IEEE ac: A Performance Assessment of Single-User Transmit Beamforming and Multi-User MIMO Transceiver Architectures

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1 IEEE 802.ac: A Performance Assessment of Single-User Transmit Beamforming and Multi-User MIMO Transceiver Architectures Roger Pierre Fabris Hoefel Department of Electrical Engineering Federal University of Rio Grande do Sul (UFRGS) Porto Alegre - Brazil roger.hoefel@ufrgs.br Abstract In this paper, we first describe and validate an IEEE 802.ac physical layer simulator. In the following, a comparative performance evaluation, considering the packet error rate as the comparison metric, of different configurations of 802.ac systems is carried out. Single user systems, assuming transmit beamforming and spatial expansion schemes with linear zero forcing and minimum mean squared error multiple input multiple output detectors, as well as multi-user systems with linear zero forcing channel inversion and block diagonalization precoding schemes are investigated assuming realistic synchronization and channel estimation schemes. Keywords 802.ac; OFDM; Multi-User MIMO; Beamforming. I. INTRODUCTION The IEEE 802.ac amendment [], with final ratification forecasted for the beginning 204, is an evolution of the 802.n amendment [2]. IEEE 802.ac systems operate only in the 5 GHz industrial scientific and medical (ISM) band. The main physical (PHY) layer enhancements that allows increasing the maximum theoretical 802.n throughput from 600 Mbps to Gbps are summarized as follows [3]: the maximum bandwidth is increased from 40 MHz to 80 and 60 MHz; dense modulation signaling with optional 256 quadrature amplitude modulation (256QAM); multiple input multiple output (MIMO) with up to eight spatial streams (SS) for single user (SU) transmission; multi-user (MU) MIMO with maximum of four users and two SS per user. Based on the lessons learned from the exhaustive IEEE 802.n standardization process, the optional space-time block coding (STBC) schemes are only specified for 2x, 4x2, 6x3 and 8x4 configurations, and the optional transmit beamforming (TxBF) scheme is based only on the explicit compressed feedback (ECFB) technique to avoid interoperability issues. A medium access control (MAC) and PHY cross-layer simulation evaluation of 802.ac systems that implement SU- MIMO and MU-MIMO is presented in [4]. The main details of the PHY layer are abstracted to reduce the computational complexity. However, TGac channel models are included in the simulation framework in order to assess the impact of PHY layer on the MAC layer throughput. The precoding is based on zero forcing (ZF) channel inversion (CI) scheme. The authors have concluded that a dynamic switching between SU-MIMO and MU-MIMO should be implemented to optimize the global system throughput. The very high throughput (VHT) 802.ac PHY layer demands that the MIMO channel be estimated in a short period of time (i.e. during the transmission of VHT long training fields, VHT-LTF). A scheme to reduce the computational complexity of MIMO channel estimation without performance degradation when ZF-CI and minimum mean squared error CI (MMSE-CI) precoding schemes are implemented is proposed in [5]. PHY layer simulation results based on Draft 2.0 of the 802.ac amendment are presented in [6]. This industry oriented paper compares the performance of CI and block diagonalization (BD) precoding schemes coupled with linear MIMO detectors assuming the TGn D 4x2 channel [7, p. 35]. In this contribution, we investigate the 802.ac PHY layer performance using a simulator that follows strictly the IEEE 802.ac Draft. 3.0 []. In Section II, we briefly describe the linear MU-MIMO precoding techniques investigated in this paper, i.e., CI and BD schemes. Section III describes fundamental characteristics of the 802.ac simulator that we have been developing. This section also presents a first order validation of 802.ac PHY layer simulator based on theoretical results as well as by comparison with simulation results shown in [6]. A comparison between the performance of 802.ac SU-MIMO systems, assuming both TxBF and spatial expansion (SE) spatial division multiplexing (SDM) schemes, and the performance of 802.ac MU-MIMO systems that implement CI and BD precoding techniques is carried out in Section IV. The effects of feedback delay on the performance of TxBF and BD precoding schemes are researched in Section V. Finally, our main conclusions are summarized in Section VI. II. TRANSCEIVER ARCHITECTURES FOR IEEE 802.AC The 802.ac PHY layer is based on MIMO orthogonal frequency division multiplexing (OFDM). Hence, the signal processing at both transmitter and receiver sides must be done per subcarrier basis. However, in the sequel we drop out the notation that particularizes the kth OFDM subcarrier, unless it is strictly necessary to explicit it, to simplify the notation. We assume a MU-MIMO broadcast channel with K users, where the 802.ac access point (AP) has n t transmit antennas and the uth 802.ac station (STA) has n r,u receive antennas. The downlink MIMO channel matrix observed by the uth user, H u, has dimension of n r,u by n t. Hence, the broadcast (BC) MU system can be modeled as [8, p. 40]: = = += +, ()

