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A Comparison of Implicit and Explicit Channel Feedback Methods for MU-MIMO WLAN Systems

Research Paper / Feb 2014

A Comparison of Implicit and Explicit Channel Feedback Methods for MU-MIMO WLAN Systems Hanqing Lou, Monisha Ghosh, Pengfei Xia, Robert Olesen { hanqing.lou, monisha.ghosh, pengfei.xia, robert.olesen}@interdigital.com InterDigital Communications, LLC Abstract— In this paper we compare the implicit and explicit methods of providing channel state information (CSI) to the transmitter in a multi-user multiple-input-multiple-output (MU- MIMO) system as specified in the draft specification IEEE 802.11ac [1]. The comparison is made on the basis of both overhead requirements and packet-error-rate (PER) performance. We also propose a hybrid feedback scheme that combines the explicit and implicit feedback methods thus benefiting from more frequent calibration without incurring extra overhead. Index Terms—MU-MIMO, implicit feedback, explicit feedback, beamforming, MIMO, precoding I. INTRODUCTION Multi-User Multiple-Input-Multiple-Output (MU-MIMO) techniques are considered to be the cornerstone of next generation multiple antenna systems, such as draft IEEE 802.11ac [1]. Since a MU-MIMO system uses space division multiple access, or simultaneous transmission to multiple users, it enables an improved system spectral efficiency over that attainable with Single User-MIMO (SU-MIMO) techniques [2]. The crucial requirement for making such MU-MIMO systems perform well is the availability of high quality channel state information (CSI) at the transmitter. The draft IEEE 802.11ac specification [1] allows two methods of providing this feedback: implicit and explicit. For implicit feedback, it is assumed that the physical channel is reciprocal, i.e. the uplink channel and downlink channel are the same. However, in an end-to-end system, the channel seen by the receiver is composed of filters at the transmitter and receiver in addition to the physical channel. These, in general, are not reciprocal, and hence calibration techniques are required to compensate for the effects of these filters such that the residual error is small. If these calibration errors can be made small enough to enable the use of implicit feedback, the feedback will incur less overhead since the transmitter can infer the downlink channel from the uplink channel measurements. Alternatively, when using explicit feedback, it is required that the receiver estimates the channel prior to feeding back the channel estimate. This channel estimate will include the effect of the filtering, as well as the physical channel. Explicit feedback uses a quantized representation of the estimated channel, and transmits this CSI information back to the transmitter. Hence there is a trade-off between the two methods: implicit feedback may be degraded by calibration errors whereas explicit feedback may be degraded by quantization errors. In this paper we study the performance trade off for these feedback methods in a system that is compliant with the draft IEEE 802.11ac specification [1]. The paper is organized as follows. Section II describes the explicit channel feedback method specified in IEE 802.11ac, and the associated protocols. Section III describes the implicit channel feedback protocols. In Section IV we present a hybrid protocol which combines explicit and implicit feedback methods. Section V presents an overhead comparison of the methods. Simulations are presented in Section VI comparing the effect of quantization using explicit feedback methods, and calibration error using implicit feedback methods. Finally, the results of the paper are summarized in Section VII. II. MU-MIMO WITH EXPLICIT FEEDBACK IN IEEE 802.11AC A. MU-MIMO beamforming report A wireless local area network (WLAN) in Infrastructure Basic Service Set (IBSS) mode has an Access Point (AP) and one or more stations (STAs) associated with the AP. In this paper we only consider downlink MU-MIMO, i.e. the AP transmitting to multiple STAs. We assume that the AP has antennas and uses these to transmit to K users, STA1,…, STAK where user k has antennas. With the assumption that all the STAs have the