Adaptive Switching between Spatial Diversity and Multiplexing: a Cross-layer Approach

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1 Adative Switching between Satial Diversity and ultilexing: a Cross-layer Aroach José Lóez Vicario and Carles Antón-Haro Centre Tecnològic de Telecomunicacions de Catalunya (CTTC) c/ Gran Caità -4, Barcelona (SPAI) mail: {jose.vicario, carles.anton}@cttc.es Abstract In this aer, we roose a cross-layer aroach to solve the roblem of switching between multilexing and diversity modes in an HSDPA context. In articular, three transmission modes are considered: diversity, satial multilexing and a hybrid diversity/multilexing mode. The main urose of this work is to achieve the maximum ossible data rate according to scenario conditions rather than minimize the symbol error rate. To do that, both the transmission mode and the modulation scheme are jointly selected aimed at maximizing link layer throughut. Hence, a cross-layer methodology is addressed in the sense that hysical layer arameters are adjusted with the aim of imroving link layer erformance. Comuter simulation results show the considerable erformance gains of the roosed crosslayer aroach for which comutational comlexity still remains affordable. Index terms Diversity, satial multilexing, cross-layer, IO, adative modulation. I. ITRODUCTIO IO techniques are aimed at either enhancing diversity or roviding satial multilexing caabilities. Satial diversity rovides a means to imrove link reliability. On the contrary, the multile aths rovided by such IO schemes are used in a satial multilexing context to transmit indeendent information streams. ost of current research in IO is focused on making use of only one aroach, but, recently, studies that combine both schemes have aeared in the literature. In that direction, a system based on switching between multilexing and diversity is roosed in. According to instantaneous channels conditions, the transmission mode is switched in order to minimize the resulting Symbol rror Rate (SR). For a constant data rate, it was shown that by choosing the best mode for a given channel realization, better results can be obtained than with the original aroaches searately. In order to imrove granularity in terms of SR, a third transmission mode that combines the advantages of both IO aroaches was included in 3. In articular, four transmit antennas are considered and the D-STTD technique 4, which consists in transmitting an indeendent Alamouti scheme in each air of transmit antennas, is taken as the hybrid mode. On the other hand, switching between transmission modes can be used in order to increase the data rate. For instance, in 0 This work was funded by the the uroean Commission under rojects IST and IST , those transmission modes that maximize the sectral efficiency for a re-determined target SR are selected according to channel conditions. That is, the selection algorithm chooses the transmission mode with the highest data rate for which the resulting SR is below a secific threshold. However, in ractical communications systems, link quality is determined not only by the erformance of the hysical layer rocedures but, also, by the secific rotocols used in uer layers (such as Automatic Reeat Request (ARQ)). Some otimization criteria aimed at maximizing link layer throughut, are resented in 6 7, showing considerable imrovement with resect to conventional hysical layeroriented designs. In this aer, a system caable of adatively switching between multilexing and diversity is roosed. The urose of this work is to achieve the maximum ossible throughut according to scenario conditions, rather than minimize the overall SR. In articular, by considering constant transmit ower, data rate is adated by jointly selecting the transmission mode and the modulation scheme. To do that, in a ractical system (as HSDPA), where all the system characteristics are secified, an aroriate otimization criterion is directly the maximization of the link layer throughut instead of the selection of the maximum transmission data rate subject to SR constraints. Hence, we address a cross-layer (CL) methodology in the sense that hysical layer arameters are adjusted aimed at imroving link layer erformance. This aer is organized as follows. In Section II, we describe the signal and system model. In section III, the different transmission modes available at the Base Station are resented. Then, we exlain the roosed cross-layer switching criterion in Section IV. Simulation results are discussed in Section V and, finally, we close the aer with the conclusions section. II. SIGAL AD SYST ODL Consider an HSDPA transmission link between an - antenna Base Station (BS) and an -antenna User quiment (U), and assume an ideal sreading/desreading rocess (see Figure ). By stacking T consecutive data samles, the received vector at the i-th sensor, (r i =r i (),.., r i (T ) T ), can be written r i = Sh i + n i ()

