S 1 S 2 -S 2 * S 1 0 T 2T. TSG-RAN WG1 meeting #5 TSGR1#5(99)572 Cheju Korea, 1-4, June Mobile Antenna. Path 1. Ant 1.

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1 TSG-RN WG meeting #5 TSGR#59957 Cheju Korea, -4, June 999 Open loop downlink transmit diversity for TDD: STTD for TDD Texas Instruments, May 5 th, Introduction In the WG # 4, the time switched time diversity TSTD was accepted as the open loop antenna diversity technique for the downlink of the WCDM TDD systems. owever, TSTD suffers from the power amplifier P imbalance at the base station and results in a higher peak to average ratio PR. lso, TSTD does not yield full path diversity and only yields the diversity going through the interleaver. ence, the TSTD diversity gains are dependent upon the switching patterns and the interleaving scheme chosen. Further, we find that the TSTD raw ER performance is actually slightly worse than the nodiversity ND performance when half the users are switched on the first antenna and the other half are switched on the second antenna to maintain P balance. On the other hand, Space time block coding based transmit antenna diversity STTD is a P balanced scheme and yields full path diversity. ence, STTD has been accepted as the open loop antenna diversity technique for the WCDM FDD system. In this document we propose STTD for the WCDM TDD mode systems. We first derive the combined STTD decoder and the interference canceller, in particular for the zero forcing block linear equalizer ZF-LE, for the TDD systems. We denote this as the exact STTD ZF-LE. We then present a simplified STTD ZF-LE whose performance is the same as the exact STTD ZF-LE, but has lower complexity. ased upon the raw ER simulations, we find that the E b /N 0 gain for the simplified STTD ZF-LE over no-diversity ZF LE systems is between d and that over the TSTD ZF-LE is slightly higher and is between.-3.5 d. The total complexity increase of the simplified STTD ZF-LE over the overall complexity of the approximate no-diversity ZF- LE ND ZF-LE [4] is expected to be about 0-5 %, which is not a significant increase. We thus show that STTD gives substantial performance gains for the TDD system without significantly increasing the complexity of the user equipment UE..0 Open loop transmit Diversity. The space time transmit diversity STTD scheme for TDD The basic STTD encoder for TDD is the same as the FDD system [,, figure8 in 8] and is shown in figure for illustration. S S nt Path Mobile ntenna 0 S S STTD encoder T T -S S 0 T T nt Path j N data Figure : The block diagram of an STTD encoder for data is shown

2 TSG-RN WG meeting #5 TSGR#59957 Cheju Korea, -4, June 999 ence forth, we follow the same notation as that followed in [3] for analyzing the exact STTD ZF-LE. Similar to [3], let K be the number of users and M be the number of symbols transmitted, Q the spreading factor and the matrix denote the composite response of the antenna including multi-path. Similar to equation 6 in [3], the total received signal for STTD encoded data is now given by; e d d n.. where d is composite transmitted data vector equation of [3] and d is its conjugate. The form of the matrix is similar to that of matrix with a slight rearrangement of elements due to the STTD encoding as shown in figure and it is the composite channel response for d transmitted from antenna. We now write equation from equation above; e d n.. e d n e d n Letting E, C e, D and N we can rewrite the equation d n as; E CD N.3. ecause the rows of the top and bottom half of matrix C are linearly independent, the matrix C has full rank. The vector E in equation 3 can now be considered to be the net received vector corresponding to the equation 6 in [3]. Following the same procedure as in [3] to derive the ZF-LE, the corresponding form of equation 5 in [3] is; D ˆ ZF LE C RN C C RN E 4 T where C C. gain letting RN σ I KM KM the noise correlation matrix we get the exact STTD ZF-LE to be; D ˆ ZF LE C C C E.5 Notice that the above equation gives the estimate for both the vectors d and d. owever, by the construction of equation, both the estimate of d and the conjugate of the estimate of d are exactly the same. ence, it is not essential to obtain the estimates for both d and d, and an estimate for only one of them is sufficient.. Simplified STTD ZF-LE In equation 5 of the previous section we have presented the exact STTD ZF-LE. In this section we present the simplified STTD ZF-LE to reduce the complexity of the exact STTD ZF-LE. We can see that the main complexity increase for the exact STTD ZF- LE is the matrix inversion for the matrix C C in equation 5. The size of C C is x as against the matrix inversion involved in an ND ZF-LE equation 5 of [3] where in the matrix inversion is only of size x. ence, we now look into the details of the matrix inversion of C C. Expanding C C we get;

