Time Domain CSI report for explicit feedback Month Year doc.: IEEE 802.11-yy/xxxxr0 Time Domain CSI report for explicit feedback Date: 2010-05-17 Authors: John Doe, Some Company

Abstract MU-MIMO technology essentiality for TGac is no longer to demonstrate We need to make sure that this technology is efficient and performant. In [1], it has been shown that with explicit feedback, the amount of uncompressed MU-MIMO CSI report was increasing strongly compared to SU-MIMO CSI report As this important feedback duration can strongly affect MAC efficiency for MU-MIMO and reduce its usage, It was accepted that a deeper reflection on compressed MU-MIMO was needed In this presentation, we show that the time representation of the channel provides an important compression of the feedback information By optimizing the transfer function between the frequency and the time domain, we show that this compression even leads to improvements of the performances Slide 2

Frequency domain and time domain representations of the channel: interest toward time domain feedback By construction, the impulse response of the channel is not longer than the cyclic prefic duration CP In the time domain, the feedback of the taps of the channel (Ntap <= CP) is sufficient to retrieve the complete channel state information It's then obvious that a CSI feedback in the time domain could get a compression gain at least equal to 4 over a CSI feedback in the frequency domain, without any loss of information CSI feedback in the frequency domain lead to the feedback of a correlated information Feedback Feedback Frequency domain Time domain Representation of the channel Slide 3

Frequency domain and time domain representations of the channel: interest toward time domain feedback Explicit feedback of the impulse response of the channel: compressed feedback Sum up of the mathematical process: Hf,STA  htime  Hf,AP Fft Ftf First straightforward assumption: Fft can be an iDFT and Ftf can be a DFT STA AP Sounding LS frequency channel estimation Hf, STA Transfer matrix (frequency to time domain) Fft Feedback of only the significant taps (nb samples <=CP) Feedback detection htime Time domain channel impulse response htime Transfer matrix (Time to frequency domain) Ftf frequency channel estimates Hf, AP G Slide 4

Finding channel impulse response based on the frequency channel estimation: case of iDFT for Fft (1/4) Assuming the channel impulse response of the channel with i, j the index of the transmit and receive antennas l the index of the taps, τ,h the delay and amplitude/phase of each tap CP the number of samples in the cyclic prefic The result of an iDFT applied to frequency domain least square LS channel estimates equals to with N=NFFT, the OFDM FFT size M=NMOD, the number of modulated subcarriers (1) Slide 5

Finding channel impulse response based on the frequency channel estimation: case of iDFT for Fft (2/4) If NMOD=NFFT, Following equation (1), the channel impulse response is located in the first CP elements of the time domain vector htime, as we wanted The reason for that is because the transfer matrix iDFT is well conditioned (conditional number of 1 for a squared iDFT) NFFT Amplitude Fft 1 NFFT iDFT NFFTxNFFT Singular values of Fft NFFT Slide 6

Finding channel impulse response based on the frequency channel estimation: case of iDFT for Fft (3/4) However, due to the tone allocation with guard and DC null subcarriers, NMOD < NFFT Following equation (1), the channel impulse response is no longer located only on the first CP elements of the time domain vector htime, which is now problematic The reason for that is because the transfer matrix iDFTmod is not well conditionned (conditionnal number >> 1) NFFT Amplitude NMOD NMOd 1 iDFT NFFTxNFFT Fft NFFT NMOD NMOD Singular values of iDFTmod iDFTmod NMOD Slide 7

Finding channel impulse response based on the frequency channel estimation: case of iDFT for Fft (4/4) However, due to the tone allocation with guard and DC null subcarriers, NMOD < NFFT When performing an IDFT on the frequency domain channel estimate vector for an OFDM symbol the estimate of the channel impulse response is corrupted with inter-tap interference, that spreads the impulse response far beyond the CP first samples The compression gain is partially lost NMOD NMOD Frequency domain Time domain Slide 8

