased by one and the variable ce (Df , Dt ) changes from a local minimum

LS channel estimator

0.5

0

10 Dt

20

30 Df

40

50

60

Fig. 2. The red solid curve represents the coefficient ce (Df , Dt ) versus Dt while keeping Df = 7. The blue dashed curve shows the behavior of the coefficient ce (Df , Dt ) versus Df while keeping Dt = 7. Both curves are shown for an LS channel estimator.

to a local maximum, the amount of the pilot-symbols in the frequency direction is decreased by one. This behavior can be clearly observed in the red solid curve in Figure 2, which shows the value of the variable ce (Df , Dt ) versus Dt while keeping Df fixed. The sawtooth behavior originates from the fact that we consider only 14 OFDM symbols in order to be able to consistently compare the proposed system with a conventional LTE system. Therefore, the number of data positions to extrapolate is always significant compared to the total number of data positions. Note that the maximum distance between pilots in the time direction is 26. This distance value ensures that at least two pilot-symbols in the time direction are utilized within the considered 14 OFDM symbols. Figure 3 shows the behavior of the interpolation error d (Df , Dt , Rh ) for a varying distance in the frequency direction while the distance in the time direction is fixed (blue dashed line) and the corresponding case, in which the distance in the time direction is varied while the distance in the frequency direction is fixed (red solid line). The behavior of both curves is intuitive to understand, as an increase in the distance in either direction causes an increase in the interpolation error. Note that the interpolation error depends on the second-order statistics of the channel. If the correlation is strong, the interpolation error is small [24]. Figure 3 shows a bound on the best performance of an LS estimator for a Doppler frequency of 350 Hz under the VehA channel model. Even if no noise and no ICI are present, the overall MSE is equal to d (Df , Dt , Rh ), as can be inferred from Equation (7). At this point, we can analytically express the performance of a linear channel estimator as a function of Df and Dt for diamond-shaped pilot-symbol patterns. With this knowledge it is possible to maximize the average post-equalization SINR in Equation (14) simply by maximizing the power allocation function in Equation (15) [10]. However, the optimal values of Df and Dt and the optimal power distribution between the pilot- and the data-symbols cannot be found exclusively

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-10

-15 interpolation error d [dB]

variables B (Df , Dt ), ce (Df , Dt ), and d (Df , Dt , Rh ) on the variables Dt , Df , and Rh in the above equations. The ultimate target from physical-layer perspective is to maximize throughput. As throughput is very difficult if not impossible to track analytically [26], we require an alternative analytical performance measure that allows to predict throughput in the best way possible. The presented upper bound of the constrained capacity fulfils these requirements. In this work we consider a case in which the entire available power is utilized for the transmission, and therefore, σd2 and σp2 can be expressed in terms of the variable poff defined as the ratio between the power of the pilot-symbols and of the data-symbols

Df Dt

-20

-25

-30

-35

-40

VehA channel model Doppler frequency 350 Hz LS channel estimator

0

10 Dt

20

30 Df

40

50

60

Fig. 3. The red solid curve represents the interpolation error d (Df , Dt , Rh ) versus Dt while keeping Df = 7. The blue dashed curve shows the behavior of the interpolation error d (Df , Dt , Rh ) versus Df while keeping Dt = 7. Both curves are shown for an LS channel estimator and VehA channel model for a Doppler frequency of 350 Hz..

by maximizing the post-equalization SINR. Such an approach leads to a solution with small distances between adjacent pilot-symbols in the time and frequency directions, which would decrease the available bandwidth for data transmission. Therefore, another cost function is required that includes a penalty due to the bandwidth occupied by the pilot-symbols. The constrained capacity is a natural choice for the new cost function since it provides a more accurate estimate of the expected throughput than capacity [25], [26] C = B (Df , Dt ) log2 (1 + γl ) ,

(19)

where B (Df , Dt ) is the bandwidth utilized for the data transmission which clearly depends on the number of employed pilot-symbols. The constrained capacity in Equation (19) is realistic as a waterfiling solution for a temporally changing channel is not feasible. Note also that for typically measured frequency selective MIMO channels, the difference between the waterfilling solution (capacity) and the proposed constrained version is very small [27]. The impact of given precoding matrices can be included in the channel estimation, as we consider here. Variable γl represents the instantaneous post-equalization SINR. However, Equation (19) cannot be directly utilized as a cost function, since it would require the knowledge of the instantaneous channel matrix and its estimation error. These are however not available and thus we utilize an ergodic capacity in terms of its expectation value. Such ergodic capacity requires the a-priori knowledge of statistics and is in general difficult to evaluate. However, its upper bound [28] obtained by applying Jensen’s inequality when inserting the mean post-equalization SINR γ¯ from Equation (18) in the constrained capacity expression Equation (19), results in ¯ C ≤ C, C¯ = B (Df , Dt ) log2 (1 + γ¯ ) , = B log2 1 + fpow ce , d, σd2 , σp2 , σn2 σZF,G .