same number of antennas, a simplified notation Nt and Nr can be utilized to refer to the number of antennas of AP and STAs respectively. The number of total streams that can be supported by MU-MIMO transmission is limited by the total number of transmit/receive antennas. In IEEE 802.11ac, a compressed beamforming report is generated per user, based on the Singular Value Decomposition SVD of the channel [1][3]. Let ( ) be the channel matrix on a sub-carrier , with being the number of receive antennas and being the number of transmit antennas. Without loss of generality, we assume throughout this paper. The channel matrix is first estimated at the receiver by frequency domain channel estimation based on the received long training field (LTF). SVD is then applied on the estimated channel matrix, leading to ( ) ( ) ( ) ( ) (1) where ( ) is the diagonal singular value matrix containing the singular values in a decreasing order on the diagonal, ( ) is the left singular matrix containing left singular vectors in corresponding order, and ( ) is the right singular matrix containing right singular vectors in the same order. The matrix ( ), of size , is semi-unitary and satisfies ′( ) ( ) . SVD-based single user beamforming in IEEE 802.11ac requires that the right singular matrix be decomposed, quantized, and then fed back to the transmitter for efficient transmit beamforming. Specifically, the following steps are implemented at the receiver after channel estimation has been performed to estimate ̂( ): 1) SVD decomposition: using equation (1) on ̂( ). 2) Initialization: post-multiply ( ) by a proper diagonal matrix ( ) and overwrite ( ). As a result, the entries in the last row of ( ) become non-negative real values. The post-multiplication matrix ( ) is parameterized by angles . 3) Realization: pre-multiply ( ) by a proper diagonal matrix ( ) and overwrite ( ). As a result, entries in the first column of ( ) become non-negative real values. The pre-multiplication matrix ( ) may be parameterized by ( ) angles 4) Diagonalization (Givens rotation): pre-multiply ( ) by a Givens rotation matrix and overwrite ( ). is obtained by replacing the first 2 x 2 sub- matrix of the identity matrix by the following matrix: [ ( ) ( ) ( ) ( ) ] (2) 5) As a result, the second entry in the first column becomes zero. The pre-multiplication matrix is parameterized by the angle . 6) Repeat step 4) until all entries in the first column (except the diagonal entry) become zero. 7) Repeat steps 3)-5) for all columns, until all entries in all columns (except the diagonal entries) become zero. 8) Quantize and feed back all angles. With the above steps, a semi-unitary matrix may be decomposed as: {[∏ ( ∏ ) ( ) ] } (3) where is an identity matrix with extra rows filled with zeros; is the Givens rotation matrix to nullify the (j,i)-th entry and is represented by the angle ; is the diagonal rotation matrix to remove the imaginary parts from the ith column, and may be represented by the angles , . It can be shown that the angles ’s do not need to be transmitted since the diagonal matrix A(k) may be absorbed into ( ) which will be estimated at the receiver during transmission. Hence, IEEE 802.11ac requires that only the angles ’s and ’s be fed back to the transmitter. There are two quantization choices specified: (i) Type 0: 5 bits for ( ) and 7 bits for( ) and (ii) Type 1: 7 bits for ( ) and 9 bits for( ). Since this feedback is for each sub-carrier, the standard also allows grouping of either 1, 2 or 4 sub-carriers in a group in order to reduce the feedback overhead. The group length is defined by , and the 802.11ac specifications allows [ ]. In addition to the channel feedback as described above, in order to derive precoder matrices for MU-MIMO, the signal to noise ratio (SNR) per carrier also needs to be reported for each user. This is done by reporting the average SNR across carriers as well as the “delta-SNR” which is the difference in SNR from the mean for each carrier. B. MU-MIMO Protocol based on Explicit Feedback In IEEE 802.11ac, a null data packet (NDP) is defined as a sounding packet sent out by the AP, to enable channel estimation at each STA. A NDP only contains the physical layer (PHY) preamble with long training fields (LTFs), short training fields (STFs) and the signal (SIG) field, with no data. For control/management purpose, a NDPA frame (NDP announcement) is transmitted before the NDP. Usually, the NDPA frame contains the address of the intended STAs, type of feedback requested and spatial rank of the requested feedback. NDPAAP1 STA1 STA2 NDP Fdbk1 Fdbk2 Spatial tx 1&2Poll Figure 1 MU-MIMO protocol based on explicit feedback. Once the AP makes the decision to group a number of users for downlink MU-MIMO transmission, the following procedure is followed: A1. The AP transmits an NDPA frame, which includes the addresses of the STAs and the requested feedback type. Upon receiving this NDPA frame, the STAs addressed (STAs 1 and 2 in Figure 1) prepare for performing channel estimation and beamforming report, while other STAs may choose to hibernate. A2. The AP transmits an NDP packet to STA1 and STA2. STA1 estimates the downlink channel . At the same time, STA2 estimates the downlink channel . A3. STA1 feeds back the channel state information corresponding to , using the Givens decomposition based beamforming report described in Section IIA as well as the mean SNR and delta-SNRs. A4. The AP then polls STA2 to request the channel feedback A5. STA2 feeds back channel state information corresponding to , using the Givens decomposition based beamforming report described in Section IIA as well as the mean SNR and delta-SNRs. A6. The AP then calculates the precoder matrix it will use based on , and the SNR feedback. Any linear precoder, such as a zero-forcing (ZF) precoder [6][4] or a max-SLNR precoder [4][5], may be used. A7. The AP transmits precoded MU-MIMO packets to STA1 and STA2 using the calculated precoders. The LTFs and the data need be precoded using the same precoders so that the composite channel (precoder + channel) can be estimated at each user. III. MU-MIMO WITH IMPLICIT FEEDBACK Based on the pioneering study of electromagnetic reciprocity by H. A. Lorentz in 1896 [6][7], it can be shown that the far-field transmit/receive beam patterns for an antenna are equivalent. Hence, for WLAN systems using TDD (time division duplexing), the propagation channel in the downlink (from AP to STA) is reciprocal to the propagation channel in the uplink (from STA to AP) [8][2]. Mathematically, . Here is of size , with being number of receive antennas at STA side and being number of transmit antennas at AP side. However, the interference is not reciprocal. In WLAN systems, interference signals could be WiFi signals from an adjacent AP/STA, or Bluetooth/microwave signals. More importantly, different I/Q mixers, amplifiers and path lengths are used in the transmitter path and receiver path (see Figure 2Figure 2). Hence, the overall channel which includes the radio propagation path as well as the analog frontend is not reciprocal. As widely accepted in the literature [9], the RF distortion may be modeled as a diagonal matrix (4) where ( ), represents the amplitude error on the nth antenna path and represents the phase error on the nth antenna path. The diagonal structure of the distortion matrix stems from the assumption that antenna coupling is very low, which is true in most cases [9]. Antenna calibration as specified in [1] may be used to remove the antenna distortion. In practice, due to internal temperature change in the electronics and oscillator drifts, frequent antenna calibration may be necessary. This is further evidenced by field measurements in [8][10][10]. IV. MU-MIMO HYBRID FEEDBACK PROTOCOLS We will show in Section V that the overhead for MU- MIMO explicit feedback can be fairly large. Since calibration errors can also affect the performance, it is crucial to have frequent calibrations for implicit feedback. In this section we present a hybrid protocol that is based on both implicit and explicit feedback that allows frequent calibrations without excess overhead. A. Calibration procedure It should be emphasized here that the calibration required is between the transmit-receive chains of the AP. Hence it is sufficient to perform the calibration procedure with any one STA. In order to perform a calibration procedure at the AP, the AP just