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Apr 20, 2010 - University of the Balearic Islands, 07122 Majorca, Spain e-mail: [email protected] F. Riera-Palou e-mail: [email protected]

Wireless Pers Commun (2011) 56:599–609 DOI 10.1007/s11277-010-9992-9

Cross-Layer Fast Link Adaptation for MIMO-OFDM Based WLANs Gabriel Martorell · Felip Riera-Palou · Guillem Femenias

Published online: 20 April 2010 © Springer Science+Business Media, LLC. 2010

Abstract This paper considers the use of cross-layer fast link adaptation (FLA) for WLANs employing a MIMO-OFDM physical layer. A packet error rate (PER)-based FLA technique that, without loss of generality, makes use of the exponential effective SNR mapping (EESM) is proposed. Additionally, an FLA scheme relying on bit error rate (BER) metrics is introduced that simplifies the link adaptation procedure without any significant performance degradation. Results show that both PER- and BER-based FLA techniques optimize the data throughput while satisfying prescribed quality of service constraints. Channel estimation errors have also been considered, revealing the importance of good channel estimators in order for FLA strategies to work satisfactorily. Keywords Fast link adaptation · MIMO-OFDM · IEEE 802.11n · Link quality metrics · Cross-layer design · Adaptive modulation and coding

1 Introduction Most current WLAN networks are based on one of the flavours of the IEEE 802.11 family of standards, notably, IEEE 802.11a/g. The physical layer of these standards typically employ orthogonal frequency division multiplexing (OFDM) and adaptive modulation and coding (AMC) based on bit interleaved coded modulation (BICM). Ideally, and based on some form of channel state information (CSI), AMC strategies are used to select a combination of modulation and coding scheme (MCS) aiming at the optimization of the spectral efficiency

G. Martorell (B) · F. Riera-Palou · G. Femenias Mobile Communications Group, Department of Mathematic and Informatics, University of the Balearic Islands, 07122 Majorca, Spain e-mail: [email protected] F. Riera-Palou e-mail: [email protected] G. Femenias e-mail: [email protected]

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subject to quality of service (QoS) constraints such as, for instance, a maximum average packet error rate (PER) outage probability, Pout , for a given target PER, P E R0 . Mathematically, the instantaneous PER of MCS m ∈ M , where M denotes the set of MCSs, can be expressed as Pm = Fm (SNR, L , H ) ,

(1)

where SNR is the received average signal-to-noise ratio, L is the packet length in number of information bits, H denotes the channel realization and Fm (·) represents an MCS-dependent mapping function. Thus, the optimum MCS selection process can be formulated as m ∗ = arg max ηm = arg max Tm (1 − Pm ) m∈M

subject to

m∈M

Pr {PER > P E R0 } ≤ Pout ,

(2)

where ηm and Tm denote the instantaneous throughput and transmission rate of MCS m, respectively. This optimization process, usually known as fast link adaptation (FLA), clearly shows a close interaction between the physical layer (PHY) and the medium access control (MAC) layer and claims for a PHY-MAC cross-layer design. Despite this claim, legacy WLAN standards only specify which MCSs are allowed for which types of MAC frames, but not how and when to switch between the permitted rates. Furthermore, there is no signaling mechanism specified that would allow a receiver to inform the transmitter about the actual link quality or the rate to be used. In order to overcome the lack of Rx-Tx feedback, the AutoRate Fallback (ARF) link adaptation protocol and its modifications (see [1] and references therein) have been widely used in legacy WLANs. In these methods, the PHY layer automatically switches to a lower rate after two consecutive transmission errors (missed ACKs) and switches to a higher rate either after ten successful transmissions (ACK reception) or after a time out. The rationale behind these approaches is that for the MCS set used in legacy systems and for a given SNR, a higher transmission rate in the MCS implies a higher instantaneous PER. The next mainstream WiFi technology, named IEEE 802.11n, has been recently approved by the IEEE 802.11 High Throughput Task Group committee [2]. The new standard supports much higher transmission rates thanks to the use of multiple-input multiple-output (MIMO) antenna technology, the possibility of operating on a 40 MHz bandwidth (employing more subcarriers) and transmission modes using a reduced guard interval. Furthermore, the MAC layer does incorporate mechanisms to feedback information regarding MCS selection, thus making FLA a feasible option. In MIMO systems, in addition to MCS selection, link adaptation algorithms face another challenge, the MIMO mode selection. In this case, a higher transmission rate in the MCS does no longer imply a higher instantaneous PER and thus, the traditional link adaptation algorithms used in single-input multiple-output (SIMO) legacy systems become hardly effective. This motivates the development of cross-layer FLA algorithms for MIMO-OFDM systems. As it can be inferred from (2), the key elements of the FLA optimization process are, on one hand, a high quality instantaneous PER prediction tool at the PHY layer for all possible MCS/MIMO modes, packet lengths and channel realizations, and, on the other hand, an MCS/MIMO mode selection methodology at the MAC layer that ensures the fulfilment of QoS constraints. In contrast to SISO systems, where approximate PER closed-form expressions are available [3], in the MIMO-OFDM case there is no simple and systematic approach for predicting PER assuming arbitrary MCS/MIMO modes, packet sizes, and channel realizations in frequency selective channels with arbitrary channel correlations. Unlike previous related works such as [4–6], this paper proposes PHY abstraction techniques that enable accurate PER