(20) (21) (22)

Due to space limitations, we omit the dependency of the

poff =

σp2 . σd2

(23)

Consequently, the variables σd2 and σp2 can be expressed in terms of the variable poff and the numbers of the pilot- and data-symbols as Np + Nd = poff σd2 , Nd + N p poff + N N p d σd2 = . Nd + Np poff

σp2 =

(24) (25)

Therefore, the cost function depends on only three variables poff , Dt , and Df for a given channel autocorrelation matrix Rh . With the cost function defined in Equation (22), we can formulate the optimization problem as maximize poff ,Dt ,Df

subject to

C¯ (poff , Dt , Df ) Nd σd2 + Np σp2 ≤ constant B (Df , Dt ) ≤ constant

(26)

To solve the above optimization problem, we first find numerically the optimal value of poff for all possible combinations of the variables Df and Dt . Consequently, we maximize the cost function over the variables Dt and Df in order to find the optimal triple (poff , Dt , Df ). Figure 4 illustrates the number of the pilot-symbols in optimal pilot-symbol patterns as a function of Doppler frequency with granularity of 50 Hz, for a fixed Channel Quality Indicator (CQI) 7 corresponding to an Additive White Gaussian Noise (AWGN)-equivalent SNR of 4.6 dB for various numbers of transmit antennas. The optimal number of pilot-symbols is increasing with increasing Doppler frequency. The required amount of pilot-symbols is also increased when multiple transmit antennas are utilized, since more channel coefficients have to be obtained by the channel estimator. Note that in the given bandwidth of 1.4 MHz an LTE-compliant system utilizes 48 pilot-symbols in the case of a single transmit antenna, 96 and 144 pilot-symbols in the cases of two and four transmit antennas, respectively. D. Adaptive Pilot Pattern In this subsection, we describe the concept of adaptive pilot patterns and briefly explain how to choose pilot patterns to allow a simple implementation into already existing standards.


100

80 number of pilot-symbols Np

E. Complexity

1×1 2×2 4×4

90

LS channel estimator AWGN equivalent SNR 4.6 dB RMS delay spread 400 ns

70

4×4

60 50 40

2×2

30 20

1×1

10 0

0

200

4711

400 600 800 Doppler frequency [Hz]

1000

1200

Fig. 4. Number of the pilot-symbols in optimal pilot-symbol patterns as a function of Doppler frequency for a fixed SNR and RMS delay spread of 400 ns for various numbers of transmit antennas.

Let us consider an LTE system for a moment. This system for wireless transmission allows to adapt coding rate, modulation alphabet, precoding and some other important parameters of the transmission according to the quality of the channel. The main idea in LTE is the usage of the so-called CQI that is reported by the user equipment back to an eNodeB. The CQI is not only a measure of the channel quality, it also defines two important transmission properties, the coding rate and the modulation alphabet. There are 15 different CQIs defined in LTE. The CQI corresponds to an AWGN equivalent SNR value of a channel realization. Therefore, for each CQI value, an optimal pilot pattern should be defined. This allows to distinguish various SNR values without any additional feedback. We propose to define 15 different pilot-symbol patterns each one corresponding to one of the 15 different CQIs and avoid to create any additional overhead to the already existing feedback. Therefore, if CQI ”1” is transmitted, the first pilotsymbol pattern is utilized, and so on. Such an approach avoids the necessity of an extra feedback for the pilot-symbol pattern, but with such zero overhead we fail to distinguish specific channel types with different temporal or frequency dispersion. In order to allow the pilot pattern to adapt to varying user mobility, pilot patterns for various Doppler spreads (user velocities) have to be defined [29]. In [30], it was shown that in order to support various Doppler frequencies up to 1200 Hz with adaptive pilot-patterns, it is sufficient to divide the support range into four bins and define only one pilot pattern for each bin. Additionally, it was also shown that in order to support channels with an RMS delay spread up to 800 ns, it is sufficient to divide the given range into four bins and define an optimal pilot pattern for each bin. These additionally defined pilot patterns require four bit of extra feedback if coded brute forcely. Since the pilot-symbol pattern is used across the entire transmission bandwidth, the amount of required feedback bits is negligible compared to the amount required by other narrow-band feedback indicators (CQI, rank indicator, precoding matrix indicator).

