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ZENITH CONFIDENTIAL v1.0 1

Advanced 8-VSB Equalizer Research


Contents • Acronym List • Goals for 2004 • Personnel Overview • Purdue/Zenith Basic Time Domain DFE (single antenna) with Major Computational Blocks – block diagram • General Comments • Basic Equalizer Architectures – Time Domain, Single and Multi-Antenna • Major Computational Blocks

- Introduction - a-BLUE Initial CIR Estimate - CIR Estimate Update Calculation - DFE MMSE tap Weight Update Calculation

• Tap Weight Update Strategies for Dynamic Channels

- Main Concepts - Reducing the Update Delay-2 methods - Reducing the Update Delay - ZTD/LTD Combination

• Simulation Results, Single Antenna

- Compare CIR Estimate Update Methods - Compare Tap Weight Update Methods

• Simulation Results, 2 Antenna Diversity

- Introduction - Dynamic Diversity Channel Model - Purdue/Zenith Basic Time Domain DFE (2 antennas) with Major Computational Blocks – Block Diagram - Review of Previous Results for Static Channels - Review of Previous Results for Doppler Channels - CIR Estimate and Tap Weight Update - New DFE Results for Static Channels - New DFE Results for Dynamic Channels - New LE Results for Dynamic Channels

ZENITH CONFIDENTIAL

• DFE with EVSB Decoder - Single Antenna, Preliminary Results

v1.0 3

• Application of Zenith Research Ideas to LGE 5th Gen Style Architecture

- Introduction - Initial Simulation Results – Static Channels, Single Antenna - Initial Simulation Results – Doppler Channels, Single Antenna - Preliminary Conclusions - Block Diagrams

• Initial DFE Results with Data Capture Streams • To Be Done Next • References


Acronym List a-BLUE: approximate Best Linear Unbiased Estimate BLUE: Best Linear Unbiased Estimate CIR: Channel Impulse Response CG: Conjugate Gradient CG/FFT: Conjugate Gradient utilizing Fast Fourier Transform CMF: Channel Matched Filter CMMSE: Constrained Minimum Mean Square Error DFE: Decision Feedback Equalizer FF: Feed Forward FB: Feed Back LE: Linear Equalizer LS: Least Squares LTD: Long Delay Trellis Decoder (full traceback depth) MMSE: Minimum Mean Square Error PCG: Pre-conditioned Conjugate Gradient PCG/FFT: Pre-conditioned Conjugate Gradient utilizing Fast Fourier Transform pDFE: Predictive Decision Feedback Equalizer (as in LGE 5th Gen) ZTD: Zero Delay Trellis Decoder (traceback depth = 1)


Goals for 2004

• Demonstrate Substantially Improved Equalizer Architectures

- Fast dynamic channel tracking - Exploitation of diversity for pedestrian/mobile applications - Application of advanced methods to both time domain DFE and LGE 5th gen type pDFE - Reduce computational complexity - Examine effect of EVSB on equalizer performance over a range of mix rates

• Data Capture

- Build system for lab and field data capture with 1 and 2 antennas - Use captured data to evaluate sync and equalizer methods

• Demonstrate Robust Carrier, Symbol Clock and Frame Synchronization

- Minor modifications to improve 5th gen methods if possible - Derive new methods, especially for carrier recovery when the pilot carrier nulled out by multipath

• Propagation Studies/Antenna Design

- Characterize real world propagation conditions for better channel modeling, especially indoor and outdoor to indoor situations

- Use improved modeling to evaluate the potential benefits of spatial, polarization, beam pattern and antenna selection diversity

- Create useful antenna designs based on above results (small reconfigurable, integrated into TV chassis, etc.)

- Smart/steerable antennas; sync and equalizer interaction with antennas


Personnel Overview • Director - Jong Kim • Equalization

- Zenith: Mark Fimoff, Chris Pladdy, Jin Kim, Murthy Nerayanuru - Purdue: Prof. Michael Zoltowski, Bill Hillery (post-doc) - Izmer Institute of Technology: Asst. Prof. Serdar Ozen

• Synchronization

- Zenith: Tyler Brown, Bruno Amizic, Mark Fimoff, Jin Kim, Rudy Turner - Purdue: Prof. Michael Zoltowski, Bill Hillery (post-doc), Perry Ding (Ph.D. student)

• Propagation Studies

- Zenith: Jong Kim, Tyler Brown, Pierre Dobrovolny - Virginia Tech: Prof. William Davis, Prof. Carl Dietrich, Gaurav Joshi (Ph.D. student) - Izmer Institute of Technology: Asst. Prof. Serdar Ozen

• Data Capture

- Zenith: Ray Hauge, Tom Horwitz, Gary Jones, Steve Heinz, Peter Kirsch

Purdue/Zenith Basic Time Domain DFE (single antenna) with Major Computational Blocks


General Comments • The Purdue-Zenith DFE is an indirect equalizer which calculates tap weights from a periodically

updated CIR (channel impulse response) estimate • The initial CIR estimate is efficiently and accurately calculated from the training sequence using the a-BLUE method [1, 2] • An updated least squares CIR estimate [11, 12] is calculated from the most recent 2-3 segments of trellis

decoder symbol decisions in a sliding window overlapping manner

• Updated MMSE [6] DFE tap weights (or CMMSE [8, 9, 10]) are calculated based on the latest CIR estimate