2 where the received signal for the uth user is given by = + ; u=, K. (2) The column random vector z is composed of K zero-mean circular symmetric complex Gaussian (ZMCSCG) random vectors =z,,z,, z,, where, (=,.., ) are independent and identical distributed (i.i.d) ZMCSCG random variables (r.v.) with variance N 0. The vector transpose operation is denoted by (.) T. The transmitted symbols at the output of the antenna elements can be stated as =, where P is a pre-coding matrix with dimension n t by,. The total number of spatial streams is given by, =,, where n ss,u is the number of SS used by uth user. The transmitted symbols for all K users is given by s=,,, where the symbols transmitted to the uth STA are modeled by the column vector =,,,,,S,,. The downlink transmitted symbol to the uth user at jth SS is denoted by,. A. Channel Inversion (CI) The objective of the CI pre-coding scheme is to eliminate both the interference generated by the multiple SS transmitted by the same user (i.e. the inter-antenna interference) and interference due to multiple user transmission (i.e. the MU interference). Consequently, the pre-coding matrix is given by the pseudoinverse of the downlink channel matrix: =β ZF =β ZF ( ), (3) where (.) H denotes the Hermitian transpose operation. A necessary condition for the existence of the pre-coding matrix P ZF is,, where, =, is the total number of receive antennas. The normalization of the transmitted power at the pre-coder output is obtained by setting the constant β ZF as = where tr(a) denotes the trace of matrix A. B. Block Diagonalization (BD), (4) The target of the BD pre-coding scheme is to decrease the noise enhancement due to the constraints of joint intra-antenna and MU interference cancellation of the CI scheme. In order to accomplish it, a precoder scheme that cancels only the MU interference is designed, while the intra-antenna interference is coupe with MIMO detection schemes (e.g., linear ZF or MMSE equalization, sphere decoding, etc.). The MU interference noticed by the uth user is cancelled if the following set of equations are attainable [8, p. 405]: =, u=,,k e, (5) where the precoder matrix for the kth user is denoted by C,. The pre-coder can be designed by first defining the MU- MIMO interference channel matrix observed by the uth user: =, (6) and then performing the singular value decomposition (SVD) of, i.e., = =. (7) The matrices C,,,, and C, contain the left and right singular vectors, respectively, of matrix. The matrix of singular values of is denoted by C,,,, where the matrix that contains only the non-zero singular values is denoted by C,,,,. The matrices C,, and C, have the right singular vectors that correspond to the non-zero and zero singular values, respectively, of matrix. is an orthonormal basis for the null space of. Therefore, the precoding matrix that cancels the MU interference can be stated as =, (8) where the power normalization factor is given by =. (9) C. Zero Forcing (ZF) Equalization The 802.ac receiver must implement MIMO detection schemes to provide reliable metrics to the channel decoder. Notice that in the real world there are both intra-antenna and multi-user interference even if the ZF precoding scheme is implemented due to synchronization issues, imperfect channel estimation, realistic feedback and so forth. The automatic gain control (AGC) at the receiver side compensates the normalization factor β introduced at the transmitter side. The signal at the output of the MIMO detector for the uth user is given by = = ( + ), (0) where the received signal for the uth user is given by (2). The MIMO ZF detection scheme for the uth user is given by, = ( ). () III. IEEE 802.A SIMULATOR The 802.ac PHY layer simulator is based on the Draft. 3.0 [], released in June of 202, which has been used as a baseline for the first-wave of 802.ac products [3]. Fig. shows a simplified block diagram for the Data field of a 20 MHz, 40 MHz or 80 MHz MU physical layer protocol dada unit [, p. 200]. The full understanding of the 802.ac simulator requires the study of the clear 802.ac Draft 3.0 []. An 802.n referential book, written by Perahia and Stacey [7], also contains extremely valuable information since the 802.ac is an evolution of the 802.n amendment.