Based on the above considerations about feedback requirements of the proposed adaptive pilot pattern scheme, it is required to generate 15 · 4 · 4 · 3 = 720 different pilot patterns if applied in LTE to support 15 different SNR values, four different Doppler frequency regions, four different RMS delay spread regions and three different transmit antenna setups. Let us stress again, only four additional wide-band feedback bits would be required in LTE [30], owing to the already provided feedback. Since we utilized an upper bound of the constrained capacity as the cost function, the optimal pilot patterns are independent of the actual channel realization and therefore they can be calculated off-line. In general, we need to consider the complexity requirements at the transmitter and at the receiver. At the receiver two additional estimators are required compared to an OFDM system with a fixed pilot pattern; an estimator on Doppler frequency and an estimator on RMS delay spread. Note that since only four bins are required to support Doppler frequencies up to 1200 Hz and only four bins to support an RMS delay spread up to 800 ns, very course estimators are sufficient. Therefore, the extra complexity is negligible. At the transmitter, an evolved frame-builder is required that supports different placements of pilot-symbols. Its complexity is higher compared to a standard frame-builder. The complexity of such a frame-builder is not within the scope of this paper. IV. S IMULATION R ESULTS In this section, we present simulation results and compare performance of a transmission system employing the proposed adaptive pilot patterns with an LTE transmission system under doubly selective channels. All results are obtained with the Vienna LTE Link Level Simulator version ”r1089” [16], [17], which can be downloaded from www.nt.tuwien.ac.at/ltesimulator. All data, tools and scripts are available online [18] in order to allow other researchers to reproduce the results shown in this paper. In all figures that show simulations results, we plot 95% confidence intervals to indicate the precision of the presented simulation results. Note that the simulator performs all routines according to the standard [19]. We utilize a channel model with an exponentially decaying power delay profile with a variable RMS delay spread. This allows us to consider channels with different amounts of frequency selectivity. In order to generate channels with an arbitrary RMS delay spread, we utilized the model presented in [31]. For generating channels with an arbitrary Doppler spread, we utilized the modified Rosa Zheng model, presented in the appendix of [32]. In order to investigate the performance of the proposed solution, we show throughput simulation results. We decided to show this performance metric, because we believe that from a physicallayer point of view, throughput is the metric that is of the most importance for service providers and service users. We define throughput as the number of data bits in a successfully decoded transport block per time unit. This definition reflects the fact that a transport block is discarded if its forward error mechanism cannot recover from its bit errors. Table II presents the most important simulator settings.

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TABLE II S IMULATOR SETTINGS

20 optimal pilot pattern optimal power allocation LTE pilot pattern

18

throughput [Mbit/s]

16

Doppler frequency 200 Hz RMS delay spread 400 ns LS channel estimator

4×4

200

150

2×2 100

50

1×1

4×4 0

Doppler frequency = 200 Hz RMS delay spread 400 ns LS channel estimator

14

1×1 2×2 4×4

250

Value 1.4 MHz 1, 2, 4 1, 2, 4 ZF Open-loop spatial multiplexing adaptive 2.5 GHz

throughput gain [%]

Parameter Bandwidth Number of transmit antennas Number of receive antennas Receiver type Transmission mode MCS carrier frequency

300

0

5

10

15 SNR [dB]

20

25

30

12

Fig. 6. Throughput gain as a function of SNR of a system utilizing adaptive pilot-symbol patterns relative to an LTE compliant system for various numbers of transmit and receive antennas at a fixed Doppler frequency of 200 Hz and a fixed RMS delay spread of 400 ns.

10 8

2×2 6 4

1×1

2 0

0

5

10

15 SNR [dB]

20

25

30

Fig. 5. Throughput comparison between an LTE compliant system with a system utilizing adaptive pilot-symbol patterns for various numbers of transmit and receive antennas at a fixed Doppler frequency of 200 Hz and a fixed RMS delay spread of 400 ns.