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prediction based on frame-by-frame bit error rate (BER) prediction. These techniques are based on a common approach that maps system parameters like the selected MCS/MIMO operation mode and channel realization onto a link quality metric (LQM) that can be associated to the PER by means of simple look-up-tables, which are independent of the packet length. Consequently, the approach presented in this paper greatly simplifies the calibration process of these look-up tables without significantly affecting system performance. Furthermore, appropriate LQMs are derived for different MIMO detection strategies used at the receiver side that allow the use of SDM- and STBC-based transmission modes. An MCS selection approach that fulfils the optimization constraint on the PER outage probability is introduced. Moreover, the impact of channel estimation errors on the performance of FLA techniques for IEEE 802.11n networks is considered.1

2 System Model Without loss of generality, our study focuses on the IEEE 802.11n standard [2]. Information bits are first encoded with a rate R = 21 convolutional encoder with generator polynomials [133, 171] and then punctured to one of the possible coding rates Rm ∈ {1/2, 2/3, 3/4, 5/6}. Depending on the selected MIMO configuration, the resulting bits are demultiplexed into Ns spatial streams. For each stream, the coded bits are interleaved and then mapped to symbols from one of the allowed constellations (BPSK, QPSK, 16-QAM or 64-QAM). In accordance with the selected MIMO configuration, the symbols are then either STBC encoded or antenna mapped on the available N T transmit antennas. The resulting symbols are finally supplied to a conventional OFDM modulator consisting of an IFFT and the addition of a guard interval. For simplicity of exhibition, this paper focuses on a 2 × 2 MIMO system (N T = 2 and N R = 2), implying that MCSs with Ns = 1 and Ns = 2 spatial streams employ STBC [? ] and SDM [8], respectively.2 Reception begins by inverting the OFDM modulation (e.g. GI removal and FFT processing) to obtain the received baseband samples, which for the kth subcarrier at time instant t can be expressed as r t [k] = H t [k]s t [k] + ηt [k]   s [k] r t [k] = H t [k] t,1 + ηt [k] st,2 [k]  ∗  −st,2 [k] r t+1 [k] = H t+1 [k] + ηt+1 [k] ∗ [k] st,1

(SDM)

(3)

(STBC)

(4)

where H t [k] denotes the N R × N T MIMO channel matrix affecting subcarrier k, s t [k] =  T st,1 [k], st,2 [k] is the N T × 1 vector of transmitted symbols with E{s t [k] s t [k] H } = (PT /N T )I NT , ηt [k] is the N R × 1 thermal noise vector characterized as a zero-mean additive white Gaussian noise (AWGN) with E{ηt [k] ηt [k] H } = σ 2 I N R . 1 Notational remark: vectors and matrices are denoted by lower- and upper-case bold letters, respectively. The superscripts (·)T and (·) H are used to denote the transpose and conjugate transpose of the corresponding

vector/matrix, respectively. The symbol I Q represents the Q-dimensional identity matrix, whereas E{·} is used to denote the expectation operator. Finally, given a matrix A, the notation [A] j,i is used to identify the element situated on the ith column and jth row. 2 Extension of this work to the use of cyclic delay diversity (CDD) is straightforward as the CDD processing can be effectively modeled as a simple modification of the channel delay profiles.