needs to know the uplink channel and downlink channel for any one STA. Thus, once STA1 is calibrated by , the same calibration may be applied for STA2 from the AP side. This makes explicit feedback of STA2’s channel unnecessary. B. MU-MIMO Protocol based on Hybrid Feedback The proposed hybrid protocol is shown in Figure 3 and described below: B1. The AP transmits an NDPA frame, which includes STA1’s address, STA2’s address and also specifies that STA1 will perform explicit feedback while STA2 will perform implicit feedback. On receiving this NDPA frame, STA1 will prepare for channel estimation and beamforming report, while STA2 will prepare for uplink sounding. Other STAs could choose to hibernate. B2. The AP transmits an NDP packet to STA1 and STA2. B3. STA1 feeds back the CSI corresponding to , using the beamforming report. This beamforming report should be sent with , so that the calibration may be done by the AP. The LTFs in the feedback packet enable the AP to estimate the uplink channel from STA1. B4. Upon receiving the STA1 feedback, the AP reconstructs the downlink channel from the beamforming report. At the same time, the AP estimates the uplink channel directly based on the LTFs. With these two estimates, the AP is then able to calculate the instantaneous calibration correction matrix using equation (4). B5. The AP then transmits a poll packet requesting STA2 to send a sounding packet. B6. STA2 sends out an uplink sounding packet. The AP estimates the uplink channel based on the LTFs in the preamble of the sounding packet. B7. The AP estimates the downlink channel using the e mated channel as well as the uplink/downlink calibration correction matrix B8. The AP then calculates the precoder based on and . Any linear precoder, such as a ZF precoder [6][4] or a max-SLNR precoder [5], may be used. B9. The AP transmits MU-MIMO packets to STA1 and STA2 using the calculated precoders. IQ PA PA IQ LNA LNA I Q STA1 STA2 PA PA LNA LNA Q IQ I IQ STA1 STA2 (a) downlink channels AP AP DLH ,1 DLH ,2 ULH ,1 ULH ,2 (b) uplink channels Figure 2 Transceiver paths for MU-MIMO. Formatted: Font: 10 pt Formatted: Font: 10 pt, Not Italic, Check spelling and grammar NDPAAP STA1 STA2 NDP Fdbk1 Sounding Spatial tx 1&2ack Explicit feedback Implicit feedback Figure 3 MU-MIMO protocol based on hybrid feedback. Note that the algorithm may be extended to more than two users easily. It is only necessary that one STA is selected to perform explicit feedback, the rest of the STA(s) may perform implicit feedback only. V. OVERHEAD ANALYSIS In this section, we compare the overhead of implicit feedback, explicit feedback and hybrid feedback. Let us assume that the AP has 4 transmit antennas and will transmit to 2 to 4 single-antenna STAs simultaneously. With explicit feedback, each STA needs to feed back a 4 x 1 complex matrix for each, or a group of, subcarriers. With Givens rotation, the STA needs to feed back three pairs of angles . Type 0 feedback uses 7 bits for the ’s and 5 bits for the ’s for a total of 36 bits to feedback one 4 x 1 matrix V whereas Type 1 feedback uses 9 bits for and 7 bits for for a total of 48 feedback bits. The 20 MHz bandwidth mode uses 52 data tones. The AP could choose to require feedback of CSI for a subcarrier group. The group length is defined by Ng, and 802.11ac specifications allow [ ]. The total number of subcarriers needed to be fed back is [ ] respectively according to [1]. Table 1 VHT Compressed BF Field and MU Exclusive BF Report field. Ng Compressed BF Type 0 Compressed BF Type 1 MU Exclusive BF Report 1 1880 bits 2504 bits 120 bits 2 1088 bits 1448 bits 64 bits 4 584 bits 776 bits 40 bits The MU Exclusive Beamforming Report field is used to carry the delta-SNR information. The delta-SNRs are quantized to 4 bits and computed for each space-time stream of a subset of the subcarriers spaced apart, where is the subcarrier grouping index. The average SNR is quantized to 8 bits and is carried in the very high throughput (VHT) Compressed BF Field with the compressed V matrix. Table 1Table 1 shows the number of bits needed for transmitting the VHT Compressed BF field and the MU exclusive BF report field. Table 2 VHT compressed BF PPDU size (in OFDM