Closed-Loop Transmit Diversity for FDD WCDMA Systems

Transcription

1 Closed-Loop Transmit Diversity for FDD WCDMA Systems Jyri ämäläinen Nokia Networks, PO Box 319 FN 9051 Oulu, Finl Risto Wichman Nokia Research Center, PO Box 07 FN 0005 NOKA GROUP, Finl Abstract Transmit diversity techniques provide attractive solutions for increasing downlink capacity in 3G systems within low-mobility environments Open-loop closed-loop transmit diversity modes with two transmit antennas have already been included into 3GPP WCDMA Release, at the moment schemes exploiting a larger number of transmit antennas are being developed System capacity can be increased from that of open-loop modes if the transmitter is equipped with additional side information of the downlink channel n an FDD system this means that the receiver has to provide the information through some feedback mechanism n this paper we give a general algorithm by which it is possible to design a large variety of different closed loop schemes depending on the feedback capacity of the system The quantization of the transmit weights can be reduced to an eigenvalue problem by using linear functions of order statistics of the underlying probability distribution This provides a simple analytical tool for the design of feedback algorithms Furthermore, we provide analytical results for the transmit weights in the case of single path Rayleigh fading channels 1 ntroduction The uplink capacity of the proposed third generation CDMA systems can be enhanced by various techniques including multi-antenna reception multi-user detection Techniques that increase the downlink capacity have not been developed in recent years with the same intensity owever, it is understood that the capacity dem imposed by the projected data services (eg nternet) burdens more heavily the downlink channel ence, it is important to find techniques that improve the capacity of the downlink channel Bearing in mind the strict complexity requirements of terminals, the characteristics of the downlink channel, a brute-force application of advanced detectors with multiple receive antennas is not seen as the desired solution to the downlink capacity problem Alternative solutions have been proposed suggesting that multiple transmit antennas at the base station will increase downlink capacity with only minor increase in terminal implementation Open-loop transmit diversity techniques apply various linear or non-linear preprocessing techniques to combat the fading channel Recently, the linear filtering approach has been generalized in [1] A coding perspective to transmit diversity was contributed in [, 3] with the introduction of space-time codes that can be optimized to fading channels The simplest space-time code [] has been adopted into 3GPP WCDMA stard as an open-loop transmit diversity method The paper is structured as follows: Section summarizes the current closed loop transmit diversity modes in 3GPP WCDMA Release Section 3 introduces the system model which is further utilized in the analysis of the feedback algorithms in Sections 5 The paper is concluded in Section Summary of the Current Feedback Modes Closed loop transmit diversity techniques are designed to improve the system performance over the open loop ones particularly within low mobility environments The prevailing 3GPP FDD WCDMA transmit diversity concept assumes two transmit antennas in the base station which are sufficiently close to each other so that the propagation delays between each transmitting element the mobile station are effectively identical The antennas need not be calibrated There are currently two different feedback modes with slightly different tradeoffs in effective constellation resolution signaling robustness n mode 1 the length of the feedback word is one bit, the base station interpolates between two consecutive feedback words making the transmit weight to follow a time-varying QPSK constellation n mode the feedback word consists of four bits where three