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Appropiate spatial processing takes place on the received baseband samples. Particularly, if Ns = 1, STBC has been applied at the transmitter side and usual Alamouti decoding is conducted. Assuming ideal CSI and that the channel’s coherence time is long enough to ensure that H t+1 [k] = H t [k], the MRC estimate can be obtained as3 y STBC [k] =

NR       h 1,n [k]2 + h 2,n [k]2 s[k] + η˜ [k]  k s[k] + η˜ [k] r r

(5)

nr =1

with h n t ,nr [k] denoting the channel coefficient linking Tx antenna n t with Rx antenna nr , and η˜ [k] is a zero-mean AWGN vector with E{η˜ [k] η˜ [k] H } = k σ 2 I 2 . The output SNR corresponding to transmitted symbol j can then be calculated as SNR j [k] =

PT k . NT σ 2

(6)

Alternatively, if Ns = 2, a linear MMSE detector is applied on the received samples in order to decouple the two streams. That is, −1  y SDM [k] = W [k]r[k] = H H [k] H [k] + N T σ 2 I NT H H [k] r[k]. (7) In this case, the post-MMSE equalizer SNR of transmitted symbol j is given by

−1 −1 PT H H [k] H [k] + I NT − 1. SNR j [k] = NT σ 2

(8)

j, j

It is well-known that soft decoding yields important benefits over hard-decision decoding. To this end, soft information in the form of likelihood ratios (LLRs) is computed following the technique proposed in [9]. The resulting LLRs are reformatted into streams and deinterleaved. Finally, spatial deparsing is applied and the output LLR sequence is supplied to a soft Viterbi decoder after suitable depuncturing.

3 Fast Link Adaptation 3.1 PER Prediction Methodology As shown in (1), the PER can be expressed as a function of MCS m∈M , the received SNR, the packet length L and the channel realization H . In MIMO-OFDM systems, each subcarrier on each spatial channel experiences a different channel response. Consequently, the function Fm in (1) must consider each individual subcarrier/spatial response in order to predict the PER for a given system configuration. It is difficult to find out a closed-form expression that accurately relates all the channel parameters into a single PER value. Different approaches have been proposed in order to map the instantaneous channel parameters onto a single link quality metric (LQM) that could be associated to the PER by means of look-up tables obtained from off-line simulations (see, e.g., [4,10] and references therein). Among all the proposed prediction strategies, those based on a one-dimensional mapping between a particular LQM, called effective SNR, and the PER are particularly interesting as demonstrated in [10]. Given an MCS m∈M , the corresponding effective SNR can be defined 3 In order to simplify the notation and due to independence among the transmitted/received symbol blocks,

the time subindex t is dropped from this point onwards.

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as the SNR that would be required by this MCS on an AWGN channel to attain the same PER obtained over the frequency selective fading channel realization. For a particular channel realization H , the effective SNR for a given MCS can be expressed as ⎛  ⎞ Nd NS   SNR [k] 1 j (m) (m) ⎠ SNRe f f = α1 J −1 ⎝ (9) J (m) N S Nd α j=1 k=1 2 where SNR j [k] is the post processing SNR, J (·) is a model-specific LQM function and (m) (m) J −1 (·) is its inverse. The parameters α1 and α2 allow the model to be adapted to the characteristics of the corresponding MCS and they are calculated off-line using a calibration procedure. As it can be deducted from the effective SNR definition, the look-up tables are the AWGN channel curves that take care of mapping the SNR to the PER system performance over the AWGN channel. Different LQM functions can be employed to perform the effective SNR mapping (see, for instance, [10]). In this paper, and without loss of generality, we concentrate on the EESM-based PER prediction strategy with J (γ ) = exp(−γ ). The proposed FLA scheme consists of an off-line calibration procedure and an on-line MCS selection process. In the off-line phase, a large set of channel realizations is used to obtain system performance results in terms of PER. These results then serve to calibrate the parameters of LQM functions, that can later be used during the on-line operation in order to determine the best MCS for the current channel realization, packet length and SNR. Calibration procedure (off-line): The optimum values for the fitting parameters α1(m) and (m) α2 in (9) are obtained off-line as     (m) (m) (m) (m) 2 E − SNR (10) α1 , α2 = argmin SNR α1 ,α2 H ,P ef f AWGN  opt opt (m)