• FB filter length = assumed maximum channel length

• FF filter length maximum channel length in order to optimally combine path energy ≥

• Zero delay trellis decoder in DFE feedback loop for error propagation reduction

• Simulations show successful tracking of moderate to high Doppler rates at CIR estimate/tap weight update rates on the order of once per segment

• Dynamic channel performance is primarily limited by the CIR estimate/tap weight update rate and

update delay (latency) as limited by computational complexity



General Comments (cont.) • This work has been applied to a multi-antenna receiver where the DFE has multiple forward filters

jointly optimized with feedback filter (or other alternative sub-optimal methods ) • Our equalization methods require the frequent solution of large systems of equations

- we have derived very efficient techniques for iteratively solving these systems - based on applying the FFT to the pre-conditioned conjugate gradient algorithm (PCG/FFT) - this greatly reduces the complexity of our computational subsystems

• Equalizer can have 2 modes

- Fast tracking mode – taps weights are updated about once per segment based on latest CIR estimate – best for fast dynamic channels

- Averaging mode – tap weights are updated about once per segment based on average of previous N CIR estimates - provides a better DFE SINR output for static or very slowly changing channels

- Equalizer can automatically determine best mode based on measured differences between latest 2 CIR estimates

Basic Equalizer Architectures – Time Domain, Single and Multi-Antenna (note that decision device is zero delay trellis decoder)

CIR Est.

MMSE TapWeight

Calculator

Decisiondevice

FBF:

Two Antenna

FFF2:

FBF:

CIR Est.

MMSE TapWeight

Calculator

Decisiondevice

FFF1:

Single Antenna

FFF:



Major Computational Blocks - Introduction • Initial CIR Estimate Calculation – a-BLUE Method • CIR Estimate Update Calculation – PCG/FFT Least Squares Solution • MMSE Tap Weight Calculation - PCG/FFT MMSE Solution

Major Computational Blocks – a-BLUE Initial CIR Estimate • A fairly accurate initial CIR is required for the single antenna case, somewhat less so for the multi-antenna case

• The initial a-BLUE CIR estimate is given by

( ) yKAAKAh 1110

~~ˆ −−−= appT

appT

where A is a convolution matrix of training symbols, y is the received data vector that includes the training symbols and adjacent unknown symbols and appK~ is a simple approximation of the channel covariance matrix [2], given by

HHdapp QQHHK 2~~~

2~

ησε+=

where H~ is a “no ghost” channel convolution matrix based that on the raised cosine pulse shape, 2~ησ is a non-critical

assumed moderate noise variance, dε is the symbol variance and Q is a convolution matrix based on the matched filter

• This allows us to pre-calculate and store in ROM the matrix

( ) 111 ~~ −−−app

Tapp

T KAAKA

• is calculated from a matrix vector multiply requiring 1,268,736 real multiplies and ROM size = 1,268,736 (assumed CIR length is 512)

0h

• This yields a very accurate - simulations show that a-BLUE provides sufficiently accurate initial CIR estimates to enable DFE convergence for severe multipath channels, for the case of a single antenna with CIR lengths up to 512

0h

• Note that a full BLUE CIR estimate would take O(1010) multiplies and is only slightly more accurate

• Can trade off accuracy and estimated CIR length

• Less accuracy is required for the 2 antenna case, therefore a longer CIR can be estimated


Major Computational Blocks – CIR Estimate Update Calculation • Calculation

- Based on a block by block LS (least squares) solution of a large system of equations - Calculated on the order of once per segment - Calculation is based on a vector of between 2 and 3 of the most recent segments of trellis

decoder decisions (about 2 ½ seems best) - LS system of equations can be efficiently iteratively solved with the PCG/FFT algorithm

• The system to be solved is given by [11,12] , where B is a (4096 – 512 + 1) x 512 convolution matrix of most recent 2-3 ( ) yBBBh TT

LS1ˆ −

= segments of trellis decoder decisions and y is the received data vector

• The exact solution of this system requires on the order of 600 x 106 real multiplies

• This can be greatly reduced by using PCG/FFT iterative method initialized with the previous CIR estimate [11]. This requires about 1 x 106 real multiplies to execute 5 CG steps.

• Recent work has substantially reduced this overhead - FFT size reduced (from 4k to 2k) with “FFT length shortcut” method, very small performance

loss [11] - For an additional small loss in Doppler performance we need only a single CG step per CIR

estimate update and we have eliminated the need to calculate the alpha parameter [11] - This requires about 3 x 105 real multiplies (PCG/FFT)

• Required FFT precision is 16 bits, α and β parameter calculations may require 24 bits



Major Computational Blocks – DFE MMSE tap Weight Update Calculation

• MMSE Tap Weight Update Calculation [4, 5, 6]

- FF/FB jointly optimized tap weights calculated from most recent CIR estimate - MMSE system of equations is solved iteratively with the PCG/FFT algorithm

• PCG/FFT Algorithm Tap Weight Vector Initialization for Each Update [6] - Before using PCG/FFT to calculate the tap weight vector, we must give that tap weight vector

an initial value - Most obvious choice is the previous tap weights – but other choices work better for Doppler

channels - Algorithm works better with zero vector tap weight initialization - Algorithm also works better with initilization directly from CIR estimate - P-1b initialization

Major Computational Blocks – DFE MMSE tap Weight Update Calculation (cont.)