symbols). Ng Type 0 Type 1 1 98 122 2 65 79 4 45 52 Both the VHT Compressed BF Field and the MU Exclusive Beamforming Report field are transmitted in the VHT Compressed Beamforming Frame. Other than the two fields mentioned above, the frame also includes other information, such as category field, VHT Action field and VHT MIMO control field. All these fields are of fixed length, with a total length of 40 bits. Since the VHT compressed beamforming frame is an action frame, the overhead due to the MAC header and FCS should be also considered, i.e., 28 bytes. If we assume that the beamforming feedback frame is transmitted using the most robust mode, which is BPSK and rate ½ coding, with the mixed mode preamble (10 OFDM symbols for PLCP header if single data stream is transmitted), then the size of the PLCP protocol data unit (PPDU) which carries the beamforming feedback frame is shown in the Table 2Table 2. The procedure of explicit MU-MIMO feedback mechanism is shown in Figure 1Figure 1. The proposed hybrid implicit and explicit MU-MIMO feedback mechanism is shown in Figure 3Figure 3. The frame size of the VHT compressed beamforming frame (Fdbk_x in the figures) is given in Table 2Table 2. In order to perform the overhead analysis, we assume that the NPDA, Beamforming Report Poll and ACK frames are transmitted using BPSK and rate ½ coding, and that the mixed mode preamble is utilized. The NDPA frame contains 21 + [4, 6, 8] bytes corresponding to [2, 3, 4] MU-MIMO users. Thus, the total number of OFDM symbols needed for NDPA frame are [18, 19, 19] symbols. The Beamforming Report Poll frame contains 21 bytes, which corresponds to a PPDU packet size of 17 OFDM symbols. The ACK frame contains 14 bytes, which is 15 OFDM symbols. The NDP frame has no MAC body, but has a full set of LTF sequences, requiring 13 OFDM symbols. The PPDU size of other types of frames shown in the feedback procedure is given in Table 3Table 3. Note that the sounding packets which are utilized in implicit feedback and hybrid feedback need not be counted as extra overhead for MU- MIMO transmission, since they carry useful uplink information. However, we consider the worst case, and assume that the STAs use NDP-like packets for implicit sounding. In this case, the AP may reply with an ACK frame which is also overhead for MU-MIMO training. Table 3. PPDU size (in OFMD symbols) of Different Frame Types Frame Type NDPA NDP Poll ACK Size ([2,3,4] users) [18,19,19] 13 17 15 According to 802.11ac specifications, each OFDM symbol is 4 s and the short interframe spacing (SIFS) time is 16 s. For K users, we have the following: The MU-MIMO training overhead for implicit feedback mechanism is: K * (NDP + ACK + SIFS) MU-MIMO training overhead for explicit feedback mechanism is: NDPA + NDP + K * FDBK + (K-1) * Poll + ( 2 + 2 * (K-1)) * SIFS MU-MIMO training overhead for hybrid feedback mechanism is: NDPA + NDP + FDBK + (K-1) * (NDP + ACK) + ( 2 + 2 * (K-1)) * SIFS Formatted: Font: 10 pt Formatted: Font: 10 pt, Not Italic, Check spelling and grammar Formatted: Font: 10 pt Formatted: Font: 10 pt, Not Italic, Check spelling and grammar Formatted: Font: 10 pt Formatted: Font: 10 pt, Not Italic, Check spelling and grammar Formatted: Font: 10 pt Formatted: Font: 10 pt, Not Italic, Check spelling and grammar Formatted: Font: 10 pt Formatted: Font: 10 pt, Not Italic, Check spelling and grammar Formatted: Font: 10 pt Formatted: Font: 10 pt, Not Italic, Check spelling and grammar The results of the detailed overhead analysis is shown in Table 4Table 4. For the 2 user case, explicit feedback with Type 0 and Type 1 feedback requires around 306% and 381% extra overhead respectively compared to implicit feedback, whereas with hybrid feedback 170% and 208% extra overhead is required for Type 0 and Type 1 feedback respectively. With 4 users, 295% and 370% extra overhead is required for explicit feedback with Type 0 and Type 1 feedback respectively compared to implicit feedback, whereas with hybrid feedback, 91% and 110% extra overhead is required with respect to Type 0 and Type 1 feedback. Table 4 Overhead comparison of implicit, explicit and hybrid feedback. No. of Users Implicit (s) Explicit (s) Type0 Type 1 Hybrid (s) Type 0 Type 1 2 256 1040 1232 692 788 3 384 1532 1820 836 932 4 512 2024 2408 980 1076 VI. PERFORMANCE COMPARISONS In this section, we present simulation results to compare the PER performance of implicit and explicit feedback. We simulate several different cases, with number of users K = 2 and 4 respectively. Each user is equipped with one receive antenna while the AP is equipped with four transmit antennas. IEEE 802.11 Channel Model D [11]11] is used, which has a delay spread of 50 ns and represents indoor multipath situations. A simple LS channel estimation Error! Reference source not found.