2 Q-OSTBC data source H-ARQ D-STTD obile radio channel H ZRO FORCIG H-ARQ data sink Satial multilexing Transmission configuration command (3 bits) Fig.. Block diagram of a IO communication system with an adative switching of the transmission mode. where S is the T symbol matrix that describes the transmission block code, according to the modulation scheme (R), h i =h i,.., h i T is the channel vector corresonding to the i-th receiver, and n i stands for an additive Gaussian noise vector of comlex, random variables with zero mean and variance σ (accounting for both intra- and inter-cell interference, since long scrambling codes are used). The channel imulse resonse is assumed to exhibit block Rayleigh flat-fading characteristics ( ms frames, with edestrian users moving at 3 km/h). Besides, it is also considered that erfect Channel State Information (CSI) is available at the receive side, where, in order to kee comutational comlexity moderate, a Zero- Forcing (ZF) detection scheme is used for all the transmission modes. Channel knowledge is used at the receiver to jointly estimate both the otimal transmission mode and modulation scheme maximizing link layer throughut according to the H-ARQ strategy under consideration (see section IV). Once the transmission configuration is selected, a low-rate error-free feedback channel is utilized to convey this information to the transmitter. At the transmit side, ower is evenly distributed among transmit antennas, that is, roortional to /. In order to roerly analyze the different transmission modes with a minimum number of receive antennas at the U, the number of transmit and receive antennas will be set to = =4. The reason for that being that an even number of transmit antennas 4 is required for the D-STTD scheme at the transmit side, whereas at the receiver, a number of antennas is needed for the satial multilexing mode. At the link level, a Tye III Hybrid-ARQ is adoted 8. In articular, in order to minimize signalling and buffering requirements at the U, the Sto-and-Wait (SAW) with chase combining method is used 9. Regarding the acket combining, this is done by simly averaging soft symbols at the outut of the ZF scheme 0. Therefore, the resulting symbol estimates after consecutive retransmissions can be exressed y = y ZF,i () where y ZF,i denotes the soft-symbol vector at the outut of the ZF scheme at the i-th transmission. III. TRASISSIO ODS This section is devoted to resent the different transmission schemes available at the Base Station. The corresonding signal-to-noise ratio for each transmission scheme is also given since this exression will be used in the next section to derive the link layer throughut. A. Diversity mode A Quasi-Orthogonal STBC (Q-OSTBC) code is considered for the diversity mode. Although full diversity is not obtained, this strategy is adoted since full rate (r =) is achieved. oreover, better erformance than with orthogonal designs is obtained over the low-sr range. The symbol block matrix, S is given by: s s s 3 s 4 S = s s s 4 s 3 s 3 s 4 s s (3) s 4 s 3 s s otice that, the diversity mode will be usually selected in the low-sr region.

3 For the ease of notation, the received signal can be rewritten y i = H i s + v (4) where vectors y i and v i have been redefined y i =r i,ri,ri 3,r i4 v i =n i,n i,n i 3,n i4 T (5) resectively, and H i stands for the equivalent sace-time channel matrix: h i h i h i3 h i4 H i = h i h i h i 3 h i 3 h i h (6) i h i4 h i3 h i h i As commented in the revious section, a ZF detector is adoted in all the transmission modes. Prior to detection, the received signal at the different branches are match-filtered and coherently combined: z = H H i y i = H H i H i s + H H i v i (7) After that, the transmitted symbols can be estimated ŝ = H H i H i z = s+ H H i H i H H i v i (8) The signal-to-noise ratio corresonding to the k-th symbol can be estimated k ρ k = σ w k k =,,...,, (9) where w k stand for the row vector in matrix W: W = H H i H i = w T w T w T 3 w T 4 H H i (0) When considering an SAW hybrid ARQ strategy in combination with a chase-combining scheme, ρ k will ultimately deend on the actual number of recombined soft-symbol ackets. Hence, the effective SR can be exressed as ρ k, = α ρ k, where is the accumulated number of transmissions and α is the chase-combining efficiency that models the combining gain loss resect to the theoretical model. otice that, from a maximum number of acket transmissions (P ) on, the effective SR no longer imroves and, thus, it is needed to limit the number of acket transmissions ( P ). Since all the row-vector norms are identical 3, the signalto-noise ratio corresonding to the diversity mode can be written ρ DIV, = α k σ w () It is worth noting that, the vector norm can be comuted without resorting to any matrix inversion (details are omitted here for brevity, see 3). B. Hybrid mode The hybrid mode is based on transmitting four different symbols during two consecutive time intervals. Then, at the exense of half diversity gain, data rate is doubled (r =). In articular, a D-STTD