Figure 5 shows throughput curves for two different wireless transmission systems. The solid curves represent an LTE compliant system for various numbers of transmit and receive antennas. The dashed lines represent a system that is the same in all aspects as the LTE system except for the utilized pilot-symbol patterns. The second system utilizes the adaptive pilot-symbol patterns as proposed in Section III. The adaptive pilot-symbol pattern consists of 15 different pilot patterns, each associated with a single CQI value. Note that the pilot patterns were designed based on the framework introduced in Section III-C for a channel with an RMS delay spread of 400 ns and a fixed Doppler frequency of 200 Hz. In LTE, the amount of pilot-symbols located at the third and fourth antenna is only half of the number of pilot-symbols located on the first and second transmit antennas. The pilot-symbol reduction is achieved by removing pilot-symbols in the time dimension. Therefore, the throughput for a 4 × 4 transmission system is more significantly improved when employing adaptive pilot patterns compared to 1 × 1 and 2 × 2 transmission systems. Figure 6 shows the achieved relative throughput gain versus SNR of the transmission system utilizing adaptive pilotsymbol patterns compared to the LTE-standard compliant system. The throughput gain is larger for lower SNR values, in which a precise channel estimate can be obtained via power increase at the pilot-symbols. The gain in Figure 6 is decreasing with increasing SNR since the relative improvement of the channel estimation quality compared to an LTE system is more significant for lower SNR values. The throughput gain of a 1×1 system at an SNR of 30 dB is close to zero, therefore

we can conclude that the LTE pilot pattern is close to optimal for such a situation. The gain of a 4 × 4 system at low SNR values is infinitely large, since the standard compliant LTE system shows zero throughput in this SNR region. Figure 7 shows throughput curves as function of Doppler frequency with a fixed SNR of 14 dB and a fixed RMS delay spread of 400 ns for two different wireless transmission systems. The solid curves represent an LTE compliant system for various numbers of transmit and receive antennas. The dashed lines represent a system that is the same in all aspects as the LTE system besides the utilized pilot-symbol pattern. The second system utilizes the adaptive pilot-symbol pattern as proposed in Section III. We generated a pilot pattern for each CQI value with Doppler frequency granularity of 50 Hz. An LTE system utilizing a 4 × 4 antenna setup delivers poor performance at high velocities. This is caused by the sparse pilot-symbols over the time dimension at the third and fourth antennas. A significant improvement of the system utilizing adaptive pilot patterns when transmitting with four antennas can be explained by the placement of additional pilot-symbols in the time dimension that improves the quality of the channel estimates. Figure 8 shows the achieved relative throughput gain as function of Doppler frequency for the transmission system utilizing adaptive pilot-symbol patterns when compared to the LTE-standard compliant system. With increasing Doppler frequency, the throughput gain increases for all antenna configurations. Throughput is increased approximately by 100% for 1 × 1 and 2 × 2 systems at high Doppler frequency and for a 4 × 4 system throughput is more than 850% higher than in an LTE-standard compliant system. In Figure 9, throughput versus RMS delay spread for LMMSE and LS channel estimators for a time-invariant channel (at a Doppler frequency of 0 Hz) is shown. The throughput of all presented curves is approximately constant with a slight decrease when the RMS delay spread increases. The dashed lines represent transmission systems employing LTE pilot patterns. These systems are always outperformed


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6

6 SNR = 14 dB RMS delay spread 400 ns LS channel estimator

5

5

4×4

LMMSE channel estimator throughput [Mbit/s]

throughput [Mbit/s]

2×2 4

3

1×1

2

optimal pilot pattern optimal power allocation LTE pilot pattern

1

0

SNR = 14 dB 3

2 optimal pilot pattern LTE 1

200


1000

1200

Fig. 7. Throughput comparison between an LTE compliant system with a system utilizing adaptive pilot-symbol patterns for various numbers of transmit and receive antennas at an SNR of 14 dB versus Doppler frequency for a channel with an RMS delay spread of 400 ns.

