ON THE IMPACT OF RESIDUAL CFO IN UL MU-MIMO

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1 ON THE IMPACT O RESIDUAL CO IN UL MU-MIMO eng Jiang, Ron Porat, and Tu Nguyen WLAN Group of Broadcom Corporation, San Diego, CA, USA {fjiang, rporat, tun}@broadcom.com ABSTRACT Uplink multiuser MIMO (UL MU-MIMO) is a new feature introduced in ax (currently under development). Tis paper investigates te residual carrier frequency offset (CO) impact on te performance of UL MU-MIMO ODM systems. We sow tat if a station (STA) as zero residual CO, ten its packet error rate (PER) will not suffer from oter STAs tat ave residual CO wen a zero-forcing (Z) or linear minimum mean squared error (LMMSE) MIMO receiver is used at te access point (AP). To reduce te impacts of residual CO on system PER performance, two CO correction metods are designed to compensate for te pase sift and cancel te inter-user interference caused by te residual CO. Several simulation examples are provided to verify te results. Index Terms MU-MIMO; zero-forcing MIMO receiver; residual CO; CO correction 1. INTRODUCTION ODM is widely used in te present generation of wireless communication systems (e.g., WLAN and LTE/LTE-A). By dividing te wole bandwidt into smaller subbands and adding a cyclic prefix, ODM can effectively cancel te intersymbol interference due to multipat delay. However, te symbol error rate (SER) performance of an ODM system is vulnerable to carrier frequency offset (CO), wic will cause inter-carrier interference and pase sift to te transmitted data symbols. How to estimate and compensate te CO is a critical problem in te design of an ODM system, and tis problem as attracted a large amount of researc interest in recent years [1-5]. In [1], te SNR degradation due to CO is analyzed, and te approximate average SNR is derived. Te results indicate tat te SNR degradation increases monotonically wit an increase in CO. To reduce te impact of CO, different CO estimation and compensation metods are investigated for single-user ODM or uplink ODMA systems in [2-5], and te results sow tat after CO compensation, a system s SER can be significantly improved. Uplink multiuser MIMO-ODM (UL MU-MIMO-ODM) is a new feature introduced in ax [6]. Cannel estimation for tis new feature uses te same P matrix structure as is used for MIMO transmission in te current standards [7]. In tis paper, we consider te uplink transmissions from singleantenna stations (STAs) to a multi-antenna access point (AP). To compensate for CO, we assume tat STAs can estimate CO during te downlink trigger frame and pre-rotate te pase of data before uplink transmissions. If residual CO exists during te cannel estimation pase, STA cannel estimations will be degraded. In general, using a COcorrupted cannel estimation for a MIMO receiver introduces inter-user interference and a pase sift for data payloads. Our main result is: if a zero-forcing (Z) or linear minimum mean squared error (LMMSE) MIMO receiver is used at te AP and a STA can do a perfect job in estimating CO based on te downlink trigger frame (zero residual CO), ten te STA s packet error rate (PER) will not suffer from oter STAs tat don t do a good job in estimating CO (nonzero residual CO). Tis fundamental result provides an incentive to estimate CO at te STA as accurately as possible. To reduce te impact of residual CO, two CO-correction approaces are designed to cancel te inter-user interference and compensate for te pase sift. In section II, te impact of CO is first analyzed for a twouser case and ten te result is extended to te general case. Based on te analysis results, CO correction metods are proposed in section III. Several simulation examples are provided in section IV, and conclusions are summarized in section V. 2. ANALYSIS O PERORMANCE DEGRADATION DUE TO RESIDUAL CO It is well known tat good CO estimates improve te performance of single-user (SU) transmissions. urtermore, in uplink (UL) SU ODMA, a STA s CO estimation quality impacts its performance because users are separated in te frequency domain. In tis section, we will investigate weter tis concept olds true for UL MU-MIMO, were different users signals mix wit eac oter, and tus potentially impact eac oter s performance. Te investigation seeks to determine weter te performance of a STA tat perfectly estimates CO (no residual CO) is affected by oter STAs wit residual CO Two-User Case or analysis simplicity, we first consider a two-user case in te UL MU-MIMO transmission, were eac user as a single antenna and te AP as four antennas. To assist te AP to estimate te MIMO cannel, in te long training field (LT) of te preamble, eac user spreads eac LT symbol over multiple time instances by multiplying it by te entries belonging to a P matrix wic as ortogonal row vectors. Te detailed definition of te P matrix can be found in Section [7]. At te AP side, after receiving all te LT symbols, te AP /16/$ IEEE 3811 ICASSP 2016