[12] is assumed at the receiver with feedback quantization errors and calibration errors for explicit and implicit feedback respectively. We assume the channel stays the same for the sounding packet and the data transmission for both implicit and explicit schemes. A signal bandwidth of 20 MHz is assumed, and a PPDU length of 1000 bytes is chosen for 64QAM modulation while a PPDU length of 250 bytes is chosen for QPSK modulation. Two different modulation and coding (MCS) schemes are tested: MCS2, which is rate ¾ convolutional code with QPSK modulation and MCS5 which is rate 2/3 convolutional code with 64QAM modulation. A simple ZF precoder [6][4] is used at the AP for both implicit and explicit feedback scenarios. ZF MU-MIMO precoding matrices are calculated for each sub-carrier. With explicit feedback, compressed BF feedback with both Type 0 and Type 1 are simulated where Type 0 refers to Givens rotation compressed BF feedback with 5 bits for and 7 bits for ; and Type 1 refers to 7 bits for and 9 bits for . Since the MU-MIMO precoding matrices are calculated per sub-carrier, the STA needs to feed back one set of for each sub-carrier, i.e., . SNR feedback is also required for ZF precoding. According to IEEE 802.11ac, an average SNR of each space-time stream is quantized and fed back using 8 bits. A set of delta-SNRs which is the difference of the SNR on each sub-carrier from the average SNR is also fed back to the AP. The delta SNR is for a subset of the subcarriers typically spaced apart. Since we set , the delta SNR in our simulation is for every two sub-carriers. With implicit feedback, we have added different residual calibration errors to our simulation. The calibration amplitude error is modeled as log-normal distributed with rms (root mean square) error [0, 0.05, 0.1] dB, while the phase error is modeled as uniformly distributed with rms error [0, 0.5, 1] degree. Reasonable values of residual calibration error may vary due to different hardware implementations. The simulation results we present provide a guideline of how much residual calibration error can be tolerated with different scenarios. Three simulation scenarios are presented: 1. 4 users with MCS2 (QPSK, ¾ convolutional code) 2. 2 users with MCS5 (64QAM, 2/3 convolutional code) 3. 4 users with MCS5 (64 QAM, 2/3 convolutional code) Figure 4Figure 4 shows the simulation results of MU- MIMO with 4 users and MCS2. With this relatively low MCS level, both implicit and explicit feedback work pretty well. Implicit feedback with small residual calibration error outperforms explicit feedback with Type 0 and 1 feedback. Hence, the quantization errors from explicit feedback have more impact on performance than the small residual calibration errors. The gap between performance of explicit feedback and implicit feedback is around 1 to 2 dB. With low MCS level, even with the maximum number of users which can be supported, implicit feedback with good calibration is preferred for MU-MIMO transmission over explicit feedback. Figure 4. Performance comparisons (4 users, MCS2). Figure 5 shows the simulation results of MU-MIMO with 2 users but MCS5. With the relatively high MCS level, and fewer number of users, all the schemes work well. Performance of implicit feedback is slightly better than explicit feedback. The gap between implicit and explicit feedback is around 1 to 2 dB. Similar to the results in Figure 4, the quantization error plays an important role in the simulation results. We can conclude again that implicit feedback with good calibration is a preferred scheme for MU-MIMO transmission in this scenario. 