How to find a Fft better than iDFT In order to improve the detection of the channel impulse response when NMOD < NFFT, by reducing the inter tap interference, a solution is to find a new matrix Fft with a reduced conditional number This reduction can be done by performing a truncated SVD on iDFTmod, by keeping unchanged the singular values before the truncated threshold Th and set to zero the singular values after the threshold The new transfer matrix Fft is now a truncated iDFT (TiDFT). The transfer matrix Ftf can stay as a DFT Amplitude NMOD 1 Hf,STA  htime  Hf,AP Fft Ftf Fft TiDFT DFT NMOD TiDFT G Th NMOD Singular values of iDFTmod Singular values of TiDFT Mathematical representation of the general feedback Slide 9

How to find a Fft better than iDFT In order to improve the detection of the channel impulse response when NMOD < NFFT, by reducing the inter tap interference, a solution is to find a new matrix Fft with a reduced conditional number This reduction can be done by performing a truncated SVD on iDFTmod, by keeping unchanged the singular values before the truncated threshold Th and set to zero the singular values after the threshold The new transfer matrix Fft is now a truncated iDFT (TiDFT). The transfer matrix Ftf can stay as a DFT NMOD NMOD TiDFT Frequency domain Time domain Slide 10

How to find a Fft better than iDFT In order to find the optimum threshold, it's even more interesting to evaluate the impact of the truncation on the general feedback process, by looking at the matrix G = TiDFT x DFT The matrix G1 = iDFT x DFT with NFFT=NMOD is well conditioned because iDFT is well conditioned The matrix G2 = iDFTmod x DFT with NFFT<NMOD is not well conditioned, because iDFTmod is not well conditioned We want the matrix G3 = TiDFT x DFT with NFFT<NMOD to be well conditioned 1 1 1 Target NFFT NMOD NMOD G1 = iDFT x DFT G2 = iDFTmod x DFT G3 = TiDFT x DFT Singular values of general matrix G Slide 11

How to find a Fft better than iDFT In order to find the optimum threshold, it's even more interesting to evaluate the impact of the truncation on the general feedback process, by looking at the matrix G3 = TiDFT x DFT If we truncate to much, we will loose all the useful information If we don't truncate enough, we won't see any changes With this optimal threshold Not only will we suppress most of the inter-tap interference, and the noise on the last NMOD-CP samples of the time domain response But on the top of that, we will enable additional noise reduction by suppressing the singular values of G carrying no significant useful information Note that the threshold will be optimal independently of the channel as its optimization depend only on the tone allocation Singular values of iDFTmod Singular values of TiDFT 1 NMOD Th 1 NMOD Singular values of G3 = TiDFT x DFT Slide 12

Time domain explicit feedback performance results Frequency domain explicit feedback Time domain explicit feedback with iDFTmod Time domain explicit feedback with TiDFT Chan E 40MHz Time domain explicit feedback outperforms frequency domain explicit feedback when using the proposed TiDFT by almost 10dB Time domain explicit feedback with a classical iDFT suffers from an error floor due to inter-tap interferences Note that frequency domain explicit feedback corresponds here to least square (LS) frequency channel estimation Note also that the results with TiDFT are obtained with an optimum threshold Th=53 (optimisation and matrices in annex) Time domain explicit feedback: feedback of the first CP samples of the channel impulse response Slide 13

Conclusion Feedback compression mechanisms are important for MAC efficiency improvements of explicit feedback DL MU-MIMO Time domain explicit feedback is a very efficient solution to reduce the size of the feedbacks In order to keep all its advantages, we propose a transfer function called TiDFT which enables an efficient compression and improves the quality of the estimates compared to both iDFT time domain and frequency domain explicit feedbacks. Slide 14

References [1] Ishihara, K. and Yasushi, T., CSI Report for Explicit Feedback Beamforming in Downlink MU-MIMO, IEEE 802.11-10/0332r0, Mar. 2010 Slide 15

Annexes Slide 16

How to find a Fft better than iDFT Finding the optimum Th, example of 40MHz The figure presents the singular values of the G matrix (representing the general feedback process) obtained for different Th for the TiDFT (Fft) The value of Th=53 is the closest from the target. For 40MHz a TiDFT with Th=53 will present the best performance Singular values Singular values index Slide 17

Sensitivity to quantization: Time domain vs Frequency domain feedbacks MSE for the complete (quantized or not) feedback process without noise Time domain feedbacks are not more sensitive to quantization: Min of 6 bits for frequency or time domain explicit feedbacks Slide 18