2 can multiply te received signal wit te Hermitian of te P matrix to estimate te cannel: = ( + ) (1), were te cannel estimation at AP is = [, ], = [, ] and C, C are te cannel vectors between te STA and AP, is te additive noise on te AP and te 2x2 P matrix is defined as = Assume user 1 as zero CO and user 2 as residual CO, ten in te rigt and side of equation (1) becomes = 1 1 1, (2) tus, te cannel estimation is calculated as: = + 1! (3) = 1 +!, () were " is te pase sift due to user 2 s CO and for simplicity, te SNR is assumed to be ig enoug suc tat te additive noise terms are neglected in te above equations. or a single subcarrier, te estimated cannel can be written as: were and # are defined as: = #, (5) ', 1 0 (, ) = & ) ) +, and #. /, % * wit. = 1! and / = 1 +!. Te received signal on a single subcarrier is: 0 = 1 +, (6) were 1 is te data symbol to be detected and is te additive noise at te AP wit covariance matrix 2 3. After te Z receiver [8], te equalized signal is given by: 15 =! 6 (1 + ) = (# #) 6 # 1 + (# #) 6 # = # 6 1 +# 6 ( ) 6 = # 6 (1 + 7), (7) were 7 ( ) 6 and # =.// 1//. Equation (7) indicates tat user 1 is free of inter-user interference. Please note tat te above analysis can be directly generalized to an LMMSE receiver in te ig SNR region Extension to a General Number of Users To extend te above analysis to te general case, we assume tere are 9 single-antenna users in te uplink transmission, and at te AP te received signal for cannel estimation is: 0 : = ;< +, (8) were C = > is te cannel state matrix between te users and AP, 0 C = > and eac column of 0 : correspond to te received signal during a single LT symbol, < is te LT symbol in te LT field, and?; is te CO-corrupted P matrix. An example x?; matrix is:, (9) were is te A t user s pase sift during an LT symbol. Te cannel estimation is calculated as: = > 0 : < > ; = #, (10) were # = > ;, is te P-matrix ( = 9), and te approximation is due to te ig SNR assumption. In (10), it can be observed tat eac element of te cannel estimation is a combination of te true cannel and te residual CO of all users. Motivated by te result of te two-use case, an interesting problem to investigate is weter a user wit zero CO will see interference from users tat ave a residual CO. or analysis purposes, we can assume te first C users ave no CO and te last D users ave residual COs (total 9 = C + D users), and we can write: = E and ; = E, (11) ; ; were as size (C C), and and ; ave size (D D). (Te oter sub-matrices ave corresponding sizes.) Note te first C rows of ; are exactly te same as tose for P because te first C users do not ave CO. Since = 9, we ave: Terefore, 1 ~ 1 P = 1 1 jθ1 jθ 2 jθ3 jθ j2θ1 j2θ2 j2θ3 j2θ G H = [9 I I ]. (12) # = > ; = > E ; ; L = E I I, (13) were [ ] = O > G ; ; H, I I is te C C identity matrix, and is te C D all-zero matrix. According to (7), after te Z equalizer, te received signal becomes: 15 = # 6 (1 +7) = E 6 I I (1 + 7). (1) 3812

3 In te above equation, it can be observed tat te inter-user interference depends on te inverse matrix of E I I. According to Lemma 1 in te appendix, we ave: E I I 6 = E I I 6. (15) After plugging (15) into (1), we find tat te first C users do not suffer from te residual COs of te oter D users, but tat te D users experience degraded performance from inter-user interference. 3. RESIDUAL CO COMPENSATION Based on te analysis in te last section, altoug te uplink performance of a user wit zero CO will not degrade, te performance of users wit residual CO will suffer from interuser interference. In tis section, we will investigate ow to compensate for residual CO at te AP Modified Z (LMMSE) Receiver Equation (7) sows tat # 6 causes inter user interference and degrades te PER performance of users experiencing residual CO. A straigtforward way to cancel inter-user interference is to multiply 15 by #. Tus, we propose te following modified Z (LMMSE) receiver: QR ST = #! 6, (16) QR U==VW = # + 2 3! 6. (17) Te equalized signal after te modified Z receiver is: 1X = #! 6 0 = 1+7, (18) and we will get te same signal as Z wit perfect cannel estimation. Te modified Z (LMMSE) requires an additional matrix multiplication wit # at te traditional Z (LMMSE) receiver. If a metod wit lower complexity is preferable, te diagonal normalization metod in te next section can be used Diagonal Normalization To reduce te impact of multiplying te matrix # wit, we propose a diagonal approximation of te matrix M. We start wit normalizing te diagonal values: = Y # Y,Y, (19) were is te A-t column of is te A-t column of te cannel estimation, and is te A-t diagonal element of matrix #. We furter assume tat te residual COs are constant during different LT symbols. Tus is calculated as: = > 1 + Y + Y + + (>6) Y! = [@3\ ] (]`_) Y^ > [@3\ _ Y^ Y (]`_) Y, (20) were te approximation in (20) is due to 1. We use ; to build te Z (LMMSE) receiver: Qb ST = ; ;! 6 ;, (21) Qb U==VW = ; ; + 2 3! 6 ;. (22) Te cannel normalization metod only requires te pase rotation of eac column of te cannel estimation, and te complexity is lower tan te modified Z metod. On te oter and, as sown in te simulation results, a mild PER performance degradation will be observed for te cannel normalization metod.. SIMULATION RESULTS To verify te correctness and effectiveness of te teoretical analysis and te CO compensation metods, several simulation examples are provided. In te simulation, eac STA as a single antenna and te AP is configured wit multiple antennas. System bandwidt is assumed to be 20 MHz, and te T size is 256. or te data payload and te LT, te useful symbol lengt is 12.8 us and te cyclic prefix (CP) is 1.6 us. Te 11nD cannel model is used to model te wireless fading cannel between te STA and te AP. To make te simulation results more realistic, R impairments are considered in te simulation, including pase noise and power amplifier nonlinearity. or simplicity, we assume te time domain syncronization is perfect. In te simulation, eac packet is assumed to include 1000 bytes, and te modulation and coding sceme used is MCS 7 (6-QAM wit 3/ rate binary convolution code). To evaluate te impact of residual CO on PER performance, we assume tat te users ave a fixed CO value, for example, 1000 Hz or 00 Hz. To assist te implementation of te CO correction metods, we furter assume tat te AP as perfect knowledge of eac STA s residual CO. ig. 1 sows PER degradation for different CO values. Tere are tree users in te uplink transmission, and te AP as four antennas. To verify te analytical result tat te user wit zero CO will as no performance loss and meanwile to investigate te impact of te increasing CO on te PER performance, in te simulation we assume te first and tird users ave fixed CO (+/-1000 Hz) and te second user s CO varies from 0 to 750 Hz. A 3x3 P matrix is used for cannel estimation and te PER of te second user is plotted. In te results, it can be observed tat wen te tree users ave CO [ ] Hz and te SNR is iger tan 28 db, te second user s PER is te same as wen all tree users ave zero CO. Tis indicates tat te second user will not suffer from te CO of te first and tird users. Tis observation essentially verifies our result tat if a STA as zero CO, ten its performance will not be degraded by users tat ave 3813