for all m ∈ M , where SNR AW G N is the required SNR for mode m to obtain the same PER on the AWGN channel as on the current channel realization, H is a large set of independent channel realizations and P = [P E Rmin , P E Rmax ] represents the average PER interval subject to optimization. Figure 1 shows PER prediction results once the system has been calibrated. For single stream MCSs (upper-left), a high PER prediction accuracy can be appreciated (MSE values on the order of 10−3 ). For two-stream MCSs (lower-left), the prediction is not as tight as for single-stream MCSs (MSE values below 0.05); however, these inaccuracies do not significantly affect the performance of the FLA system. In order to fulfill the optimization constraint on the average PER outage, an effective SNR (m) threshold S N RT h is obtained for each m ∈ M such as    (m) (m) Pr PER AWGN SNRT h > PER0 = Pout , (11) (m)

where PER AWGN (·) represents the PER for mode m over the AWGN channel. This probabil(m) ity is found numerically using all realizations over the set H . The SNRT h values for several MCSs are represented using a vertical line in Fig. 1 (see the corresponding values in the table). MCS selection process (on-line): Let us define M as the ordered set of MCSs in increasing throughput order. That is, M = Q (M ) where Q represents a permutation mapping function. Using this set, an iterative process is used to select the most suitable MCS for a given channel realization. The FLA algorithm evaluates the effective SNR for the different MCSs

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α2 0.6862 1.1472 1.3612 3.1801 5.5075 15.1442 20.2077 25.2330 1.0663 2.6926 2.0792 8.9311 9.5111 32.8464 32.9344 37.9968 (m)

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Fig. 1 Effective SNR mapping for MCS6 (upper -le f t) and MCS14 (lower -le f t) and numeric calibration results (right) (calibrated over P = [0.01, 0.95] with 200 channel realizations from channel models B and E [13] and using L = 1,664 bits, PER0 = 0.1, and Pout = 0.05)

in descendent throughput order. During the evaluation of a given MCS, two situations may (m) occur: if the effective SNR of the MCS is above the corresponding S N RT h , the evaluated MCS is selected as a possible transmission mode; otherwise, the considered MCS is deemed unsuitable. This iterative procedure continues until either one MCS is selected or all MCSs have been discarded, in which case, the no transmission mode is selected. Some throughput values may be achieved using either SDM or STBC, in such cases, both MCSs are evaluated and if both are found suitable for transmission, the STBC-based one is selected due to its higher spectral efficiency at low SNR regimes [7]. 3.2 BER-Based PER Prediction Methodology The IEEE 802.11n standard does not specify a fixed packet length. Instead, the system determines dynamically the packet size in an attempt to efficiently trade system performance and data throughput [11]. Consequently, in order for FLA PER-based algorithms to be usable in IEEE 802.11n, a tedious calibration procedure would need to be conducted taking into account every possible packet length (or a representative subset of them). In order to avoid this situation, a novel solution is presented here that relies on BER, rather than PER, thus making the FLA strategy independent of the packet length L. The rational behind this strategy is the assumption that for long-enough packets4 , the BER is independent of L and consequently, if BER and PER can be related by means of a closed-form expression, PER prediction can be made on the basis of BER. The error event probability for a convolutionally encoded packet using MCS m can be approximated by (m)

Pe(m) ≈ Pb /d f ,

(12)

4 As it will be shown in the Sect. 4, this assumption does not imply any practical implementation restriction as for packet lengths on the order of a few hundred bits this approximation is already valid.