scheme is adoted, which results in the following symbol block: s s S = s 3 s 4 s s s 4 s () 3 Therefore, the equivalent sace-time channel matrix can be written H i = h i h i h i3 h i4 h i h i h i 3 (3) As in the diversity mode, the ZF detector is used. Hence, exressions (7) and (0) are still valid but taking into account the new matrix H exression given by (3). Again, no matrix inversion is required to comute the vector norms 3, but, in this case, vector norms are related by airs. That is: w = w w 3 = w 4 (4) Therefore, two different SR exressions exist for the hybrid transmission mode: ρ HYB,, = α k σ w ρ HYB,, = α k σ w 3 (5) C. Satial multilexing mode In this mode, four symbols are transmitted in arallel in each time-slot (r =4): S = s s s 3 s 4 (6) and, consequently, not transmit satial diversity can be exected (for a = =4configuration). The corresonding sace-time channel matrix can be exressed H i = h i h i h i3 h i4 (7) and exressions (7) and (0) can also be used to obtain the SR: ρ ULT,k, = α k σ w k k =,, 3, 4 (8)

4 IV. FAST ADAPTIV SWITCHIG BASD O CL DSIGS We start by deriving a closed-form exression for the linklayer throughut. By taking into account the secific modulation scheme and the transmission mode in use, a closed-form exression for the instantaneous SR can be obtained: SR DIV, = γ(ρ DIV,,R) SR HYB,k, = γ(ρ HYB,k,,R) k =, SR ULT,k, = γ(ρ ULT,k,,R) k =..4 (9) From that, we can derive an exression for the (uncoded) acket-error rate (PR) of an L -symbol acket, according to the transmission mode: PR DIV, = ( SR DIV, ) L (0) L PR HYB, = ( SR HYB,k, ) () k= 4 L PR ULT, = ( SR ULT,k, ) () k= otice that, acket size is constant for the three transmission modes but, as reflected in the above exressions, the number of redundant symbols increases when satial diversity is introduced. Finally, by estimating the average number of transmissions P =( PR )+ ( PR ) PR t (3) = t= where PR i must be aroriately chosen according to the corresonding transmission mode (equations (0)-()), the link layer throughut can be easily obtained: η SAW (m) = SAW W l r b (4) where W stands for the round-tri delay exressed in number of slots, SAW accounts for the number of concurrent SAW rocesses, l is the ratio of information bits er acket and b the number of bits er symbol, according to the modulation scheme in use. Therefore, the otimization rocess consists in jointly selecting the transmission mode and the modulation scheme that maximize this exression. otice that only three bits are required to convey that information to the transmitter via feedback channel. Given the highly non-linear nature of the otimization roblem, an exhaustive search is considered. Contributions to comutational comlexity mainly arise from the comutation of the instantaneous signal-to-noise ratio exressions (equations (), (5) and (8)) required for SR estimation, rather than from the scoring art. However, for the satial multilexing In this work, three transmission modes and two modulation schemes (QPSK and 6-QA) are considered, i.e. six transmission configurations are available at the transmitter. Throughut (b/s/hz) Diversity Hybrid Satial ultilexing Cross layer Sub otimum SR (db) Fig.. Link layer throughut vs. average SR for the different transmission schemes. (Solid lines: switching aroaches, dashed lines: QPSK, dotted lines: 6-QA) case, a reduced-comlexity version was develoed by the authors in 4. On the other hand, no matrix inversion is required for the Q-OSTBC and D-STTD schemes. Alternatively, when the receiver comutational requirements are further limited, a sub-otimum aroach based on the scenario statistics can be adoted. That is, the average link layer throughut is re-comuted for the different transmission modes and modulation schemes. Then, a set of thresholds for the average SR can be established. By doing so, the transmission mode and constellation size can be selected at the BS according to the long-term average SR of the system. V. SIULATIO RSULTS In an HSDPA context, frames for data bursts are divided into three slots, where three acket blocks of length L = 60 symbols are allocated. As far as comuter simulations are concerned, round-tri delay is assumed to be equal to W =3 slots and, thus, the number of concurrent SAW rocesses is adjusted to SAW =3. Information associated to the selected modulation scheme and transmission mode will be allocated in the Transort Format and Rate Combination (TFRC) field, as done for HSDPA coding-and-modulation modes, to be conveyed over an error-free feedback channel to the transmit side in a scenario of low mobility terminals (v U =3km/h). Transmission mode and modulation scheme configurations will be udated on a frame-by-frame basis, at most. The number of receive antennas and the maximum number of transmit antennas are equally set to = = 4. Concerning the chase combining reliability arameter, α, it was emirically set to 0.74 and 0.7 for QPSK and 6-QA, resectively, this setting the maximum number of acket transmissions to P =4.