• For a receiver with antennas, let 1≥aN [ ]TTNF

TFF a,1, ,....,ggg = be the vector containing Na feed-forward

filters, and let be the single feedback filter, then the jointly optimized MMSE tap weights are given by [7]

Bg

FTR

TKB

KNRI

TR

TKKRF a

gH∆g

δHIH∆∆IHg

=

⎟⎟⎠

⎞⎜⎜⎝

⎛+−= ++

−

1

1

2

2

)(σσν

• Straight forward solution is not practical for FF filter length 512 and FB filter length 512 - Cioffi exact solution requires about 3.5 x 106 real multiplies (single antenna) - PCG/FFT, with Chan pre-conditioner [19] with 4 steps per update requires about 4.9 x 105 real

multiplies per update (single antenna) - PCG/FFT, with “Jin Kim” pre-conditioner [20] with 2 steps per update requires about 3.9 x 105

real multiplies per update (single antenna) – with only a very small performance loss

• For 2=aN- tap weight computation increases by a factor of 4 for joint optimization - a suboptimal method increases computation only by a factor of 2 with only a small performance

loss (discussed later)

• Required FFT precision is 16 bits, α and β parameter calculations may require 24 bits



Tap Weight Update Strategies for Dynamic Channels – Main Concepts • Update Delay – Tracking performance is affected by the latency caused by

- LTD (long delay trellis decoder) symbol decision delay plus - time delay for calculation of CIR estimate update plus - time delay for calculation of MMSE tap weight estimate

• Update Rate – CIR estimate/tap weight update frequency also affects tracking performance • We want the shortest update delay and the fastest update rate possible to maximize DFE

tracking ability • Reducing the computational complexity of the CIR estimate update calculation and the tap

weight update calculation helps both the update delay and the update rate • Two other specific methods can be used for reducing the update delay


Tap Weight Update Strategies for Dynamic Channels - Reducing the Update Delay – 2 methods • Turbo/data recirculation methods [13]

- Last group of symbols of each segment is run through the DFE twice - Group size is equivalent to the long trellis decoder delay - 1st pass with old tap weights, 2nd pass with new tap weights calculated from 1st pass - Substantial improvement in Doppler tracking, but adds hardware complexity

• ZTD/LTD combination

- CIR estimate update is based on a 2-3 segment long vector consisting of [11] ° LTD (long delay trellis decoder) decisions for earlier symbols ° ZTD (zero delay trellis decoder) decisions for most recent symbols

- Eliminates contribution of LTD delay to the update delay - Improves Doppler performance (not as much as turbo), does not increase hardware

complexity

Tap Weight Update Strategies for Dynamic Channels - Reducing the Update Delay - ZTD/LTD Combination

• Want simple method to effectively reduce tap weight update delay

• Assume for simplicity that the DFE delay is ½ segment, LTD delay is ½ segment, CIR estimate plus tap weight update computation time is one segment; CIR estimate based only on LTD decisions (3 segments)

• Reduce update delay by using a combination of LTD and ZTD symbol decisions [11] for the CIR estimate; does not increase complexity


Simulation Results, Single Antenna – Compare CIR Estimate Update Methods

• Compare 2 CIR estimators under dynamic channel conditions - CG/FFT 5 steps vs. 1 step

Table I

Max Doppler (Hz) Channel /

SNR 5 step CG/FFT 1 step CG/FFT

Brazil A 26 dB 200 170Brazil B 26 dB 83 67Brazil C 26 dB 55 50Brazil D 26 dB 70 63Brazil E 32 dB 45 45

• Small reduction in Doppler performance for 1 step, big reduction in complexity • Compare 2 CIR estimators under dynamic channel conditions

- CG/FFT 1 step without and with “FFT length shortcut” Table II

Max Doppler (Hz) Channel /

SNR 1 step CG/FFT no shortcut

1 step CG/FFT with shortcut

Brazil A 26 dB 170 157Brazil B 26 dB 67 63Brazil C 26 dB 50 43Brazil D 26 dB 63 50Brazil E 32 dB 45 37

• Further small reduction in Doppler performance for shortcut, big reduction in complexity Note – Tap weight update for above used PCG/FFT, 4 steps


Simulation Results, Single Antenna – Compare CIR Estimate Update Methods (cont.) • Performance of LTD/ZTD combination method vs. LTD only method Table III (all CIR estimates CG/FFT 1 step with fixed alpha)


Maximum Doppler (Hz)

Channel/SNR LTD only

3 seg support (from Table II col 2)

LTD/ZDT 3 seg support

LTD/ZDT 2.5 seg support

LTD/ZDT 2 seg support

Brazil A / 26 dB 157 180 197 177 Brazil B / 26 dB 63 67 77 67 Brazil C / 26 dB 43 50 55 50 Brazil D / 26 dB 50 57 63 60 Brazil E / 32 dB 37 43 43 43

• LTD/ZTD combination is better then LTD only - because of reduced update delay • Note that turbo/data recirculation methods can further improve Doppler performance (25-35%), but do add complexity

• Add Chan pre-conditioning [17, 18, 19] to CG/FFT (PCG/FFT) to the above LTD/ZTD combination method Table IV – Chan Preconditioner


