In this one-year renewal of NASA Contract No. 2-304, basic research, development, and implementation in the areas of modern estimation algorithms and digital communication systems have been performed. In the first area, basic study on the conversion of general classes of practical signal processing algorithms into systolic array algorithms is considered, producing four publications. Also studied were the finite word length effects and convergence rates of lattice algorithms, producing two publications. In the second area of study, the use of efficient importance sampling simulation technique for the evaluation of digital communication system performances were studied, producing two publications

Balakrishnan, A. V.

Kung, Yao

English

NASA Technical Reports Server

. 
Final Report 
to 
NASA-Ames Research Center 
Moffett Field, CA 94034 
Contract No. NAG 2-304 
June 15,1987 -June 14,1988 
on 
A Survey of the State of the Art and 
Focused Research in Range Systems 
(bASA-CR-184SSS) A S U R V E Y  CP THE H89- 1 4 7 26 
SZATE-OF-!€HE-ARI A I D  FCCUSEC R E ~ E A E C B  IN 
B A H G E  S P S T E ~ ~ S  F i n a l  Beport, 1 5  dun.  1987 - 
1 4  Jun. 1588 (Califoraia U a i v . )  11  p Oncla E 
CSCL 098 G3/61 0179883 
Principal Investigator 
Professor Kung Yao 
Co - Principal Investigator 
Professor A.V. Balakrishnan 
NASA Technical Officer 
Mr. Karl Anderson 
Laboratory for Flight Systems Research 
University of California 
Los Angeles, CA 90024-1594 
https://ntrs.nasa.gov/search.jsp?R=19890005355 2020-03-20T05:01:21+00:00Z
TABLE OF CONTENTS 
1 . Introduction ............................................ 1 
2 . Modern Estimation Algorithms and Applications ........... 2 
3 . Efficient Simulation of Digital Communication Systems .... 7 
4 . Publications in Contract Period ......................... 9 
1. Introduction 
In this one year renewal of NASA Contract No. 2-304, we have 
performed basic research, development, and implementation in the 
areas of modern estimation algorithms and digital communication 
systems. In the first area, we considered basic study on the 
conversion of general classes of practical signal processing 
algorithms into systolic array algorithms. In this area, we have 
four publications. We also studied the finite word length 
effects and convergence rates of lattice algorithms. There are 
two publications in this area. In the second area, we studied 
the use of efficient ttimportance samplingtt simulation technique 
for the evaluation of digital communication system performances. 
There are two publications in this area. 
-1- 
2. Modern Estimation Algorithms and Applications 
a. Systolic Array Algorithms 
In paper 111, we considered a novel use of the modified 
square-root information filter approach to obtain a jointly 
time update and measurement update systolic Kalman filter. By 
using the matrix decomposition method, the Kalman filter is 
formulated as a SRIF data processing problem followed by a QR 
operation. 
approach, this approach simplifies the computational structure 
and is more reliable when the system has a singular or near 
singular coefficient matrix. By skewing the order of input 
matrices, fully pipelined systolic Kalman filtering operation can 
be achieved. 
the system throughput rate is of the O(n). The numerical proper- 
ties of the systolic Kalman filtering algorithm under finite word 
length effect are studied via analysis and computer simulations, 
and are compared with those of conventional approaches. 
Compared with the previously known covariance 
With the number of processing units of the O(n2 ) , 
In paper [Z], by recognizing that various systolic QR algo- 
rithms can be delivered under an one-row time updating operation, 
we propose a generalized format for systolic QR estimation algo- 
rithm by taking the normalized form of two input data rows into 
consideration. From this approach, the basic relationship bet- 
ween Givens reduction and modified-Gram-Schmidt transformation 
can easily be understood. This generalized form enables us to 
derive new algorithms with efficiency. 
lation, a new systolic QR algorithm, called a modified fast 
Based on this new formu- 
-2- 
Givens algorithm (MFG), is proposed. It also can be shown that 
all existing systolic QR estimation algorithms can be classified 
as special cases under this generalized formulation. With sys- 
