1. Time Domain CSI report for explicit feedback
Month Year
doc.: IEEE yy/xxxxr0
Time Domain CSI report for explicit feedback
Date:
Authors:
John Doe, Some Company

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

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
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

10. 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

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 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

12. 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

13. 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

14. 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

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

16. Annexes
Slide 16

17. 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

18. 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