Channel/SNR LTD/ZDT, CG/FFT 1 step 2.5 seg support

(from Table III col 3) LTD/ZDT, PCG/FFT 1 step

2.5 seg support

Brazil A / 26 dB 197 230 Brazil B / 26 dB 77 83 Brazil C / 26 dB 55 57 Brazil D / 26 dB 63 73 Brazil E / 32 dB 43 43

• Chan pre-conditioner yields good performance improvement with small additional complexity


Simulation Results, Single Antenna – Compare CIR Estimate Update Methods (cont.) Summarizing – • Compared CG/FFT 5 step CIR estimator vs. CG/FFT 1 step CIR estimator for dynamic channels – 1 step method yields

small reduction in performance but large reduction in complexity • Compared CG/FFT “FFT length shortcut” CIR estimator to non-shortcut CIR estimator for dynamic channels – shortcut

method is much simpler with only a small to moderate loss in performance • Compared LTD based CIR estimator to LTD/ZTD based CIR estimator – improves Doppler performance • Determined best sample support length of about 2 ½ segments • Added Chan pre-conditioner to CG/FFT (PCG/FFT) – improves performance at a small cost in complexity • Turbo/data recirculation methods can give further boost to Doppler performance, but may be too complicated at this

time Conclusion -

Best practical choice seems to be PCG/FFT CIR estimator with “FFT length shortcut”, single step, with LTD/ZDT combination

Simulation Results, Single Antenna – Compare Tap Weight Update Methods

• Results for DFE using best MMSE PCG/FFT tap weight update methods (with P-1b init) [6,7] (Note: simulation uses Chan preconditioned PCG/FFT CIR estimator )

• Compare Chan preconditioner to Jin Kim preconditioner

• Static Channel Results

DFE SINR Out (dB)

Channel/SNR

4 step Chan PCG/FFT

2 step

Chan PCG/FFT

2 step

Kim PCG/FFT 1 step

Kim PCG/FFT

Brazil A / 22 dB 19.40 19.27 19.27 19.15 Brazil B / 22 dB 17.09 16.33 16.88 15.86 Brazil C / 22 dB 16.34 15.83 16.10 15.73 Brazil D / 22 dB 16.96 16.36 16.92 16.21 Brazil E / 30 dB 18.86 diverges 17.57 diverges

• Doppler Channel Results Maximum Doppler (Hz)

Channel/SNR

4 step Chan PCG/FFT

2 step

Chan PCG/FFT

2 step

Kim PCG/FFT 1 step

Kim PCG/FFT

Brazil A / 26 dB 225 230 225 227 Brazil B / 26 dB 93 77 90 75Brazil C / 26 dB 57 53 57 20 Brazil D / 26 dB 77 55 73 53 Brazil E / 32 dB 45 20 45 20


Channel/SNR

4 step Chan PCG/FFT

2 step

Chan PCG/FFT

2 step

Kim PCG/FFT 1 step

Kim PCG/FFT

Brazil A / 26 dB 225 230 225 227 Brazil B / 26 dB 93 77 90 75Brazil C / 26 dB 57 53 57 20 Brazil D / 26 dB 77 55 73 53 Brazil E / 32 dB 45 20 45 20

• Jin Kim preconditioner (3rd column) produces excellent results with only 2 CG steps per update



Simulation Results, 2 Antenna Diversity - Introduction • 2 antenna diversity is easily exploited by a DFE with 2 FF filters and 1 FB filter using joint

optimization • Substantial improvement in SNR performance due to signal combining • Results in reduced FB tap energy reduced error propagation improved Doppler

tracking • 2 antenna diversity is also easily applied to LE (2 FF filters) and 5th gen pDFE with 2 FF

filters • This can be extended to N antenna diversity • Spatial, polarization, and beam pattern diversity will be studied (simulations so far are only

for spatial diversity)


Simulation Results, 2 Antenna Diversity – Dynamic Diversity Channel Model • 1 to N channels (antennas) • Doppler rate selectable for each ghost (up to 4 kHz) • Doppler rates can be selected in terms of vehicle speed • Rayleigh or Ricean channels • Carrier frequency is selectable • Antenna spacing selectable in terms of wavelengths or actual distance • Angles of arrival may be random or specifically selected • Path attenuation and delay may be random or specifically selected • Indoor field data is needed for a more accurate model

Simulation Results, 2 Antenna Diversity – Dynamic Diversity Channel Model (cont.)


3-D antenna geometry with far-field assumption

Time varying CIR for 2 antennas

Simulation Results, 2 Antenna Diversity – Purdue/Zenith Basic Time Domain DFE (2 antennas) with Major Computational Blocks


Simulation Results, 2 Antenna Diversity – Review of Previous Results for Static Channels

• 2 antenna simulations for jointly optimized 3 filter DFE show substantial improvement in SNR threshold

- Black curve establishes baseline performance for one antenna - Top most blue curve shows improved performance for 2 antennas (spacing = λ )

λ- Blue curve labeled 0.1 has much closer spacing, but still shows improved performance

- Similar results for both Brazil C and D

- Big advantage for 2 antenna DFE is large reduction in FB tap weights which reduces error propagation


Simulation Results, 2 Antenna Diversity – Review of Previous Results for Static Channels (cont.)