SNR = 14 dB RMS delay spread 400 ns LS channel estimator

700 600

4×4

30 25

500

20 15

400

0

6

throughput [Mbit/s]

800

LMMSE channel estimator LS channel estimator

5 0 200

400

500

100

1×1 200

LMMSE channel estimator

SNR = 14 dB

2 optimal pilot pattern LTE LMMSE channel estimator LS channel estimator

600

2×2 0

800

3

200

0

600

4

1 300

400 RMS delay spread [ns]

SNR = 30 dB

10

300

200

Doppler frequency 0 Hz 1×1 transmission system

5

1×1 2×2 4×4

900


Fig. 9. Throughput versus RMS delay spread for LMMSE and LS channel estimators at a Doppler frequency of 0 Hz and SNR of 14 dB and 30 dB.

1000

throughput gain [%]

4

0 0

SNR = 30 dB


1000

0

0

200



RMS delay spread 400 ns 1×1 transmission system

1000

1200

1200

Fig. 8. Throughput gain versus Doppler frequency of a system utilizing adaptive pilot-symbol patterns relative to an LTE compliant system for various numbers of transmit and receive antennas at an SNR of 14 dB for a channel with an RMS delay spread of 400 ns.

by the corresponding systems utilizing optimal pilot patterns (solid lines). The throughput gain when applying optimal pilot patterns compared to LTE pilot patterns for an LMMSE channel estimator is approximately 2.5% at an SNR of 14 dB and 4.5% at an SNR of 30 dB. The gain when utilizing optimal pilot patterns for an LMMSE channel estimator is significantly lower than for an LS channel estimator, especially for an SNR of 14 dB. It is remarkable that the throughput of optimal pilot patterns for LS and LMMSE channel estimators is almost identical with a small performance gain when applying an optimal LMMSE channel estimator. Therefore, when utilizing the proposed adaptive pilot patterns under time-invariant channels, the performance of an optimal LMMSE estimator can almost be achieved by an LS channel estimator of lower complexity. Figure 10 displays the throughput as a function of Doppler frequency for LMMSE and LS channel estimators at a fixed RMS delay spread of 400 ns and an SNR of 14 dB and 30 dB. The throughput of all considered systems decreases with an

Fig. 10. Throughput versus Doppler frequency for LMMSE and LS channel estimators at an RMS delay spread of 400 ns and SNR of 14 dB and 30 dB.

increasing Doppler frequency. The most significant throughput decrease occurs when employing LS channel estimators under LTE fixed pilot patterns. When utilizing an LMMSE channel estimator instead, the performance is significantly improved compared to an LS channel estimator. The gain obtained via adaptive pilot patterns for an LMMSE channel estimator ranges between 2% and 7% at an SNR of 14 dB and between 3% and 15% at an SNR of 30 dB. The system throughput for a low complex LS channel estimator with the proposed adaptive pilot patterns is close to the system with a fixed LTE pilot pattern employing a high complex LMMSE channel estimator. Therefore, we can conclude that with the proposed adaptive pilot patterns, it is possible to decrease the computational complexity at the receiver side while almost achieving the performance of an LMMSE channel estimator with fixed pilot pattern. In [20], throughput comparisons of various linear channel estimators is provided. V. C ONCLUSIONS In this work, we showed how to design optimal pilotsymbol patterns with an optimal power distribution among the pilot- and the data-symbols for doubly selective channels.