3 environments are shown in Fig. 2. The classical canonical flat fading model is assumed, i.e., the i.i.d. flat fading Rayleigh channel. Fundamentally, we can see a close agreement between analytical and simulation results for MCS0 (BPSK, BCC, with code rate r=/2) and MCS5 (64QAM, r=/2) for both SISO and MISO environments when ideal channel estimation and perfect synchronization are assumed. The theoretical results for binary phase-shift keying (BPSK) and quadrature-amplitude modulation (QAM) are based on the mathematical expressions derived in [3]. Finally, we can see a power loss between 2 and 3 db when both realistic temporal auto-correlation synchronization scheme and LS MIMO channel estimation scheme are implemented. Figure - "Transmitter block diagram for the Data Field of a 20 MHz, 40 MHz or 80 MHz MU PPDU" [, p. 200]. A complete list of parameters used in the 802.ac simulator is not shown in this paper due to space constraints. Although, we show fundamental parameters of the IEEE 802.ac simulator in Tab. I in order to provide the basic definitions necessary to reproduce the results shown in this paper. Notice that the implementation of space-time block coding (STBC) is optional and it is not taken into account in this paper. Tab. I ac Parameters: GI=Guard Interval, MCS=Modulation Code Scheme, BCC=Binary Convolutional Coder. Parameter Value Parameter Value Carrier Frequency 5.25 GHz MCS 0-7 Bandwidth 20 MHz PPDU Format VHT Mode GI Length 800 ns Synchronization Auto-Correlation [9] Modulation Binay Convolutional Coder BPSK,QPSK, 6-QAM, 64QAM BCC: r=/2,r=2/3, r=/3/4, r=5/6 MIMO Channel Estimation Channel Decoder Least Square (LS) [7, p.94] Soft-Decision Viterbi Decoding The metrics used for soft-viterbi decoding that take both the interference and frequency selectivity into account are derived in [0]. In this paper, the SU-MIMO channels follow the TGn channel models [], while the extension models to MU- MIMO are implemented according to the TGac addendum [2]. Hereafter, we label the channels models as TGn even when the modifications that consider the multi-user scenario are implemented. A. First Order Validation of IEEE 802.ac Simulator The results shown in the sequel do not model the feedback delay and quantization issues, unless it is explicitly observed. The signal-to-noise (SNR) ratio is estimated using Eq. (2) of [9], i.e. a fundamental remark to reproduce the results shown in this research report. Fig. 2 shows a comparison between analytical and simulation results for the raw bit error rate (BER) at the input of the Viterbi decoder assuming an IEEE 802.ac system where the transmitter implements the SU-MIMO ZF CI scheme and the receiver implements linear ZF equalization (i.e., the ZF-CI+ZF scheme). Results for single input single output (SISO) and multiple input single output (MISO) Raw BER E SNR (db) Black: Analytical Results White: Ideal Channel Estimation Black&White: Real Channel Est. ZF-CI+ZF Trasceiver FLAT FADING MCS5 x MCS5: 2x MCS x Figure 2. Analytical and simulation results for the raw BER at the Viterbi decoder input for canonical SISO and MISO Rayleigh flat fading channels. Analytical results: black symbols. results with ideal synchronization and channel estimation: white symbols. results with realistic synchronization and channel estimation: black& white symbols. Fig. 3 shows simulation results for the medium access control packet data unit (MPDU) packet error rate () as function of SNR for MU-MIMO system loaded with two users. The 4x2 TGn B channel (residential channel model with delay spread of 5 ns and maximum delay of 80 ns) and 4x2 TGn D (typical office environment with delay spread of 50 ns and maximum delay of 390 ns) [-2] are assumed in Fig. 3. The MPDU length has 000 bytes. Our simulation results are compared to the simulation results obtained from [6], where a channel bandwidth of 80 MHz is assumed and the pre-coded transmit symbol x is given by =. (2) Notice that a square multi-user channel matrix is postulated in (2). The term in the denominator, which depends on both the channel matrix and transmitted symbols, normalizes the transmit power. Finally, we remark that the simulation results from [6] shown in Fig. 3 assume linear MMSE equalization. We can verify, analyzing carefully the Fig. 3, a close agreement between both simulation results for both MCS4 (6QAM, r=/2) over the TGn B 4x2 channel and MCS7 (64QAM, r=5/6) over the TGn D 4x2 channel. However, discrepancies between 4-5 db are seen for lower values of the SNR when MCS4 over the TGn D 4x2 channel is assumed. Fortunately, these differences decrease for less than db when lower values of the are taking into account.