5 Diversity Hybrid Satial ultilexing Cross layer Sub otimum VI. COCLUSIOS In this aer, a cross-layer design to switch between multilexing and diversity was derived. In order to obtain a customized design for an HSDPA system, an algorithm that jointly selects the otimal transmission mode and the modulation order maximizing the link layer throughut exression was adoted. It was mentioned that comutational comlexity considerations are not restrictive in ractical systems, but, still, in order to decrease receiver requirements, a statistical sub-otimum aroach was also derived. Regarding system erformance, both the roosed aroaches were shown to exhibit suerior erformance in comarison with the original IO techniques searately. Particularly, a considerably gain was obtained with the fast adative cross-layer technique since instantaneous variations of the scenario conditions are taken into account. Future work in the field will encomass an extension to multi-user scenarios and the study of the roosed transmission schemes in more realistic environments. For instance, scenarios where the correlation between transmit antennas is not neglected, or where effects such as errors or delay are introduced in the feedback channel. Average number of transmissions SR (db) Fig. 3. Average number of transmissions vs. average SR for the different transmission schemes. (Solid lines: switching aroaches, dashed lines: QPSK, dotted lines: 6-QA) Figure is devoted to show how both the roosed crosslayer design and the sub-otimum aroach make the most of the different transmission modes and modulation schemes as a function of the long term average SR. Clearly, considerable erformance gains can be obtained with an adative switching aroach with resect to using the original schemes searately. It is also clear that, for the whole range of SR, suerior erformance gain is obtained with the fast adative crosslayer technique since this aroach takes advantage of those instantaneous scenario conditions that allow higher throughut. Finally, one can observe that in terms of transmission delay (see Fig.3), the CL aroach in combination with H- ARQ mechanisms rovides a means to effectively kee the number of individual acket transmissions low for the whole range of signal to noise ratios (less than ). RFRCS L. Zheng and D. Tse, Diversity and multilexing: a fundamental tradeoff in multile-antenna channels, I Trans. on Inform. Theory, ay 003. R.W. Heath Jr. and A.J. Paulraj, Switching between satial multilexing and transmit diversity based on constellation distance, in Proc.of Allerton Conf. on Comm. Cont and Com., C.-B. Chae,. Katz, C. Suh, and H. Jeong, Adative satial modulation for IO-OFD, in Proc. I WCC, Double-STTD scheme for HSDPA systems with four transmit antenn Link level simulation results. Temorary document (0)-070, 3GPP TSG RA WG, June 00, release 5. 5 A. Forenza, A. Pandhariande, H. Kim, and R.W. Heath Jr., Adative transmission scheme selection for IO systems, in Proc. WWRF, J. Lóez-Vicario and C. Antón-Haro, Transmit antenna selection for rate adatation in HSDPA systems, in Proc. WWC, ay , Joint transmit antenna selection and adative modulation in crosslayer oriented designs for hsda systems, in Proc. I SA, July UTRA high seed downlink acket access, Technical Secification, 3rd Generation Partnershi Project, vol , arch 00, release 4. 9 Physical layer asects of UTRA high seed downlink acket access, Technical Secification, 3rd Generation Partnershi Project, vol , arch 00, release Onggosanusi, A. Dabak, Y. Hui, and G. Jeong, Hybrid ARQ transmission and combining for IO systems, in Proc. I ICC, vol. 5, , ay 003. H. Jafarkhani, A quasi-orthogonal sace-time block code, I Commun. Letters, Jan. 00. F. Frederiksen and T.. Kolding, Performance and modeling of WCDA/HSDPA transmission/h-arq schemes, Proc. I Vehicular Technology Conference Fall, Vancouver (Canada), vol., , Set J.L. Vicario and C. Anton-Haro, Receiver erformance of Quasi- Orthogonal STBC and D-STTD schemes, available for downloading from htt:// 4 J. Lóez-Vicario, C. ecklenbräuker, and C. Antón-Haro, Reducedcomlexity methods for throughut maximization in IO channels, in Proc. I ICC, June 004.