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We utilized an upper bound of the constrained capacity based on the post-equalization SINR including channel estimation errors. With this relatively simple framework, pilot-symbol patterns can be designed for a given second-order statistics of the channel. Furthermore, we proposed a so-called adaptive pilot-symbol patterns that adjusts to the changing channel statistics. We present a throughput comparison between an LTE-standard compliant system with a system utilizing the proposed adaptive pilot-symbol patterns supporting a Doppler frequency up to 1200 Hz and an RMS delay spread up to 800 ns with only four additional wide-band feedback bits. The system utilizing adaptive pilot pattern outperforms an LTE-standard compliant system in all considered situations. The performance gain for an SISO system ranges between 3% and 80% depending on the considered scenario. For a 4×4 transmission system the performance gain is significantly higher and can reach up to 850% compared to a conventional LTE system. ACKNOWLEDGMENT The authors would like to thank the LTE research group and in particular C.F.Mecklenbräuker for continuous support and lively discussions. This work has been funded by the Christian Doppler Laboratory for Wireless Technologies for Sustainable Mobility, KATHREIN-Werke KG, and A1 Telekom Austria AG. The financial support by the Federal Ministry of Economy, Family and Youth and the National Foundation for Research, Technology and Development is gratefully acknowledged. The authors are also thankful to CNPq and FAPERJ for their financial support to the second author. R EFERENCES [1] R. Negi and J. Cioffi, “Pilot tone selection for channel estimation in a mobile OFDM system,” IEEE Trans. Consumer Electron., vol. 44, no. 3, pp. 1122–1128, Aug. 1998. [2] I. Barhumi, G. Leus, and M. Moonen, “Optimal training design for MIMO OFDM systems in mobile wireless channels,” IEEE Trans. Signal Process., vol. 51, no. 6, pp. 1615–1624, June 2003. [3] B. Hassibi and B. Hochwald, “How much training is needed in multipleantenna wireless links?” IEEE Trans. Inf. Theory, vol. 49, no. 4, pp. 951–963, Apr. 2003. [4] S. Adireddy, L. Tong, and H. Viswanathan, “Optimal placement of training for frequency-selective block-fading channels,” IEEE Trans. Inf. Theory, vol. 48, no. 8, pp. 2338–2353, Aug. 2002. [5] W. Zhang, X. Xia, and P. Ching, “Optimal training and pilot pattern design for OFDM systems in Rayleigh fading,” IEEE Trans. Broadcasting, vol. 52, no. 4, pp. 505–514, Dec. 2006. [6] X. Cai and G. Giannakis, “Error probability minimizing pilots for OFDM with M-PSK modulation over Rayleigh-fading channels,” IEEE Trans. Veh. Technol., vol. 53, no. 1, pp. 146–155, Jan. 2004. [7] L. Tong, B. Sadler, and M. Dong, “Pilot-assisted wireless transmissions: general model, design criteria, and signal processing,” IEEE Signal Process. Mag., vol. 21, no. 6, pp. 12–25, Nov. 2004. ˇ [8] M. Simko, S. Pendl, S. Schwarz, Q. Wang, J. C. Ikuno, and M. Rupp, “Optimal pilot symbol power allocation in LTE,” in Proc. 2011 IEEE Veh. Technol. Conf. – Fall. ˇ [9] M. Simko and M. Rupp, “Optimal pilot symbol power allocation in multi-cell scenarios of LTE,” in Conf. Record 2011 Asilomar Conf. Signals, Syst. Comput. ˇ [10] M. Simko, Q. Wang, and M. Rupp, “Optimal pilot symbol power allocation under time-variant channels,” EURASIP J. Wireless Commun. Netw., July 2012. ˇ [11] M. Simko, P. S. R. Diniz, Q. Wang, and M. Rupp, “Power efficient pilot symbol power allocation under time-variant channels,” in Proc. 2012 IEEE Veh. Technol. Conf. – Fall).