2 / e!! J % x J O bits are assigned to phase one bit to gain Thus, mode 1 maintains equal power transmission from both antennas while with mode the antennas transmit with different powers A detailed description of frame slot structures can be found in [] t is well know that the optimum transmit weight is the eigenvector corresponding to the maximum eigenvalue of the channel autocorrelation matrix, where! refers to the impulse response between the "#$ transmit antenna the terminal n FDD systems can be estimated by the terminal only therefore some related side information must be signaled to the base station Naturally, the signaling overhead should be minimized n the WCDMA system, terminal can obtain % by measuring % % from the common pilot channel 3 System Model Consider a system with transmit antennas in the base station a single receive antenna in the mobile station For the analysis we adopt! a single path Rayleigh fading channel model Since is now a complex scalar rather than vector, we denote! ( instead of ) * +,- instead of Mobile station receives the signal from the dedicated channel as (0/35 where /7 9:;9<=>>?9@ BA 5 is the transmitted symbol, is zero-mean Gaussian noise, consists of transmit weights signaled from the C mobile station components of the channel vector >>? * are zero-mean F;G Gaussian rom variables with the common variance D We assume that channel coefficients are independent n later sections it will be denoted! (J! J The mathematical formulation / for the problem of finding the best possible transmit weight becomes (1) /LKMN O J P/QKRJS 7TVU;W J P/[J X<YZ 7\/ ]^9:_9@S?>>_9` aabo9<!]dc it f Find N where has been assumed that e n the following section we give two low-complexity suboptimal algorithms which are able to find a good solution for the problem (1) The performance of the algorithms is illustrated using the expected SNR improvement factor g ih@\jj P/[J c k lh@\nm?o=pqbd3srjt:uvwcmxym?o=pzb<3h`\)rjtuvc), which provides the upper bound for the system capacity improvement in a fading channel because Two Feedback Algorithms The first algorithm has been addressed previously in [5], where it has been assumed that a feedback word of length, bits is provided to the base station having antenna elements Thus, it consists of information about the state of each relative phase between reference antenna other antennas A generalization utilizing } feedback bits/antenna is given by the following algorithm Algorithm Assume that + ) } bits of \ side information is available Then the transmit weights ~!Mc! % are chosen by using the condition 3 ~!! J= TVU;W 3 ~!! J () ƒys Fx where " \nˆ= Š ŒRŽ? _ GS 57 S S0c That is, we adjust each phase independently against the phase of the first channel t should be noticed that the complexity of the example algorithm increases linearly with additional antennas, ie, complexity is proportional to )_ Previously, feedback schemes have been considered assuming unquantized transmit weights [] Algorithm applies only phase adjustments owever, given the limited capacity of the feedback channel it is also reasonable to consider schemes where the best antennas in terms of gains are selected first then phase adjustments are applied to the selected antennas Two such schemes for transmit antennas have been proposed in [] The first scheme selects strongest channels adjusts their phase difference with } ] while the second scheme selects 3 strongest antennas A natural generalization to the above scheme is to weight transmit amplitudes in addition to adjusting phase differences ntuitively, the stronger the channel, the more power should be transmitted through it Bearing this in mind we give the following general feedback scheme!mc! ad- \ Algorithm Receiver ranks some or all \ justs the phase differences of the corresponding!0c!< by applying Algorithm Order phase difference information is signaled to the transmitter which then chooses appropriate amplitude phase weights from a finite quantization set Note that this is a suboptimum algorithm because amplitude phase weights are determined separately One of the crucial questions when applying Algorithm is the selection of suitable quantizer Uniform quantizer suffices for the quantization of phase differences, but finding a good quantizer for transmit powers is not any more a trivial task f the number of transmit antennas is small then the quantization for amplitude weights can be found using simulation