- 2 Antenna Simulations for jointly optimized LE (2 filters-no feedback) show interesting results (red curves)

- For single antenna case, linear equalizers show a severe noise enhancement problem, hence a DFE (or a pDFE) is recommended - For 2 antenna case, if antennas are far enough apart, linear equalizer results may be better than that of the DFE - Advantages of 2 antenna linear equalizer

° less degradation due to error propagation ° efficient FFT version of filters easily implemented; much simpler hardware ° nearly same performance as diversity DFE if antenna spacing is correct ° can have a faster update rate (better Doppler tracking) in hardware because tap weight update calculation is trivial compared

to that of a DFE - Disadvantages of 2 antenna linear equalizer

° if antenna spacing too close, large performance degradation


Simulation Results, 2 Antenna Diversity – Review of Previous Results for Static Channels (cont.) • Further effect of antenna spacing on the 2 antenna linear equalizer is shown below. It can be seen that performance

tends to improve as antenna spacing increases, but not monotonically (for just one set of angles of arrival)



Simulation Results, 2 Antenna Diversity – Review of Previous Results for Doppler Channels • Simulation based on a single random set of angles of arrival

Maximum Doppler (Hz) Channel/SNR 1 ant DFE 2 ant DFE 2 ant LE Brazil C, 26 dB 45 Hz 90 Hz 105 Hz Brazil D, 26 dB 55 Hz 100 Hz 120 Hz • 2 antenna receivers seem very promising for dynamic channel tracking, but…. • We need further simulations with many random angles of arrival

Simulation Results, 2 Antenna Diversity – CIR Estimate and Tap Weight Update • PCG/FFT CIR estimate updates are needed for each channel (antenna) • For DFE, joint MMSE optimization (using PCG/FFT) of tap weights requires about 4 times the computation of the

single antenna case [7] because the system matrix is 4 times larger

- For a single antenna DFE, to get the optimal tap weights, we must solve a system of the form

dIAAg12

11

−

⎥⎥⎦

⎤

⎢⎢⎣

⎡+=

I

T

εση

where g is the FF filter

- For a 2 antenna DFE, to get the optimal tap weights, we must solve a system of the form

dIAAAAAAAAg

12

2212

2111

−

⎥⎥⎦

⎤

⎢⎢⎣

⎡+⎥

⎦

⎤⎢⎣

⎡=

ITT

TT

εση

where g is a stacked vector of both FF filters

- A sub-optimal simplification would be to solve the system (2 times the computation of the single antenna

case)

dIAA00AAg

12

22

11

−

⎥⎥⎦

⎤

⎢⎢⎣

⎡+⎥

⎦

⎤⎢⎣

⎡=

IT

T

εση

where g is a stacked vector of both FF filters

• As previously discussed, these systems may solved by inverting the system matrix (exact solution), but that is too

complicated for actual hardware – so we use PCG/FFT.


Simulation Results, 2 Antenna Diversity – New DFE Results for Static Channels

• Static channels, 10 different sets of randomly selected angles of arrival for ghost paths of each channel • Antenna spacing 2 wavelengths; optimal vs. sub-optimal exact tap weight solution

Brazil A / 22 dB/ 2 wavelengths apart DFE SINR Out

optimal sub-optimal Angles of Arrival

exact soln exact soln

Set 1 23.10 22.73Set 2 23.03 22.78Set 3 23.10 22.73Set 4 23.03 22.79Set 5 22.86 22.75Set 6 23.15 22.75Set 7 23.11 22.62Set 8 22.89 22.90Set 9 22.73 22.69

Set 10 22.86 22.68mean 22.99 22.74

Brazil B / 22 dB/ 2 wavelengths apart DFE SINR Out




Set 10 22.88 21.67mean 22.60 21.57

Brazil C / 22 dB/ 2 wavelengths apart DFE SINR Out




Set 10 22.36 21.50mean 21.94 20.80

Brazil D / 22 dB/ 2 wavelengths apart DFE SINR Out




Set 10 22.36 21.05mean 22.11 21.09

Brazil E / 27 dB/ 2 wavelengths apart DFE SINR Out




Set 10 27.53 24.16mean 26.66 24.68

• For exact solution, in most cases the optimal solution is better, but the sub-optimal solution is close


Simulation Results, 2 Antenna Diversity – New DFE Results for Static Channels

• Static channels, 10 different sets of randomly selected angles of arrival for ghost paths of each channel • Antenna spacing 2 wavelengths; optimal vs. sub-optimal PCG/FFT MMSE tap weight calculation

Brazil A / 22 dB/ 2 wavelengths apart DFE SINR Out

optimal sub-optimal Angles of Arrival PCG

(4 steps) PCG

(4 steps) Set 1 18.75 21.93Set 2 18.29 22.02Set 3 18.75 21.93Set 4 18.29 22.02Set 5 21.95 21.76Set 6 21.51 21.97Set 7 21.89 21.48Set 8 15.42 22.46Set 9 19.52 22.05

Set 10 20.85 21.92mean 19.53 21.95

Brazil B / 22 dB/ 2 wavelengths apart DFE SINR Out


(4 steps) PCG


Set 10 20.21 19.70mean 19.26 19.75

Brazil C / 22 dB/ 2 wavelengths apart DFE SINR Out


(4 steps) PCG


Set 10 17.86 19.87mean 18.43 18.90

Brazil E / 27 dB/ 2 wavelengths apart DFE SINR Out


(4 steps) PCG


Set 10 26.10 17.21mean 24.05 19.43

Brazil D / 22 dB/ 2 wavelengths apart DFE SINR Out


(4 steps) PCG


Set 10 19.32 18.85mean 19.16 19.36

• For PCG/FFT solution, often sup-optimal is better (except for Brazil E), why ?