[12] O. Simeone and U. Spagnolini, “Adaptive pilot pattern for OFDM systems,” in Proc. 2004 IEEE International Conf. Commun., vol. 2, pp. 978–982. [13] C.-H. Kim and Y.-H. Lee, “Adaptive pilot signaling in the uplink of OFDM-based wireless systems,” in Proc. 2007 IST Mobile Wireless Commun. Summit, pp. 1–5. [14] J.-C. Guey and A. Osseiran, “Adaptive pilot allocation in downlink OFDM,” in Proc. 2008 Wireless Commun. Netw. Conf., pp. 840–845. [15] P. Han, J. Wang, and P. Xu, “Adaptive pilot design based on doppler frequency shift estimation for OFDM system,” in Proc. 2010 International Conf. Comput. Design Applications, pp. V4–533–V4–536. [16] C. Mehlführer, M. Wrulich, J. C. Ikuno, D. Bosanska, and M. Rupp, “Simulating the long term evolution physical layer,” in Proc. 2009 EUSIPCO. ˇ [17] C. Mehlführer, J. C. Ikuno, M. Simko, S. Schwarz, M. Wrulich, and M. Rupp, “The Vienna LTE simulators—enabling reproducibility in wireless communications research,” EURASIP J. Advances Signal Process., pp. 1–13, July 2011. [18] “LTE simulator homepage.” Available: http://www.nt.tuwien.ac.at/ ltesimulator/ [19] 3GPP, “Evolved universal terrestrial radio access (E-UTRA); Physical channels and modulation,” 3rd Generation Partnership Project (3GPP), TS 36.211, Sept. 2008. Available: http://www.3gpp.org/ftp/ Specs/html-info/36211.htm ˇ [20] M. Meidlinger, M. Simko, Q. Wang, and M. Rupp, “Channel estimators for LTE-A downlink fast fading channels,” in Proc. 2013 International ITG Workshop Smart Antennas 2013 (WSA 2013), Stuttgart, Germany, Mar. 2013. [21] D. Gore, R. Heath Jr., and A. Paulraj, “On performance of the zero forcing receiver in presence of transmit correlation,” in Proc. 2002 IEEE International Symp. Inf. Theory, p. 159. [22] P. Li, D. Paul, R. Narasimhan, and J. Cioffi, “On the distribution of SINR for the MMSE MIMO receiver and performance analysis,” IEEE Trans. Inf. Theory, vol. 52, no. 1, pp. 271–286, Jan. 2006. [23] J. Choi and Y. Lee, “Optimum pilot pattern for channel estimation in OFDM systems,” IEEE Trans. Wireless Commun., vol. 4, no. 5, pp. 2083–2088, Sept. 2005. ˇ [24] M. Simko, P. S. R. Diniz, Q. Wang, and M. Rupp, “New insights in optimal pilot symbol patterns for OFDM systems,” in Proc. 2013 IEEE WCNC [25] C. Mehlführer, S. Caban, and M. Rupp, “Cellular system physical layer throughput: how far off are we from the Shannon bound?” IEEE Wireless Commun., vol. 18, no. 6, pp. 54–63, Dec. 2011. ˇ [26] S. Schwarz, M. Simko, and M. Rupp, “On performance bounds for MIMO OFDM based wireless communication systems,” in 2011 Signal Process. Advances Wireless Commun., pp. 311–315. [27] M. Rupp, J. Garcia-Naya, C. Mehlfuhrer, S. Caban, and L. Castedo, “On mutual information and capacity in frequency selective wireless channels,” in Proc. 2010 IEEE International Conf. Commun.. [28] S. Loyka and A. Kouki, “New compound upper bound on MIMO channel capacity,” IEEE Commun. Lett., vol. 6, no. 3, pp. 96–98, Mar. 2002. ˇ [29] M. Simko, Q. Wang, and M. Rupp, “Optimal pilot pattern for time variant channels,” in Proc. 2013 IEEE International Conf. Commun. ˇ [30] M. Simko, P. S. R. Diniz, and M. Rupp, “Design requirements of adaptive pilot-symbol patterns,” in Proc. 2013 ICC Workshop: Beyond LTE-A. [31] K. Hassan, T. Rahman, M. Kamarudin, and F. Nor, “The mathematical relationship between maximum access delay and the RMS delay spread,” in Proc. 2011 International Conf. Wireless Mobile Commun., pp. 18–23. [32] T. Zemen and C. Mecklenbräuker, “Time-variant channel estimation using discrete prolate spheroidal sequences,” IEEE Trans. Signal Process., vol. 53, no. 9, pp. 3597–3607, Sept. 2005.