14 16 18 20 22 24 26 28 30 32 34 10 -3 10 -2 10 -1 10 0 SNR dB P E R Tx 4, 4 Users, MCS 2, Real channel estimation, Channel D Implicit, (amp:0.05dB,phase:0.5) Implicit, (amp:0.05dB,phase:1) Implicit, (amp:0.1dB, phase:1) Implicit, no error Explicit, Type 1 Explicit, Type 0 Formatted: Font: 10 pt Formatted: Font: 10 pt, Not Italic, Check spelling and grammar Formatted: Font: 10 pt Formatted: Font: 10 pt, Not Italic, Check spelling and grammar Figure 5. Performance comparisons (2 users, MCS5). Figure 6 shows the simulation results of MU-MIMO with 4 users but MCS5. With the higher MCS level and larger number of users, both Type 0 explicit feedback, and implicit feedback with a relatively large calibration error are unable to reach 1% PER. The performance of Type 1 explicit feedback is similar to that of implicit feedback with a residual 0.05 dB rms amplitude calibration error and 0.5 degree phase calibration error and about 2 dB worse than the implicit case with perfect calibration. Therefore, in order to support high MCS levels with 4 users, the accuracy of CSI used at transmitter side to calculate MU-MIMO precoding weights is very important. Explicit with Type 1 feedback may be a good candidate though the overhead of the feedback is significant. Figure 6. Performance comparisons (4 users, MCS5). VII. CONCLUSIONS In this paper we compared the overhead and PER performance of the explicit and implicit methods of CSI feedback that are specified in the IEEE 802.11ac draft specification. We have shown that explicit feedback for MU - MIMO requires a higher precision feedback mode, and hence a larger overhead, in order to minimize implementation loss and maintain satisfactory performance. We have also shown that for a fewer number of users, and lower MCS modes, implicit feedback with reasonable calibration errors can reduce overhead significantly, without sacrificing performance. In order to support higher MCS and larger number of users, explicit feedback with high resolution feedback (and hence increased overhead), or implicit feedback with very accurate calibration may be necessary. Hence, if accurate calibration is available, implicit feedback is more desirable while explicit feedback with high precision is the preferred option when such calibration is not feasible. We also proposed a hybrid feedback scheme that allows calibration to take place more frequently, and hence can improve the performance of downlink MU- MIMO, without incurring extra too much overhead. 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Wireless Communications, Vol. 6, No. 5, May 2007, pp. 1711-1721 [6] H. A. Lorentz, “The theorem of Poynting concerning the energy in the electromagnetic field and two general propositions concerning the propagation of light,” Versl. Kon. Akad. Wentensch. Amsterdam, vol. 4, p.176, 1896. [7] G. S. Smith, “A Direct Derivation of a Single-Antenna Reciprocity Relation for the Time Domain,” IEEE Transactions on Antennas and Propagation, vol. 52, no. 6, June 2004. [8] E. Perahia, R. Stacey, Next Generation Wireless LANs: Throughput, Robustness and Reliability in 802.11n, Cambridge University Press, 2008. [9] A. Bourdoux and J. Liu, “Transceiver non-idealities in multiantenna systems,” Chapter 4 of “Smart Antennas: State of the Art”, Hindawi Publishing, 2005. [10] S. Haile, “Investigation of Channel Reciprocity for OFDM TDD systems,” Master Thesis, University of Waterloo, 2009. [11] V. Erceg, L. Schumacher et al., “TGn channel models,” IEEE 802.11-03/940r4. [12] J. van de Beek, O. Edfors, M. Sandell, S. K. Wilson, P. O. Borjesson, “On Channel Estimation in OFDM Systems,” IEEE VTC Conf. 1995. 16 17 18 19 20 21 22 23 24 25 26 10 -3 10 -2 10 -1 10 0 SNR dB P E R Tx 4, 2 Users, MCS 5, Real channel estimation, Channel D Implicit, (amp:0.05dB,phase:0.5) Implicit, (amp:0.05dB,phase:1) Implicit, (amp:0.1dB, phase:1) Implicit, no error Explicit, Type 1 Explicit, Type 0 25 30 35 40 45 50 55 10 -3 10 -2 10 -1 10 0 SNR dB P E R Tx 4, 4 Users, MCS 5, Real channel estimation, Channel D Implicit, (amp:0.05dB,phase:0.5) Implicit, (amp:0.05dB,phase:1) Implicit, (amp:0.1dB, phase:1) Implicit, no error Explicit, Type 1 Explicit, Type 0

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