4 Figure 3. MU-MIMO channel inversion scheme: comparison between simulation results from reference [6] and the simulation results obtained using the developed IEEE 802.ac PHY layer simulator. Fig. 4 is analogous to Fig. 2, except that the pre-coding is based on the BD algorithm with ZF MIMO detection (i.e., the BD+ZF scheme). We can a see a close agreement between both simulation results for MCS4 (6QAM, r=/2) and MCS7 (64QAM, r=5/6) over the TGn B and D channels, respectively. Although mismatches between 2.5 and 5 db are observed for MCS4 over the TGn D channel MCS 4 (6QAM, r=3/4) TGn B: 4x2 MCS 7 (64QAM, r=5/6) Figure 4. MU-MIMO block diagonalization scheme: comparison between simulation results from reference [6] and the simulation results obtained using the developed IEEE 802.ac PHY layer simulator. Finally, we believe that the simulation results shown in this section may give credibility regarding the correctness of our complex PHY layer 802.ac simulator. We emphasize as well that is not an easy task to match perfectly simulation results obtained using independently developed IEEE 802.ac simulators due to the multitude of details involved (e.g., channel modeling, synchronization and channel estimation schemes, phase tracking algorithms and so forth). IV. IEEE 802.AC FORMANCE EVALUATION This section presents a performance comparison between SU-MIMO (assuming with spatial expansion, SE, and TxBF schemes) and MU-MIMO 802.ac with BD+ZF transceiver architecture. The quantization effects of the feedback are not taken into account. A. SU-MIMO Schemes MCS 4 (6QAM, r=3/4) TGn B: 4x2 MCS 7 (64QAM, r=5/6) 2 Users: 4x2 ZF-CI+ZF MPDU: 000 bytes 2 Users: 4x2 BD+ZF The TxBF transceiver architecture evaluated in this section are labeled as TxBF+ZF and TxBF+MMSE. These labels indicate that the transmitted signal is pre-coded using the matrix V, but only the ZF or MMSE equalizer is implemented at the receiver side. Consequently, the signal at the MIMO detector output is given by = (+)= ( +)=+, (3) where the matrix F denotes the MIMO detector (e.g., see [8, p. 39] for ZF equalization and [8, p. 32] for MMSE equalization). The main objective of the SE technique is to use all radio frequency (RF) chains of the analog front-end and, consequently, avoiding power loss when the number of SS is lower than the number of transmit antennas and the implementation of TxBF is not feasible. In this paper, due to space restrictions, we only analyze the SE scheme for the MIMO 4X2 configuration, where the fixed pre-coding matrix for the kth subcarrier is given by [7, p.9] 0, = 0 exp j2πkδf( 200ns) 0, (4) 0 exp j2πδf( 200ns) where f denotes the subcarrier spacing (e.g., f=32 khz for the 20 MHz bandwidth). Figures 5 and 6 show a performance comparison between 802.ac SU and MU-MIMO systems. The SU-MIMO system implements either TxBF or SE techniques with ZF (Fig. 5) and MMSE (Fig. 6) MIMO detectors. The MU-MIMO 802.ac system (loaded with 2 users) implements BD precoding and ZF MIMO detector. The TGn D 4x2 channel is assumed in these figures. Tab. II summarizes the SNR necessary to obtain a of % for the SU and MU schemes. The TxBF+MMSE has a power gain in relation to the SE+MMSE scheme of 8 db and 0.5 db for MCS4 and MCS7, respectively. The implementation of MMSE equalizer detector in the TxBF scheme allows a power gain between.5-2 db in relation to the ZF equalizer, while no significant differences for the SE scheme are observed. The joint effects of frequency and spatial diversity of the TGn D 4x2 channel coupled with spatial-frequency interleaving reduce the effects of noise enhancement due to the ZF equalization. Tab. II also shows that the MU system with BD precoding and ZF equalizer presents a power loss of almost 20 db in relation to TxBF scheme when the MCS4 is assumed. Notice that for the MCS7 a of % is not attainable even with an unrealistic SNR of 55 db. Table II - SNR required for a of %: TGn D 4x2 channel. SU SE SU TxBF Multi-User ZF MMSE ZF MMSE BD+ZF CI+ZF MCS 4 34 db 34 db 27.5 db 26 db 43 db 42.5 db MCS 7 45 db 44.5 db 36 db 34 db > 55 db 55 db