ˇ Michal Simko was born in Bratislava, Slovakia, in October 1985. In June 2009, he received his Dipl.Ing. degree (with highest honors) and in May 2013 his Ph.D. degree (with highest honors), both from Vienna University of Technology, Vienna, Austria. In June 2011, he received bachelor degree in industrial/organizational and social psychology from the Comenius University, Bratislava, Slovakia. Since August 2009 he has been working as a project assistant at the Institute of Telecommunications, Vienna University of Technology. During August and September 2010 , he was a visiting researcher at the Department of Electrical Engineering of Linköping University, Sweden. From January 2012 to June 2012, he was a visiting researcher at the Signal Processing Laboratory of Federal University of Rio de Janeiro, Brazil. His research interests include channel estimation techniques, pilot pattern optimization, and communications under time-variant channels. Michal authored and co-authored more than 30 scientific papers. He has been awarded the Best Student Paper Award by IEEE VTS Society at IEEE VTC 2011 Spring in Budapest, Hungary. Paulo S.R. Diniz was born in Niterói, Brazil. He received the Electronics Eng. degree (Cum Laude) from the Federal University of Rio de Janeiro (UFRJ) in 1978, the M.Sc. degree from COPPE/UFRJ in 1981, and the Ph.D. from Concordia University, Montreal, P.Q., Canada, in 1984, all in electrical engineering. Since 1979 he has been with the Department of Electronic Engineering (the undergraduate dept.) UFRJ. He has also been with the Program of Electrical Engineering (the graduate studies dept.), COPPE/UFRJ, since 1984, where he is presently a Professor. He served as Undergraduate Course Coordinator and as Chairman of the Graduate Department. He has received the Rio de Janeiro State Scientist award, from the Governor of Rio de Janeiro state. From January 1991 to July 1992, he was a visiting Research Associate in the Department of Electrical and Computer Engineering of University of Victoria, Victoria, B.C., Canada. He also held a Docent position at Helsinki University of Technology. From January 2002 to June 2002, he was a Melchor Chair Professor in the Department of Electrical Engineering of University of Notre Dame, Notre Dame, IN, USA. His teaching and research interests are in analog and digital signal processing, adaptive signal processing, digital communications, wireless communications, multirate systems, stochastic processes, and electronic circuits. He has published several refereed papers in some of these areas and wrote the text books Adaptive Filtering: Algorithms and Practical Implementation, Fourth Edition, Springer, NY, 2013, and Digital Signal Processing: System Analysis and Design, Second Edition, Cambridge University Press, Cambridge, UK, 2010 (with E. A. B. da Silva and S. L. Netto), and the monograph Block Transceivers: OFDM and Beyond, Morgan & Claypool, New York, NY, 2012 (W. A. Martins, and M. V. S. Lima). He has served as the Technical Program Chair of the 1995 MWSCAS held in Rio de Janeiro, Brazil. He was the General co-Chair of the IEEE ISCAS2011, and Technical Program co-Chair of the IEEE SPAWC2008. He has also served Vice President for region 9 of the IEEE Circuits and Systems Society and as Chairman of the DSP technical committee of the same Society. He is also a Fellow of IEEE. He has served as associate editor for the following Journals: IEEE T RANSACTIONS ON C IRCUITS AND S YSTEMS II: A NALOG AND D IGITAL S IGNAL P ROCESSING from 1996 to 1999, IEEE T RANSACTIONS ON S IGNAL P ROCESSING from 1999 to 2002, and the Circuits, Systems and Signal Processing Journal from 1998 to 2002. He was a distinguished lecturer of the IEEE Circuits and Systems Society for the year 2000 to 2001. In 2004 he served as distinguished lecturer of the IEEE Signal Processing Society and received the 2004 Education Award of the IEEE Circuits and Systems Society. He also holds some best-paper awards from conferences and from an IEEE journal.

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Qi Wang received the B.Eng degree in telecommunication engineering from Beijing University of Posts and Telecommunications, China in 2005, M.Sc degree in computer science and engineering from Linköping University, Sweden in 2007 and Dr. techn degree from Vienna University of Technology, Austria in 2012. From 2008 to 2012, she was with Institute of Telecommunication, Vienna University of Technology in Austria, where she worked as a research/teaching assistant. Her research interests include synchronization and channel estimation techniques, performance modeling and evaluation for modern wireless communication systems. She is currently a system engineer with AKG Acoustics GmbH, Vienna, Austria. Markus Rupp received his Dipl.-Ing. degree in 1988 at the University of Saarbruecken, Germany and his Dr.-Ing. degree in 1993 at the Technische Universitaet Darmstadt, Germany, where he worked with Eberhardt Haensler on designing new algorithms for acoustical and electrical echo compensation. From November 1993 until July 1995, he had a postdoctoral position at the University of Santa Barbara, California with Sanjit Mitra where he worked with Ali H. Sayed on a robustness description of adaptive filters with impact on neural networks and active noise control. From October 1995 until August 2001 he was a member of Technical Staff in the Wireless Technology Research Department of BellLabs at Crawford Hill, NJ, where he worked on various topics related to adaptive equalization and rapid implementation for IS-136, 802.11 and UMTS. Since October 2001 he is a full professor for Digital Signal Processing in Mobile Communications at the Vienna University of Technology where he founded the Christian-Doppler Laboratory for Design Methodology of Signal Processing Algorithms in 2002 at the Institute of Telecommunications. He was associate editor of IEEE T RANSACTIONS ON S IGNAL P ROCESSING from 2002-2005, is currently associate editor of EURASIP Journal of Advances in Signal Processing and EURASIP Journal on Embedded Systems. He is elected AdCom member of EURASIP since 2004 and served as president of EURASIP from 2009-2010. He authored and co-authored more than 400 scientific papers and patents on adaptive filtering, wireless communications, and rapid prototyping, as well as automatic design methods.