tolic array implementation, comparison of computational complex- 
ity for different algorithms can be made by comparing the number 
of operations required in each processing unit of the systolic 
array. In this paper, we study all existing systolic QR algo- 
rithms by comparing both their computational and inter-cell 
connection complexities which are relevant in VLSI implementa- 
tion. It is shown that the new MFG method has simpler computa- 
tional and inter-cell connection complexities, and is well suited 
of VSLI systolic array implementation. 
Due to advances in VLSI technology, there is much interest 
in using array processors to improve the throughput rate of 
various signal processing algorithms. In this paper [3], we 
propose a novel use of a square-root free linear systolic array 
structure that can perform the QR decomposition needed in the 
solution of the least-squares problems. Compared with the con- 
ventional triangular systolic array structure for = estimation, 
the linear array has the advantage of requiring less area and is 
simpler for V U 1  implementation. 
In paper [ 4 ] ,  new result on efficient forms of decoding 
convolutional codes based on the Viterbi algorithm by using 
systolic arrays are presented. 
lutional codes are also discussed. A technique called strongly 
connected trellis decoding is introduced to increase the effi- 
Various properties of the convo- 
-3- 
cient utilization of all the systolic array processors. The 
issues dealing with the composite branch metric generation, 
survivor updating, overall system architecture, throughput rate, 
and computational overhead ratio are also investigated. The 
scheme is applicable to both hard and soft decoding of any rate 
b/n convolutional codes. It is also shown that as the length of 
the code becomes large, the systolic Viterbi decoder maintains a 
regular and general interconnection structure as well as moderate 
throughput rate gain over the sequential Viterbi decoder. 
b. Lattice Algorithms 
Recursive least-squares lattice (RLSL) algorithms are used in 
many adaptive filtering and array processing problems. Reflec- 
tion coefficients are important parameters that characterize the 
behaviors of these algorithms. In paper [5], we consider the 
spatial RLSL algorithm and study in detail the convergent proper- 
ties as well as the finite precision round-off effects of the 
reflection coefficients. 
factor X is set equal to one, the reflection coefficients can 
converge to a constant with probability one with the rate of 
convergence being O(l/T3l2) where T is the number of terms 
involved. When O< X <1, the reflection coefficients converge 
weakly. Furthermore, the variance of the reflection coefficient 
is decreased by increasing 1. Thus, under stationary conditions 
X should be taken as large as possible, while under nonstationary 
conditions X should be taken such that the depth of memory in the 
system matches the rate of change of nonstationarity. Under 
We first show that when the forgetting 
-4- 
finite word length constraint, should be taken to be less than 
some threshold, which is a function of the number of significant 
digits, such that the system can continuously adapt. In addi- 
tion, we found the recursive form of computation for the reflec- 
tion coefficients is generally better than under direct form of 
computation. In this paper, general analytical derivations and 
numerical results are presented on the convergent and round-off 
error properties of reflection coefficients in RLSL algorithms. 
I11 conditions resulting from a wide range of signal power 
levels in an adaptive array system often lead to slow conver- 
gences. The Nolen beamforming network and direct matrix inverse 
method are two possible approaches to overcome such limitations. 
In addition, computational accuracy under a finite word length 
constraint accompanied by the ill-conditions is another important 
issue of interest. In paper [ 6 ] ,  we consider the use of a spa- 
tial lattice algorithm (SLA) in a preprocessor of an adaptive 
array to achieve fast convergence rate, robust computational 
accurate performance, and simple modular form of implementation. 
While the spatial lattice algorithm used in this paper is based 
on the pioneering work of Lee, Morf, and Friedlander, an alterna- 
tive simple and complete proof of the exact time update recur- 