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605 (m)

where d f is the free distance of the convolutional code and Pb is the decoded bit error probability of MCS m. This approximation is based on the assumption that, in the mediumto-high SNR regime, the number of bit errors per error event is approximately equal to the free distance of the convolutional code. Note that for low SNRs, where this approximation could compromise the adaptation procedure, the no transmission mode is typically selected (m) and thus it does not affect the performance of the adaptive scheme. Using Pe , and given a fixed channel realization, then 

PER

(m)

 ≈ 1 − 1 − Pe(m)

L Rm



(13)

where Rm is the MCS code rate. This approximation is based on the assumption that an error-free packet is due to the absence of error events in each possible transition along the convolutional code trellis. The BER-based estimation relies on the EESM technique introduced earlier although (m) modifying some of its characteristics. Using (9), this new method determines the SNRe f f (m)

(m)

for each channel realization with α1 and α2 obtained from a calibration phase, where (m) PER curves have been replaced by BER curves. Correspondingly, an SNRT h is determined (m) (m) for each modulation-coding scheme m ∈ M in such a way that Pr{BER AWGN (SNRT h ) > Rm

(m)

(1 − (1 − PER0 ) L )d f } = Pout , where BER AWGN (·) represents the BER for mode m over the AWGN channel. The search algorithm is not modified.

4 Numerical Results A system equipped with N T = N R = 2 and defined according to the specifications of IEEE 802.11n [2] has been used. This has been configured to use full GI and Nc = 64 subcarriers over a 20 MHz bandwidth on the 5.25 GHz carrier frequency with Nd = 52 data subcarriers (remaining subcarriers are pilots or nulls). Frequency-time selective fading channel realizations, fully compliant with the IEEE channel models [12], have been generated using the MIMO channel model generator tool described in [13]. Denoting by λ the operating wavelength, the system has been configured with a Tx antenna spacing of λ and receive antenna (m) (m) spacing of 0.5λ. In order to determine α1 and α2 , the calibration set H has been defined by a mixture of 200 channel realizations from Channel profiles B and E over the PER interval P = [0.01, 0.95] using P E R0 = 0.1 and Pout = 0.05. Figure 2a, b shows throughput results obtained under the assumption of ideal CSI for both fixed and adaptive transmission strategies when using packets of length L = 1,664 bits. For comparison purposes, the results obtained using the performance bounds algorithm (PBA) are also shown. The PBA is an ideal FLA algorithm that for any channel realization is able to select, in a genie-aided fashion, the MCS with maximum throughput while ensuring zero transmission errors [6]. The EESM FLA clearly outperforms the fixed MCS and remains within 1.5 dB of the PBA. Furthermore, EESM fulfills the QoS constraints by keeping the PER well below PER0 (see Fig. 2d, e). The large difference in actual PER and PER0 , resulting in an overly pessimistic system, is basically due to the absence of power control. In order to account for non-ideal CSI at the receiver side, the estimated channel is modelled as Hˆ [k] = H [k] + ξ where ξ is an N R × N T matrix representing the channel estimation error with each element being Gaussian distributed with zero-mean and variance MSE = σ 2 τ0 /TOFDM , where TOFDM is the OFDM symbol period and τ0 is the largest delay

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introduced by the channel. This variance corresponds to the mean square error (MSE) of the maximum performance bound of the optimal MIMO-multicarrier channel estimator proposed in [14]. As it can be observed in Fig. 2c, when transmitting over Channel E, imperfect CSI produces a non negligible throughput degradation. Additionally, notice that for low SNRs the system PER constraint is not fulfilled (see Fig. 2e). The reason for this misbehavior is due to the large temporal dispersion of Channel E, which causes a large MSE in the channel estimation process. The fulfillment of the QoS constraints could be solved by selecting more conservative SNR threshold values at the expense of an additional decrease in throughput performance. Note that for Channel B, and owing to its small temporal dispersion, imperfect CSI barely affects performance (see Fig. 2d). Figure 3 shows results obtained when using BER-based PER prediction methods with L as parameter. It has been experimentally found that, in the considered scenarios, the BER performance is barely sensitive to packet length values over a several hundreds bits. Therefore, BER curves with L = 832 bits can serve as a reference to provide calibration parameters for any longer packet length. As an illustrative example, results for L = 832 bits have been extrapolated to predict the PER performance for L = 416 and L = 1,664 bits. As it can be observed, this approach leads to almost identical performance results (Fig. 3a, b) as the PER-based approach, thus validating the BER-prediction accuracy for practical values of L. There are no significant differences between PER-based FLA and BER-based FLA for ideal channel estimation (see Fig. 3a, c) and imperfect channel estimation (Fig. 3b, d). Notice that, as shown in Fig. 3a, b, even for short packet lengths (L = 416 bits), the degradation due to the use of the BER-based approach is negligible.