Simulation Results, 2 Antenna Diversity – New DFE Results For Static Channels (cont.) • For the PCG algorithm, the number of steps required to reach the theoretical solution is equal to the number of distinct

eigenvalues of the pre-conditioned system matrix

• If the system matrix eigenvalues are clustered (in general closer to each other in value), then after a fixed number of PCG steps (say 4), we will be closer to a solution

• These plots show the eigenvalues for typical optimal and sub-optimal system matrices

• It is clear that for the sub-optimal cases, the eigenvalues are more clustered (closer to each other in value), therefore

when using PCG, we will get close to the sub-optimal solution in fewer steps than it takes to get close to the optimal solution

• Therefore it is not surprising that often the 4 step PCG solution based on the sub-optimal system matrix is close to or better in performance than the 4 step PCG solution based on the optimal system matrix


Simulation Results, 2 Antenna Diversity – New DFE Results for Dynamic Channels

• Dynamic channels, 10 different randomly selected angles of arrival for ghost paths of each channel • optimal vs. sub-optimal PCG/FFT MMSE tap weight calculation • Antenna spacing 2 wavelengths; DFE SINR output > 15 dB

Brazil A / 26 dB/ 2 wavelengths apart Max Doppler (Hz)


(4 steps) PCG

(4 steps) Set 1 250 540Set 2 220 350Set 3 240 540Set 4 215 350Set 5 250 235Set 6 450 700Set 7 475 440Set 8 210 260Set 9 280 240

Set 10 250 320mean 284 397

Brazil B / 26 dB/ 2 wavelengths apart Max Doppler (Hz)


(4 steps) PCG


Set 10 185 195mean 152 173

Brazil C / 26 dB/ 2 wavelengths apart Max Doppler (Hz)


(4 steps) PCG


Set 10 90 90mean 94 97

Brazil D / 26 dB/ 2 wavelengths apart Max Doppler (Hz)


(4 steps) PCG


Set 10 95 100mean 100 105

Brazil E / 30 dB/ 2 wavelengths apart Max Doppler (Hz)


(4 steps) PCG


Set 10 100 105mean 122 121


Simulation Results, 2 Antenna Diversity – New LE Results For Dynamic Channels

• Dynamic channels, 10 different randomly selected angles of arrival, LE SINR output > 15 dB • Antenna spacing 2 wavelengths; optimal PCG/FFT MMSE tap weight calculation

Brazil A / 26 dB/ 2 wavelengths apart Max Doppler (Hz)

optimal Angles of Arrival PCG

(4 steps) Set 1 240 Set 2 220 Set 3 240 Set 4 210 Set 5 240 Set 6 540 Set 7 510 Set 8 170 Set 9 300

Set 10 280 mean 295

Brazil B / 26 dB/ 2 wavelengths apart Max Doppler (Hz)



Set 10 170 mean 142

Brazil C / 26 dB/ 2 wavelengths apart Max Doppler (Hz)



Set 10 110 mean 112

Brazil D / 26 dB/ 2 wavelengths apart Max Doppler (Hz)



Set 10 100 mean 102

Brazil E / 30 dB/ 2 wavelengths apart Max Doppler (Hz)



Set 10 130 mean 137

ZENITH CONFIDENTIAL v1.0 • 2 antenna LE performs well if we have sufficient antenna spacing (sometimes better than DFE, sometimes not)

36


Application of Zenith Research Ideas to LGE 5th Gen Style Architecture Introduction • LG 5th Gen equalizer is based on "predictive DFE" (pDFE) architecture [14, 15] • If the filters are long enough, pDFE and DFE performance are the same • If the filters are too short, pDFE will see a bigger performance loss since its filters are not

jointly optimized • It is important to note that the large difference in dynamic channel performance between the

Purdue-Zenith architecture simulation and the LGE 5th Gen architecture is the “tap weight update method”, not DFE vs. pDFE


Application of Zenith Research Ideas to LGE 5th Gen Style Architecture Introduction (cont.) • Is it possible to apply the Purdue-Zenith tap weight update and diversity methods to the LGE

5th gen pDFE ? – yes, we call this Z-pDFE

- Use the a-BLUE method for initial CIR estimate

- Use PCG/FFT to calculate LS CIR estimate updates (once per segment)

- Linear frequency domain equalizer tap weights are easily calculated directly from the latest CIR estimate (much less computation compared to the DFE)

- We have been working on a method for calculating the noise canceller filter tap weights directly

from the latest CIR estimate update – this is the key part • This should result in much faster dynamic channel tracking for the LGE 5th Gen

architecture


Application of Zenith Research Ideas to LGE 5th Gen Style Architecture Initial Simulation Results – Static Channels, Single Antenna • We now have a Z-pDFE simulation operating with

- pDFE type equalizer - Forward filter tap weight update calculated from the newest CIR estimate - Noise canceller tap weights also calculated from the newest CIR estimate (derived and implemented by S.