4 residual CO. Wit te second user s CO increasing, te PER performance degrades monotonically due to te larger pase sift introduced by te CO and te iger inter-user interference from te first and te tird users Desired (user 2), 3x3 P matrix, 11nD, MCS7, CP=1.6µs PER performance tat is almost te same as te case wit zero CO, wic confirms tat multiplying te matrix # wit te traditional LMMSE receiver can completely cancel te interuser interference caused by te residual CO. Meanwile, te low complexity diagonal simplification metod as a PER tat is sligtly worse tan te modified LMMSE, but tere is still significant improvement compared wit te one witout CO corrections. 5. CONCLUSIONS PER ig. 1. Comparison of residual CO impacts at MCS 7. PER 10-1 CO ([-1000, 0, 1000]Hz) CO ([-1000,250, 1000]Hz) CO ([-1000, 500, 1000]Hz) CO ([-1000, 750, 1000]Hz) CO ([0, 0, 0]Hz) SNR (db) users, 8 Rx AP, xlt, 11nD, MCS7, fixed CO, wit RIMP CO:[ ]Hz CO correction, ideal CO estimation + modified LMMSE CO correction, ideal CO estimation + diagonal simplification Zero CO SNR (db) ig. 2. Performance of CO correction metods for fixed CO ( +/- 00 Hz) at MCS 7. Te modified LMMSE and diagonal simplification metods are defined in (17) and (19) respectively. Te performance of te CO correction metods are evaluated in ig. 2. In te simulation, we assume tere are six single-antenna STAs and eac STA s residual CO is set to +/-00 Hz. Te AP is configured wit eigt antennas, and to evaluate te effectiveness of te CO correction metods, te AP is assumed to ave a perfect knowledge of te residual COs. After implementing te CO correction metods, te average PER of all te STAs is used as te performance metric. Te results sow tat te modified LMMSE metod acieves a In tis paper, we studied te residual CO problem in te uplink MU-MIMO ODM transmission in te framework of IEEE ax. Our analysis indicates tat, for uplink MU- MIMO transmissions, te PER after te LMMSE or Z MIMO receiver for a user wit zero CO will not degrade wen oter users experience residual CO. However, te PER performance of users tat experience residual CO will degrade due to pase sift and inter-user interference. To reduce te performance degradation caused by residual CO, two CO correction metods (modified Z/LMMSE and diagonal normalization) were designed to completely or partially cancel te impact of residual CO. Simulation results ave verified te correctness of te matematical analysis and te effectiveness of te CO compensation metods. uture work will include te investigation of te residual CO estimation metod at te AP suc tat te CO estimations can be used as input for te CO correction metods. 6. APPENDIX Lemma 1: or a matrix # = E I I rank, we ave were N 6 K K. # 6 = E I I 6, and of full Proof: By te definition of te matrix inversion, it is sufficient to verify tat #(# 6 ) = (# 6 )# = > >, were 9 C +D. Te following equations are true since = N 6 K K, #(# 6 ) = E I I E I I 6 = E I I + K K = > >, (23) (# 6 )# = E I I 6 E I I I I = E + N 6 K K K K = > >. (2) 381

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