sions using only algebraic techniques based on the Matrix Inverse 
Lemma is presented. This is in contrast to the geometric 
approach used in the original work of Lee, Morf, and Friedlander. 
In addition to the analytical development of the spatial lattice 
algorithm, extensive numerical results, including NBN and MGS, 
-5- 
for adaptive antenna arrays are presented and compared. These 
results show that the convergence rate of the spatial lattice 
algorithm is indeed rapid and is independent of the signal condi- 
tions. Moreover, under finite precision computations, the spa- 
tial lattice algorithm is significantly more robust than other 
methods and is essentially insensitive to the spread of the 
eigenvalues in the input sample covariance matrix. In addition, 
while the complexity of the spatial lattice algorithm is O ( K 2 ) ,  
where K is the number of array elements, the throughput rate is 
O(K) due to its modular form. Thus, the spatial lattice algo- 
rithm appears to provide an attractive alternative to the pre- 
viously known algorithms for high performance adaptive arrays. 
-6- 
3. Efficient Simulation of Digital Communication Systems 
In paper [7], a new technique utilizing significantly lower 
number of samples to achieve convergence in the Monte Carlo 
simulation of digital communication systems based on the impor- 
tance sampling (IS) technique is given. Basic formulas on the 
derivation of this technique as well as the proper selection of 
parameters and the associated estimation accuracy in our modified 
form of IS (denoted by MIS) are presented. Theoretical analysis 
and actual simulations showed that our approach can reduce signi- 
ficantly the required sample size in comparison with the conven- 
tional IS approach (denoted by CIS). For one dimensional as well 
as multi-dimensional Gaussian inputs, the estimation of bit error 
rate (BER) for our approach is uniformly better than that of 
previously known CIS approach. Specifically, for Gaussian inputs 
and a BER of 1E-10 and a relative variance of 0.1, the ratio of 
sample size reduction of the know CIS as compared to our new MIS 
approaches for a zero-memory system is on the order of 12, while 
for systems with a memory of five and fifty samples, these ratios 
are 160 and 55000, respectively. 
In paper [ 8 ] ,  we derive an upper bound on the estimation 
variance and a lower bound on the improvement ratio of various 
importance sampling technique applied to the Monte Carlo simula- 
tion technique. On the basis of this bounding technique, we can 
find various sub-optimum IS parameters readily. Numerical res- 
ults indicate that this technique yields tight and useful bounds 
applicable to generalized exponential distribution noise pdfs 
-7- 
I (which include the Gaussian case) as well as linear and non- 
linear satellite communication systems with intersymbol interfer- 
ences. 
-8- 
. .  , -  
4. Publications in Contract Period 
1. M.J. Chen and K. Yao, #@Systolic Kalman Filtering based on QR 
Decomposition,@@ Proc. SPIE, Vol. 826, Aug. 1987, pp.25-32. 
2. M.J. Chen and K. Yao, @@Comparison of QR Least-Squares Algo- 
rithms for Systolic Array Processing,@@ Proc. Conf. on Inform. 
Sciences and Systems, March 1988 
3. M.J. Chen and K. Yao, @@Linear Systolic Array for Least- 
Squares Estimation," Proc. Inter. Conf. on Systolic Arrays, May 
1988, pp. 83-92. 
4. C.Y. Chang and K. Yao, @@Systolic Array Processing of the 
Viterbi Algorithm,@@ IEEE Trans. on Information Theory, Jan. 1989 
5. S.H. An and K. Yao, @@Convergent and Roundoff Error Properties 
of Reflection Coefficients in Adaptive Spatial Recursive Least- 
Squares Lattice Algorithm,I@ IEEE Trans. on Circuits and System, 
Feb. 1988, pp.241-246. 
6. S.H. An and K. Yao, @@A Fast Convergent and Robust Spatial 
Lattice Algorithm for Adaptive Arrays,@@ revised for IEEE Trans. 
on Aerospace and Electronics Systems, March 1988 
7. D. Lu and K. Yao, @@Improved Importance Sampling Technique for 
Efficient Simulation of Digital Communication Systems,@@ IEEE 
Jour. on Selected Areas in Communication, Jan. 1988, pp. 67-75. 
8. D. Lu and K. Yao, @@On Some New Importance Sampling Results 
for Simulation of Non-Linear Digital Communication Systems,@@ 
Proc. Conf. on Inform. Sciences and Systems, March 1988 
-9- 


A survey of the state-of-the-art and focused research in range systems

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server