328

The PED responds to the intensity r l = P(x, y 1’. The probability density functions (pdf) of rl can therefore be written as [ 11 1

P(rl/Hl)= [1/2(u2 +N)1 exp +gi)/2(u2 + N ) I I o

P(rl/Ho) = ( 1 / W exp [-r1/2Nl

u2 + N

where I o ( ) is the modified Bessel function. SNR z of the received signal is

z = 2cr2/N. (7)

A new random variable y is defined,

y = r1/u2

Hence

P(y/Ho) = - exp -yz/4 4

where G2 =gt!u2: A communication analogue of the receiver is shown in Fig. l(a). Lskelthood ratio can now be obtained with

A@) =P(y/Hl)/Pol/Ho)- (10)

Z (9!

At small values of G, making the approximation [ 121 that

logeIo(x) =x2/4 for x << 1 (1 1)

Y >< K 2 (12) *, Ho

where

and

Probability of error is therefore given by

Pr(e) = 4 [exp (-K;z/4) + 1.0 - Q(A, B ) ] (14)

where

A = G J X K Y

B = dK2 * ~ / ( 2 + Z ) (15)

and Q ( , ) is the Marcum Q function [ 71.

been evaluated when there is no speckle. In this case, To study the performance degradation, probability of error has also

H1:r(x,y)= l + N 1 +jN,

Ho: r (x , y ) = N1 + jN2 (16)

and

P(rl/Ho) = - exp -0 - r l / 2 N 1

2N (17)

The receiver structure is shown in Fig. l(b). Likelihood ratio can be obtained in terms of SNR

i = 1/N (18)

PROCEEDINGS OF THE IEEE, VOL. 67, NO. 2, FEBRUARY 1979

Making the approximation that at large SNR’s, the argument of IO being

log, = x. (20)

The probability of e m r is therefore

P,(e) = f [ez1’ + 10 - Q(& a 2 ) ] (2 1)

RESULTS AND DISCUSSION Probability of error has been evaluated for different SNR’s and

plotted in the Fig. 2. Probability of error in the absence of the speckle is also shown. It may be observed that speckle has a very degrading effect on the system. Even at 15-16 dB’s, the probability of error is rather high and its fall with SNR is too flat to be appreciated. While in the absence of the speckle, an acceptable value of probability of error is obtained at 15-16 dB’s and at above 20 dB’s, the value is of the order of 10-12 (not shown). Thus the performance of the system is very poor in the presence of speckle. Therefore, these days every effort has been directed at eliminating the speckle or reducing it wherever possiile. Even though the study undertaken does not take into account the detector noise, it nevertheless gives useful results in the analysis of speckled images

REFERENCES J. D. Rigden and E. I. Gordan, “The granularity of scattered opti- cal MASER light,” Proc. IRE, vol. 50, pp. 2367-2368, Nov.

B. M. Oliver, “Sparkling spots and random diffraction,” R o c . 1962.

IEEE,vol. 51, pp. 220-221, Jan. 1963.

Acoustical Holography, E. Camatini, Ed. New York: Plenum H. Kiemle, “Holographic information storage,” Optical and

A. Vanderlugt, “Holographic memories,” Optical Information Press, 1972, pp. 209-234.

Roceminp. Y. E. Nesterikhin e t al., Eds. New York: Plenum Press, 1976, pp. 347-368. C. W. Helstorm. Statistical Theorv of S i m l Detection. New York: Pergamon; 1968. J. W. Goodman, “Statistical properties of laser speckle patterns,” Loser Speckle and Rehted Phenomena, J . C. Damty, Ed. New York: Springer-Verlag, 1975, pp. 9-74. M. Schwartz et al., Communication Systems and Techniques. New York: McGraw-Hill, 1966, pp. 343-415. D. Slepian, “Linear least squares filtering of distorted images,”

I. L. Harris, Image evaluation and restoration,” JOSA, vol. 56, pp. 569-572, May 1966. J. W. Goodman, “Noise in coherent optical information pro- cessing,” Optical Information Processing, Y. E. Nesterikhin et al., Ms. New York: Plenum Press, 1976, pp. 85-104.

ceses. New York: McGraw-Hill, 1965, pp. 180-200. A. Papouli, Probability, Random Variables and Stochastic Pro-

H. L. Vantrees, Detection, Estimation and Modulation Theory, Part 1 . New York: Wiley, 1968, pp. 333-366.

_ . I

JOSA, VOI. 5:: pp. 918-922, July 1967.

The Latency Reduction of Bidirectional Magnetic Bubble Memories

CHULA NARANONG AND DAN HAMMERSTROM

Abstmct-Magnetic bubble memories have a significant advantage over rotating disk memories as they have no angular momentum. This char- acteristic theoretically allows them to remain in one position and then be started immediately in either direction. Resented rn the results of a simulation of a simple magnetic bubble

memory system, which demonstrate that an ordm of magnitude decrease in latency is po9aile by going to a bidirectional memory from a uni- directional memory.