3 ± ± «Ð D D Š Ð Û Î Í Ë Í but when the number of transmit antennas is large, it can become a cumbersome task 5 Analysis of Algorithms First we give a previously known result concerning to Algorithm [9] Proposition 1 Let be the number of transmit antennas assume that there are ) } feedback bits available Then the SNR improvement g for the Algorithm is given by (3) g d3 + l _ž>ÿqs R * d3 š vœ where Consider next a simple example corresponding to Algorithm Assume that } bits of feedback information are reserved for the phase adjustments a single feedback bit is used to inform the transmitter which base station antenna offers better received power for the mo- 9: bile Assume that 9 9@ are real positive amplitude weights such that 39 Then we have g 9 h`\ c39 h@\ c3s 9 9 h@\ c h`\n o R `c where is the adjusted phase difference between antennas Since the order of the antennas is signaled to the base station we may state that TLUWz\ c TLž?Ÿš\ c Distributions of these variables are obtained using the elementary theory of probability n the case of single path Rayleigh fading channels we find that () g /ª«P/ «( ŒS ŒS ³² «where is the correlation matrix between antennas when phase adjustments has been done Although we have assumed that the correlation between the antennas is initially zero, this will not be the case after the phase adjustment Thus, g is simply / «the largest eigenvalue of the best weight vector is the corresponding eigenvector t is interesting to note that in the case of two transmit antennas (5) Setting } C 9 w dµ d3 ŒS œ œ is analogous to the FDD WCDMA transmit / º¹=¹; =»= =¼»; diversity mode / ½j, while the stard specifies The corresponding SNR improvements become g l ¾= qà g : S ), respectively Let us now consider the general case of transmit antennas Algorithm Since the number of different per- \ mutations of! c! is Â, the number of feedback bits becomes à m>osp  Ž> B ÅÇÆ, where } is the number of phase bits/antenna n a similar manner as in the proof of Proposition 1 [9] we obtain g 3s! 9! h`\!! Ê š Ž?!< cd3s 9<!9 Ê h`\!<š Ž?!< 9<!9: h`\ Ž?!< Ž Ê cv b/ «P/ where /7 F9:;9<= 9`* the elements of matrix are given by!!l lh@\!: Ê Ž?!< c= h`\ Ž Ê c h@\ Ê!P ŽÉ_ c Ž?!< ŽÉ_ c:!p "ÌË ³Í Í S Thus, the largest eigenvalue of matrix «is equal to g the best amplitude weight vector is obtained from the corresponding eigenvector This is a general principle which is not restricted to single path Rayleigh fading channels The most difficult problem when calculating g is to find the expectation of rom variables Ž?!< correlations Ž>! Ž Ê Fortunately, in the case of single path Rayleigh fading channels this problem has been solved in [7] resulting in h@\ h@\ Ž Ê c: ³ Ž Ê Ž Ò? cv Ê Î ÏKÐ Ò Î ÏK Ê ^ÑB Ê Ò Š ÏK Ð Ê ÑBS n Í Í ² Ñ ² 3Ñ Í03bn Ê Ò_Ñw ÓRÔ Ê ÒBÑw ÓR Ö Í where coefficients Ð Ê ÒBÑ ÇÓR Î?Ø are of the form n Ê Ò^Ñw ÓR Â Ñ ² Ó ² n Í n + Í Ô Ê Ò ^Ñw ÓR` F -Í z3sñ Ó= Ù ÍP3ÚÓM3³) () is defined by ^Û Ü ^ÛaÜÏ <ÝÞß Uàw ž?ÿ Û á Ûš3Ü œ À _ž>ÿ À Uàw ž>ÿ á Û 3Ü œnœâ t is worth noticing that in [7], where is expressed in terms of Beta function since the main results are given for Weibull

4 î } ê ù N=3 SNR mprovement Factor SNR mprovement Factor N=1 N= 0 Number of Antennas Number of Feedback Bits Figure 1 SNR improvements as a function of the number of transmit antennas using Algorithm when the number of feedback bits is ãbäåçæïèqé_êìë íçîïïñðyòdóô õöw, øúù+û ( o ), ø ù ( + ) øüù,ý ( x ), where ø refers to the number of phase bits/antenna Solid line corresponds to the ideal case where the transmitter has the complete knowledge of the channel distribution owever, v in the case of Rayleigh distribution it is easy to see that has also the simpler expression () Figure 1 displays SNR improvements when applying Algorithm à m?o=p  Ž> _ ÅÇÆ feedback bits t is noticed that the SNR performance of the given scheme is very near to optimal when there are three phase adjustment bits/antenna Since the number of feedback bits is limited in practical systems, it is of great importance to design schemes that provide relatively good SNR improvement already with a small number of feedback bits Basically there are two possible ways to decrease the number of feedback bits Firstly, one can dedicate less bits for phase adjustments or secondly, one can reduce the number of bits dedicated to order information Figure 1 shows that g deteriorates quite rapidly when the number of phase bits is decreased Therefore we concentrate on reducing the number of feedback bits corresponding to order information «which translates