Ozen and C. Pladdy [16]) • Forward filter 1024 taps long (currently time domain, easily changed to frequency domain) • Noise canceller simulated with different lengths • At this time, calculating noise canceller taps from CIR estimate is complicated – but we expect to be able to greatly

reduce this using PCG/FFT methods • Initial simulation results – prove that Ozen/Pladdy noise canceller (Z-pDFE) works correctly with static channel

simulations

SINR at Output of Z-pDFE, Static channels, single antenna Noise Canceller Length Channel @ SNR in

256 128 64 0ff

Brazil A @ 26 dB 23.040 dB 23.039 dB 23.027 dB 22.425 dB Brazil B @ 26 dB 18.806 dB 19.038 dB 18.476 dB 16.398 dB Brazil C @ 26 dB 19.467 dB 19.474 dB 19.484 dB 17.214 dB Brazil D @ 26 dB 19.174 dB 19.201 dB 19.123 dB 16.603 dB Brazil E @ 34 dB 17.705 dB 17.172 dB 14.824 dB 8.368 dB

Application of Zenith Research Ideas to LGE 5th Gen Style Architecture (cont.) Initial Simulations Results for Doppler Channels, Single Antenna

• Compare 5th Gen prototype pDFE CRC lab test results to Z-pDFE simulations Max Doppler Rate (noise canceller length 128)

Channel @ main path SNR

5th Gen pDFE CRC Lab Test

Z-pDFE simulation

# 1 @ 25 dB 1 Hz 65 Hz # 2 @ 25 dB 1 Hz 75 Hz

• O-pDFE simulation results for Brazil Doppler channels Max Doppler Rate for SINR above 15dB at Output of Z-pDFE (noise canceller length 128)

Channel @ main path SNR

Z-pDFE simulation

Brazil A @ 25 dB 170 Hz Brazil B @ 24 dB 60 Hz Brazil C @ 21 dB 45 Hz Brazil D @ 19 dB 45 Hz Brazil E @ 30 dB 30 Hz



Application of Zenith Research Ideas to LGE 5th Gen Style Architecture Preliminary Conclusions • LGE pDFE type equalizer combined with Purdue/Zenith update methods (Z-pDFE) may be

the most practical choice • FF tap weight calculation from CIR estimate is very simple • Noise canceller tap weight calculation from CIR estimate using PCG/FFT may be relatively

simple because the tap weight vector is only 128 long (compared to 512 for the DFE) – note that we have not worked this out yet

• For the 2 antenna case, we expect that the Z-pDFE will be less sensitive to antenna spacing

than the 2 antenna LE. • 2 antenna diversity simulations to be done

Application of Zenith Research Ideas to LGE 5th Gen Style Architecture – Block Diagrams Note that decision device is zero delay trellis decoder

FFT

FFT Frequency Bins

Frequency Bins

IFFT

CIR Est.

FFT MMSE TapWeight

Calculator

Noise Predictor

ek

FFT Frequency Bins IFFT

CIR Est.

FFT MMSE TapWeight

Calculator

Noise Predictor

ek

Indirect (CIR Estimate based) Frequency Domain pDFE/Combiner ( 1 antenna )

Indirect (CIR Estimate based) Frequency Domain pDFE/Combiner ( 2 antenna )

ZENITH C NFIDENTIAL 1.0 42
v O


DFE with EVSB Decoder - Single Antenna, Preliminary Results • DFE simulation has now includes the LGE designed EVSB trellis decoder (ZTD and LTD) • Static channel results for 100% EVSB, 50% EVSB and 0% EVSB • Results show input SNR required for LTD error rate (estimation of received 8 level symbols) to be less than 0.006 (this

is better than usual TOV)

8VSB Threshold for 0.006 Sym err rate EVSB Threshold for 0.006 Sym err rate Channel 100% 8VSB 50% 8VSB 0% 8VSB* 0% EVSB 50% EVSB 100% EVSB

No Ghost 17 dB 16 dB 16 dB --- 12 dB 10 dB Brazil A 18 dB 18 dB 17 dB --- 13 dB 12 dB Brazil B 22 dB 20 dB 20 dB --- 18 dB 15 dB Brazil C 22 dB 20 dB 19 dB --- 17 dB 14 dB Brazil D 21 dB 20 dB 19 dB --- 16 dB 14 dB Brazil E 27 dB 27 dB 25 dB --- 27 dB 25 dB

* Note that for 0% 8VSB/100% EVSB, we actually have about 10% 8VSB because of the RS parity symbols • Results indicate that 8VSB stream receives only a 1 – 2 dB SNR performance boost when mixed with EVSB • Doppler simulations to be done

Initial DFE Results with Data Capture Streams

Note: Simulations do not have benefit of phase tracker

• Static channel results (single antenna)

DFE SINR Out (dB) Channel/ main path SNR

Channel Model Simulation

Data Capture Simulation

Difference

Brazil A/25 dB 23.62 22.79 0.83Brazil B/25 dB 20.87 19.64 1.23Brazil C/25 dB 24.10 23.12 0.98Brazil D/25 dB 22.96 19.97 2.99Brazil E/25 dB 17.20 17.14 0.06

• Performance difference between channel model and data capture simulations is small except for Brazil D – we are investigating the reason for this


Initial DFE Results with Data Capture Streams (cont.)