3 TSG-RN WG meeting #5 TSGR#59957 Cheju Korea, -4, June C C T T..6 where,,. The principal symbol energy terms are along the main diagonal of the matrix. The off-diagonal terms of the matrix correspond to the ISI and MI terms from antenna to antenna and antenna to antenna similar to the ND system. The matrix on the other hand consists of ISI and MI terms from antenna to antenna and vice versa. Since the principal symbol energies are all concentrated along the main diagonal terms of the matrix, we can see that det > det in all cases. In fact for, the ITU channel models indoor, indoor-tooutdoor pedestrian and the vehicular models we find that independent of the spreading gain Q, det >> det. This allows us to reduce the complexity of the inversion of the matrix C C. Invoking the matrix inversion lemma [5,.] we have, C C 7 Using the fact that the det >> det, and for a matrix Z with absdetz <, 0 i i Z Z I [6] we can approximate the in equation 7 as follows; I I 8 Substituting the above approximation back into equation 7 we now get; C C..9 We can see that in equation 9, we have to only invert a single matrix of size x as against the size x inversion required for the matrix C C. s mentioned in the end of the section. we need to estimate only either d and d. Defining, [ ] F..0 and choosing to obtain d in equation 5, and using equation 9 we now obtain the simplified STTD ZF-LE solution to be; E C F d...

4 TSG-RN WG meeting #5 TSGR#59957 Cheju Korea, -4, June 999 For the ease of understanding the simplified STTD ZF-LE, equation explicitly gives the matrix sizes for all the matrices involved. n mentioned above, the simplified STTD ZF-LE requires the inversion of the matrix of size x which the same size as that for regular no-diversity ND systems. The matrix for STTD has similar form as the ND systems, implying that its inversion complexity can be reduced in the same manner as the approximate ZF-LE [4]. Thus, the complexity of matrix inversion which is dominant complexity for a ZF-LE for STTD is the same as the ND systems. There are extra matrix multiplications as given in equation 0 for the STTD system. owever, this does not significantly increase the complexity. For the channel estimation for STTD, an orthogonal preamble will have to be transmitted implying that the channel estimation complexity is doubled. owever, since the overall complexity for the ND ZF-LE is dominated by the complexity of the matrix inversion, which is the same for both the ND and STTD systems, we would not expect significant complexity increase for simplified STTD ZF-LE over ND ZF-LE. Following a procedure similar to [4], we find that the total complexity of the simplified STTD ZF-LE including the extra matrix multiplies, channel estimation should only be about 0-5 % more than the approximate ZF-LE complexity, as reported in [4] for users K,..,. This is not a significant increase, considering the fact that we can achieve diversity gain..3 Simulations results We now do link level simulations to evaluate the performance gains of the simplified STTD ZF-LE over the ND ZF-LE. The link level simulations parameters used are given in table : Vehicular Indoor-to-outdoor pedestrian Velocity 0 kmph Figures -4 3 kmph Figures 5,6 Spreading gain SF 8, 6 8, 6 Number of users SF 8: 4 SF 6: 4, 8 SF 8:4 SF 6: 4 User allocation on antennas STTD: ll users on, ND: ll users on TSTD: alf users each on, STTD: ll users on, ND: ll users on TSTD: alf users each on, Channel Estimation Perfect Perfect FEC encoding No No Joint detection STTD: es simplified STTD ZF-LE ND: es ZF-LE TSTD: es ZF-LE Simplified STTD ZF-LE performance gain over ND ZF-LE d Simplified STTD ZF-LE performance gain over TSTD ZF-LE d STTD: es simplified STTD ZF-LE ND: es ZF-LE TSTD: es ZF-LE.0 d at raw ER d at raw ER 0 -. d at raw ER d at raw ER 0 - Table : The simulation parameters to compare the performance of STTD against the ND, TSTD system are given. We can see that the performance gains of simplified STTD ZF-LE over the ND ZF-LE are between d and that over TSTD is.-3.5 d. ecause of the time diversity at high Doppler, the raw ER chosen for Vehicular is 0 - as against the 0 - for indoor-to-outdoor pedestrian scenario. 4

5 TSG-RN WG meeting #5 TSGR#59957 Cheju Korea, -4, June 999 The performance is shown in figures -6: /home/chaitali/tdd_sttd/ps/user_4_sf_6_00hz.eps MTL, The Mathworks, Inc. Figure : Link level simulations comparing the raw ER performance of simplified STTD ZF-LE against ND ZF-LE for spreading gain 6, number of users K 4, Vehicular channel, perfect channel estimates. We can see that STTD gives a diversity gain of about d at ER 0 -. /home/chaitali/tdd_sttd/ps/user_8_sf_6_00hz.eps MTL, The Mathworks, Inc. Figure 3: Link level simulations comparing the raw ER performance of simplified STTD ZF-LE against ND, TSTD ZF-LE for spreading gain 6, number of users K 8, Vehicular channel, perfect channel estimates. We can see that STTD gives a diversity gain of about d at ER 0 - over ND and. d over TSTD. We can also see that the performance of the approximate STTD is the same as the exact STTD implying that the assumption in equation8 is valid. 5