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5 Conclusions This paper has addressed cross-layer FLA techniques within the framework of IEEE 802.11n networks. Single and double stream MCSs using STBC and SDM, respectively, have been considered. It has been shown that PER prediction EESM-based FLA with ideal channel estimation meets the prescribed quality of service constraints while performing very close (∼1.5 dB) to the PBA in terms of throughput. When channel estimation errors are considered in highly frequency-selective channels (i.e., Channel Model E), the throughput performance of the proposed FLA algorithms is significantly affected and therefore, it is important to take these effects into consideration during the system design phase. A new variant of FLA has been introduced that is based on BER prediction (rather than PER) using EESM. This technique performs almost identically to its PER-based counterpart while, due to its independence from the packet length, it simplifies the costly calibration/prediction procedure. Acknowledgments Work funded by MEC and FEDER through project COSMOS (TEC2008-02422), Conselleria d’Economia, Hisenda i Innovació del Govern de les Illes Balears through PCTIB-2005GC1-09 and a PhD grant, and a Ramón y Cajal fellowship (MEC, European Social Fund).

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Author Biographies Gabriel Martorell was born in 1984 in Porreres, Spain. He received the B.S. degree in Telecommunication Engineering from the University of the Balearic Islands (UIB), Spain, in 2006 and the M.S. degree in Telecommunication Engineering from Technical University of Catalonia (UPC), Spain, in 2008. He is currently working towards the Ph.D. degree in the mobile communications group at UIB, with funding from the government of the Balearic Islands. His main research interests are mobile and wireless communications with an emphasis on adaptation techniques suitable for future wireless communications systems. He is a research member of COSMOS (Spanish government project).

Felip Riera-Palou was born in 1973 in Palma, Mallorca (Spain). He received the M.S. degree in Computer Engineering from the University of the Balearic Islands (UIB) (Mallorca, Spain), in 1997, the M.Sc. and Ph.D. degrees in Communication Engineering from the University of Bradford (UK) in 1998 and 2002, respectively, and the M.Sc. degree in Statistics from the University of Sheffield (UK) in 2006. From May 2002 to March 2005, he was with Philips Research Laboratories (Eindhoven, The Netherlands) first as a Marie Curie postdoctoral fellow (European Union) and later as a member of technical staff. While at Philips he worked on research programs related to wideband speech/audio compression and speech enhancement for mobile telephony. From April 2005 to December 2009 he was a research associate (Ramon y Cajal program, Spanish Ministry of Science) in the Mobile Communications Group of the Department of Mathematics and Informatics at UIB. Since January 2010 he is an associate research professor (I3 program, Spanish Ministry of Education) at UIB. Dr. Riera-Palou’s current research interests are in the general areas of adaptive and statistical signal processing and their applications to wireless communications.

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Guillem Femenias (M’91) was born in Petra, Spain, in 1963. He received the Telecommunication Engineer degree and the Ph.D. degree in telecommunications from the Universitat Politècnica de Catalunya (UPC), Barcelona, Spain, in 1987 and 1991, respectively. From 1987 to 1994, he was a Researcher with UPC, where he became an Associate Professor in 1990. In 1995, he joined the Department of Mathematics and Informatics, Universitat de les Illes Balears, Mallorca, Spain, where he is currently Full Professor leading the Mobile Communications Group. He has been the Project Manager of projects ARAMIS, DREAMS, DARWIN, MARIMBA, and COSMOS, all of which being funded by the Spanish and Balearic Islands Governments. In the past, he was also involved with several European projects (ATDMA, CODIT, and COST). His current research interests and activities span the fields of digital communications theory and wireless personal communication systems, with particular emphasis on multiple-input–multipleoutput cross-layer design in radio resource management strategies applied to fourth-generation systems. Dr. Femenias is a corecipient of the Best Paper Awards at the 2007 IFIP International Conference on Personal Wireless Communications and at IEEE 69th Vehicular Technology Conference (VTC-Spring 2009). He has served for various IEEE conferences as a Technical Program Committee Member and as the Publications Chair for the IEEE 69th Vehicular Technology Conference (VTC-Spring 2009).

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