5 Results MPDU: 000 bytes MCS4: 6QAM, r=3/4 SU SE ZF SU TxBF ZF SU SE ZF SU TxBF ZF successful implementation in wireless standards as LTE Rel. 8 and IEEE 802.ac still has many challenges and open research issues, such as computational efficient pre-coding and MIMO detection schemes as well as the minimization of the feedback delay effects on the system performance. In this paper, we have investigated some of these issues related to the implementation of MU schemes in 802.ac system with both ZF-CI precoding with ZF MIMO detector and BD precoding with ZF MIMO detector. We conclude that these schemes present significant more power loss and feedback delay sensibility in relation to the TxBF SU-MIMO schemes. Figure 5. Performance comparison among MU-MIMO BD+ZF with 2 users and SU-MIMO SE+ZF and SU TxBF+ZF over the TGn D 4x2 channel. MCS4: 6QAM, r=3/4 MU-MIMO BD+ZF No Delay 3 ms 0. Results MPDU: 000 bytes MCS4: 6QAM, r=3/4 SU SE MMSE SU TxBF MMSE SU SE MMSE SU TxBF MMSE SU TxBF MCS4: 6QAM, r=3/4 No Delay 20 ms No Delay 20 ms 0.0 Figure 6. Performance comparison among MU-MIMO BD+ZF with 2 users and SU-MIMO SE+MMSE and SU TxBF+MMESE over the TGn D 4x2 channel. V. EFFECTS OF FEEDBACK DELAY ON SYSTEM FORMANCE In this section, the power spectrum (DPS) follows the 802.n TGn model [7, p. 4]. In this paper, a frequency carrier of f c =5.25 GHz and the STA speed of.2 km/h are assumed. These parameters result in a coherence time of 50 ms when correlation of 50% is assumed. Fig. 7 shows that when the feedback channel is uncorrelated then there is a power loss of approximately 9 db for both MCS4 and MCS7 when the SU TxBF scheme is assumed. The power loss is reduced to 2 db when the feedback delay is set to 20 ms. The TGn channel models assume that DPS and the azimuth power spectrum (APS) are separable and independent for each path. Therefore, the fact that the delayed precoding matrix V feedback to the transmitter side still has enough information on the spatial characteristics of the channel coupled with the implementation of MMSE MIMO detector avoid a catastrophic performance degradation even with a feedback delay of 20 ms. However, for the MU-MIMO with BD+ZF scheme, the scenario is completely different since the throughput is reduced dramatically even with feedback delays of 3ms. VI. CONCLUSIONS MU-MIMO techniques have been extensively researched since the beginning of this century [4]. However, the Figure 7. Effects of feedback delay on the performance of SU-MIMO TxBF and schemes over TGn D 4x2 channel. MPDU of 000 bytes. REFERENCES [] Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications, Amendment 4: Enhancement for Very High Throughput for Operations in Bands below 6 GHz. IEEE P802.ac/D3.0, June 202. [2] Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications, Amendment 5: Enhancement for Higher Throughput, IEEE Std 802.n-2009, [3] CISCO. 802.ac: The Fifth Generation of Wi-Fi, Technical White Paper, August, 202. [4] G. Redieteab, L. Cariou, P. Christin and J. Hélard, "SU/MU-MIMO in IEEE 802.ac: PHY+MAC performance comparison for single antenna stations," Wireless Telecommunications Symposium 202, London, 202. [5] P. Xue, K. Bae, K. Kim and H. Yang. "Progressive equalizer matrix calculation using QR decomposition in MIMO-OFDM systems," IEEE Consumer Communication and Networking Conference (CCNC), 203 [6] D. Nojima, L. Lanante Jr., Y. Nagao, M. Kurosaki and H. Ochi, "Performance evaluation for multi-user MIMO IEEE 802.ac wireless LAN system," 4 th Internation Conferenfe on Advanced Communication Tecnhology, Feb [7] E. Perahia and R. Stacey, Next Generation Wireless LANS. New York, USA: Cambridge University Press, [8] Y. S. Cho, J. Kim, W. Y. Yang and C. G. Kang, MIMO-OFDM Wireless Communications with MATLAB. Singapore: John Wiley & Sons, 200. [9] R. P. F. Hoefel. On the synchronization of IEEE 802.n devices over frequency selective TGn channel models, 25 th Annual Canadian Conference on Electrical and Computer Engineering (CCECE 202), Montreal, 202. [0] ] R. P. F. Hoefel. "IEEE 802.n: Performance evaluation of modified Viterbi metrics for TxBF, SDM and spatial spreading transceivers," WTS Wireless Telecommunications Symposium, Phoenix, April, 203. [] IEEE /6r2, TGn Indoor MIMO WLAN Channel Models. [2] IEEE /06/0569r0, TGac Channel Model Addendum Support Material, May, [3] L. Yang and L. Hanzo, A recursive algorithm for the error probability evaluation of M-QAM, IEEE Communications Letters, vol. 4, n. 0, p , October [4] Q. Spencer, C. Peel, A. Swindlehurst and M. Haardt. An introduction to the multi-user MIMO downlink," IEEE Communication Magazine, Oct