• Doppler Channel Results (single antenna) – Brazil D at 60 Hz, SNR = 33 dB

• Top trace is symbol clock frequency, bottom trace is MSE (mean square error) at DFE output • Recovered symbol clock frequency is modulated at the composite Doppler frequency • Note that MSE increase seems to track the faster excursions of the modulated symbol clock frequency • Equalizer successfully tracks channel



• Doppler Channel Results (single antenna) – Brazil C at 60 Hz, SNR = 33 dB

• Top trace is symbol clock frequency, bottom trace is MSE (mean square error) at DFE output • Recovered symbol clock frequency is modulated at the composite Doppler frequency • Equalizer successfully tracks channel



• Doppler Channel Results (single antenna) – Brazil B at 40 Hz, SNR = 28.3 dB

• Top trace is symbol clock frequency, bottom trace is MSE (mean square error) at DFE output • Recovered symbol clock frequency is modulated at the composite Doppler frequency • Note that MSE increase seems to track larger excursions of the modulated symbol clock frequency • Equalizer almost tracks the channel, but diverges toward the end of the sequence

• Reducing clock recovery loop bandwidth after acquisition would reduce symbol clock frequency modulation - would improve Doppler tracking – to be investigated



To Be Done Next • More Data Capture Simulations • Add Phase Tracker to Simulations • 2 Antenna Diversity Z-pDFE • PCG/FFT applied to Z-pDFE • Doppler simulations for EVSB • Simulations with Rayleigh Fading Channel Model • PCG/FFT applied to CMMSE tap weight calculation for DFE

ZENITH CONFIDENTIAL

13. “A Signal Re-Circulation Method that Provides for an Effective Earlier CIR Estimate Update for the CIR Estimating DFE”, Zenith patent application, M. Fimoff, M. Nerayanuru, February 2004

v1.0 49

References

BLUE, a-BLUE Initial CIR Estimation 1. “Best Linear Unbiased Channel Estimation for Frequency Selective Multipath Channels with Long Delay Spreads”, C. Pladdy, S. Ozen, M.

Fimoff, S. M. Nerayanuru, M. D. Zoltowski, internal Zenith report, March 2003 2. “A Note on Covariance Matrix Update to Aid the Initial Channel Estimation”, section 2.1, S. Ozen and M. D. Zoltowski, Zenith internal

report, 12/9/02 CG/FFT 3. Patent application for “Reduced Complexity CG algorithm Using the FFT (CG/FFT)”, M. D. Zoltowski, W. H. Hillery, TBD MMSE Tap Weight Calculation for DFE 4. “Fast Computation of Channel-Estimate Based Equalizers in Packet Data Transmission”, IEEE Transactions on Signal Processing, N. Al-

Dhahir, J. M. Cioffi, Nov. 1995 5. “A Fast Computation Algorithm for the Decision Feedback Equalizer”, IEEE Transactions on Communications, I. Lee, J. M. Cioffi, Nov.

1995 6. “CG/FFT Applied to MMSE Tap Weight Calculation”, C. Pladdy, P. Ding, J. Kim, internal Zenith report, TBD 7. “PCG/FFT Applied to Optimal and Suboptimal MMSE Tap Weight Calculation for Decision Feedback Equalizers with Multiple

Antennas”- S. Ozen, C. Pladdy, J. Kim, P. Ding, M. Fimoff, Zenith internal report - TBD CMMSE Tap Weight Calculation 8. “Decision Feedback Equalizers with Constrained Feedback Taps for Reduced Error Propagation”, M. D. Zoltowski, W. H. Hillery, M.

Fimoff, Proceedings of SPIE, 2003 9. “Matlab Simulation Report – newtrellis_sims2”, W.H. Hillery, Zenith internal report, April 2003 10. “Computation of a Constrained Decision Feedback Equalizer for Reduced Error Propagation”, W. J. Hillery, M. D. Zoltowski, M. Fimoff,

WCNC 2004 LS CIR Estimate Update 11. “A Tracking Channel Estimator for 8 VSB Receivers”, M. Fimoff, S. Ozen, M. D. Zoltowski, S. Nerayanuru, Zenith internal report,

7/18/02 12. “An Improved Efficient Tracking Least Squares Channel Estimator for 8 VSB Receivers”, Jin Kim, S. Ozen, M. D. Zoltowski, M. Fimoff,

internal Zenith report, 3/12/04 Data Recirculation (Turbo) for DFE


References (cont.) pDFE 14. “Decision Feedback Equalization”, C. A. Belfiore, J. H. Park, Proceedings of the IEEE, August 1979 15. “Digital Communications”, 3rd ed., J. G. Proakis, McGraw-Hill, 1995, section 10-3-3 Noise Canceller Derived from CIR Estimate 16. “A CIR Estimate Based Noise Canceller for Predictive Decision Feedback Equalizers”, S. Ozen, C. Pladdy, Zenith internal report , TBD CG Pre-Conditioning 17. “Preconditioned Conjugate Gradient Methods for Adaptive Filtering”, A. W. Hull, W. K. Jenkins, IEEE Symposium, June 1991, pp. 540-

543 18. “Design and Analysis of Toeplitz Preconditioners”, T. Ku, C. C. Jay Kuo, IEEE Transactions on Signal Processing, January 1992 19. “Conjugate Gradient Methods for Toeplitz Systems”, R. H. Chan, M. K. Ng, SIAM Review, Vol. 38, No. 3, Sept. 1996, pp. 427-482 20. “A Preconditioner for CIR Estimate Based Conjugate Gradient MMSE Tap Weight Calculations for Decisions Feedback Equalizers”, J.

Kim, C. Pladdy, M. Nerayanuru - TBD

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