6 TSG-RN WG meeting #5 TSGR#59957 Cheju Korea, -4, June 999 /home/chaitali/tdd_sttd/ps/user_4_sf_8_00hz.eps MTL, The Mathworks, Inc. Figure 4: Link level simulations comparing the raw ER performance of simplified STTD ZF-LE against ND, TSTD ZF-LE for spreading gain 8, number of users K 4, Vehicular channel, perfect channel estimates. We can see that STTD gives a diversity gain of about d at ER 0 - over ND and.3 d over TSTD. We can also see that the performance of the approximate STTD is the same as the exact STTD implying that the assumption in equation8 is valid. /home/chaitali/tdd_sttd/ps/user_4_sf_6_5hz.eps MTL, The Mathworks, Inc. Figure 5: Link level simulations comparing the raw ER performance of simplified STTD ZF-LE against ND ZF-LE for spreading gain 6, number of users K 4, Outdoorto-Indoor Pedestrian channel, perfect channel estimates. We can see that STTD gives a diversity gain of about 3 d at ER

7 TSG-RN WG meeting #5 TSGR#59957 Cheju Korea, -4, June 999 /home/sengupta/tdd_sttd/ps/user_4_sf_8_5hz.eps MTL, The Mathworks, Inc. Figure 6: Link level simulations comparing the raw ER performance of simplified STTD ZF-LE against ND, TSTD ZF-LE for spreading gain 8, number of users K 4, Outdoor-to-Indoor Pedestrian channel, perfect channel estimates. We can see that STTD gives a diversity gain of about 3 d at ER 0 - over ND and 3.5 d over TSTD. 3.0 Conclusions In terms of raw ER, we have shown that STTD gives significant diversity gains between d over the ND systems and.-3.5 d gains over the TSTD without significantly increasing the complexity of the zero forcing block linear equalizer in the user equipment. ased upon the framework given in this paper, the minimum mean squared error MMSE detector combined with the STTD decoding can be derived in a similar manner and it can be shown that its complexity increase over the MMSE for ND is also not significantly higher. Thus, we can conclude that using STTD for TDD systems will not significantly increase the complexity of the joint detection at the mobile. From figures 3, 4 and 6 we can see that TSTD actually does slightly worse than ND in terms of raw ER. The reason for this happening is that half of the interference comes from the transmission on the second antenna to maintain P balance, making the simulations slightly different from the ND simulation. The ZF-LE does not do a perfect interference cancellation. The net effect is that the TSTD raw ER is worse than the ND raw ER. ence the STTD gains over TSTD in terms of raw ER are nominally more than the gains over ND. Further, STTD has the advantage of being a power-balanced scheme, implying that the peak to average ratio PR of the base station power amplifier is in general lower than the TSTD scheme. lso, STTD gives the full path diversity independent of the switching patterns, as against the TSTD, whose diversity gains will depend upon the interleaving schemes and the switching pattern [7]. Similarly, STTD provides path diversity independent of the number of switching points, as against the 7

8 TSG-RN WG meeting #5 TSGR#59957 Cheju Korea, -4, June 999 closed loop diversity techniques [7], which require multiple switching points to reduce performance degradation. ence STTD s advantage in terms of providing better path diversity gains without significant increase in mobile complexity, makes it a better choice for open loop antenna diversity. References [] Texas Instruments: Space Time lock Coded Transmit ntenna Diversity for WCDM, Tdoc SMG UMTS L 66/98, elsinki, Finland, December 4-8, 998. [] Texas Instruments: dditional results for Space Time lock Coded Transmit ntenna Diversity for WCDM, Tdoc SMG UMTS L 5/99, elsinki, Finland, Janaury 999. [3] nja Klein, Ghassan Kaleh, Paul aier, Zero forcing and minimum mean square error equalization for multi-user detection in code-division multiple access channels, IEEE Transactions on Vehicular Technology, Vol. 45, No., May 996. [4] Siemens, Computational complexity of the UTR TDD mode, Tdoc STC SMG 74/98 UMTS L#, Paris, France, pril 998. [5] Thomas Kailath, Linear Systems, Prentice all Publications, 980. [6] G.. Golub and C. F. Van Loan, Matrix Computations, The Johns opkins University Press, altimore, nd Ed., 989. [7] Motorola, Transmit diversity schemes applied to the TDD mode, Tdoc 86/99, TSG-RN WG # 3, Nynashamn, Sweden, March 999. [8] 3Gpp RN WG, Physical channels and mapping of transport channels, S5.. 8