into reducing the dimension of n the following we propose two examples of such schemes n the first scheme we assume that Ð out of anten- _9@ÿL BA /þ ^9 nas are selected so that /Vÿ Now the corresponding amplitude weight vector is the eigenvector «ÿ «ÿ corresponding to the largest eigenvalue of, where is the Ð Ð «principal submatrix of A Figure SNR improvements as a function of the number of feedback bits when out of û antennas are chosen, ãbäåçæ èzé_êìë éê the number öë í î ï Vòdóô õ of feedback öw bits is scheme similar to this has been proposed in [] for transmit antennas, where or 3 strongest antennas are selected their relative phases are adjusted owever, in [] no amplitude weighting is proposed Figure shows the SNR improvement factor for different numbers of feedback bits when applying Algorithm selecting Ð out of n¼ antennas so that the number of feedback bits becomes à m?o=p  Gj Ð Ž ÿ B ÇÆ t is noticed that when the number of phase bits is large, the SNR improvement factor saturates near optimum Comparing the curves } ] shows that when the number of feedback bits is low it is more efficient to increase the number of order bits than the number of phase bits n the second scheme only the strongest antenna is sig- / (^9: 9@ naled to the transmitter so that _9@BA adjusted with } «bits/antenna so that becomes a ««phase differences with respect to the strongest antenna are matrix denoted : m?o=p ) The entries of :!<š ŽÉ B vaæ!³!<š!:! 3! are given by )!! Ê š Ê œ so that à are required When is large the number of feedback bits is far more lower that in the scheme where we put all antennas in order Figure 3 depicts

5 î References SNR mprovement Factor 0 Number of Antennas Figure 3 SNR improvements as a function of the number of transmit ãbäåçæïè é_ê antennas íjî ï^ðyòdóô õ when applying Algorithm ö feedback bits, ø¾ù û ( o ), ø ù ( + ) ø ù ý ( x ) Solid line corresponds to the ideal case SNR improvements when the last scheme is applied Comparing Figures 1 3 we find that the decrease in SNR improvement is not large Finally, we emphasize that one can design several different schemes based on Algorithm n each case the amplitude weight vector / can be obtained as the eigenvector corresponding to the largest eigenvalue of suitably modified «Conclusions We studied closed-loop transmit diversity techniques suitable to FDD WCDMA system when the number of transmit antennas is larger than two We gave a general algorithm by which it is possible to design a large variety of different feedback schemes depending on the feedback capacity of the system Furthermore, we showed that the quantization of the transmit weights can be expressed as an eigenvalue problem by using linear functions of the order statistics of the underlying probability distribution, analytical results in the case of single path Rayleigh fading channels were obtained The formulation provides a simple analytical tool by which the quantization of the transmit weights can be obtained for a general class of feedback algorithms [1] A Narula, M D Trott, G W Wornell: Performance Limits of Coded Diversity Methods for Transmitter Antenna Arrays, Trans nformation Theory, V 5, No 7, November 1999, pp 1-33 [] SM Alamouti: A Simple Transmitter Diversity Scheme for Wireless Communications, Selected Areas of Comm, V, No, Oct 199, pp 51-5 [3] V Tarokh, N Seshadri, A R Calderbank: Space- Time Codes for igh Data Rate Wireless Communications, Trans nformation Theory, V, No, March 199, pp 7-75 [] 3GPP RAN WG1: UTRA Physical Layer General Description, No 501, Ver 30, March 000 [5] A Narula, M J Lopez, M D Trott, G W Wornell: fficient Use of Side nformation in Multiple- Antenna Data Transmission over Fading Channels, Journal of Selected Areas of Comm, V 17, No, Oct 199, pp 3-3 [] M Sell, Analytical Analysis of Transmit Diversity in WCDMA on Fading Multipath Channels, nternational Symposium on Personal, ndoor Mobile Radio Communications, 1999 [7] J Lieblein: On Moments of Order Statistics From The Weibull Distribution, Ann Math Stat, 1955, pp [] 3GPP TSG RAN WG1#15: Performance Results of Basis Selection Transmit Diversity for Antennas, Tdoc R , August 000 [9] J ämäläinen, R Wichman: Multiple Antenna Transmission Utilizing Side nformation for WCDMA Systems, The» #$ CDMA nternational Conference xhibition, Seoul, Korea, November 000