I. INTRODUCTION There is currently a debate among computer designers as to the future

of bubble memories as a computer system component. Many feel that these devices will eventually be configured as electronic disks and con-

Manuscript received May 17,1978; revised lune 12, 1978.

Engineering, Footscray Institute of Technology, Footscray , Victoria, C. naRanong is with the Department of Electrical and Electronic

Australia. University, Ithaca, New York 14853.

D. Hammerstrom is with the School of Electrical Engineering, CornelJ H,

0018-9219/79/0200-0328$00.15 0 1979 IEEE

PROCEEDINGS OF THE IEEE, VOL. 67, NO. 2, FEBRUARY 1979

TABLE I SIMULATION RESULTS

. - I ’mg~m! ro t a1 Nllmber of Percentage of Unidirectional Bidirectional

!Icmor). References F a u l t i n g Rcfcrcnces S h i f t s ( k ) / F a u l t ?hirts[i)/Fault unil‘irectional k’Bi‘lirccti*’’’I . _- I

A - IN5 I C b l n t l l

-.

‘I iilJ I c 2 , 5 1 2 , 8 5 6 1 . 5 7 % 2 6 1 . 2 2 3 . 3 1 1 . 2

I3 - HAS 1 c S o r t 2 , 0 1 1 , 8 3 1 4.13“s 2 5 2 . 2 2 7 . 2 Y . 3

C - I I A S I C b h t r l x Ol’er3- 2 , 0 5 2 , 9 5 3 3 . 4 3 % 2 5 5 . 7 2 5 . 9 9 . 9 t 10115

D-RASIC P C . l l C h - mxrk 2 , 3 3 3 , 8 2 @

F - 13AS I C Eri l t i n g and Listing 94,96R 6 . 6 2 % 2 6 9 . 9 9 . 0 2 9 . 9

I ’ - ~ L \ C S O ?!oil jt o r 1 8 6 , 1 3 7 1 . 5 1 % 3 5 9 . 3 7 . 9 4 9 . 5

(:-‘.l.\CSO I P ~ l l C l l -

nl.lTk 1 5 4 , 5 8 3 I . 5?“, 3 7 2 . 3 7 . 6 4 8 . 7

4 .154 . 2 4 6 . 4 2 8 . 3 8 . 7

329

sequently replace intermediary futed-head rotating disks and drums. Their increased reliability, due to all solid state parts and simplicity, is an important advantage. There is, however, another advantage of these “electronic disks.” Magnetic bubble memories, unlike rotating disks , have no angular momentum. Therefore, they can be stopped and theoretically started in either direction. They can also be clocked at various frequencies; the shifting frequency being instantly increased or decreased. Such frequency variation has been used by Fuller and McGehearty [ 11 to reduce access latency for a CCD secondary memory system.

The purpose of this correspondence is to illustrate the magnitude of reduction in access latency that the bidirectional, stopability properties provide for a typical system. Other authors have examined bubble memories as system components in [2] and (31. Algorithms, which specifically take-advantage of the unique properties of these memories, are presented in 141. Bubbles have also been compared in a general sense to other types of sequential memories [ 51.

Because computer programs tend to have much more structure (spatial locality) than purely random referencing patterns, the above- mentioned characteristic of magnetic bubble memories makes possible significant reductions in latency over unidirectional, serial memories. In this correspondence the results of a simulation of a microprocessor based system with bidirectional and unidirectional magnetic bubble secondary memories are presented.

11. SIMULATION Magnetic bubble memories can be configured as secondary memory

between a fast semiconductor RAM and slower speed, moveable-head rotating disk memory. In this configuration bubble memories wiU be used as either a paging device for implementing virtual memory or as a cache memory for the disk system. Pages will be moved back and forth between primary memory and the magnetic bubble memory based on demand (assuming a demand paging algorithm is used). Due to the locality property of the program’s memory reference stream, references can in general be satisfied by pages residing in primary mem- ory. When a page which is not in primary memory is referenced, a fault occurs, and a request for the faulted page is made to the magnetic bub- ble memory system. It is assumed here that all of a program’s pages reside in primary or secondary memory during execution.

The page transport time T is the total time required to fetch a page from secondary memory and is defined for a serial or rotating memory

as

T = tE(k ) + tt where

t , the time required to move one page past the read head (the major loop transfer point for magnetic bubbles), which in a major-loop- minor-loop configuration is generally a single shift

k the access latency in pages, i.e., the waiting time until the de- sired page is ready to be read or written

t t the time to actually transfer the page into primary memory. In a magnetic bubble system, it would also include the time required to write the block back into the system on a read (assuming a major-loop-minor-loop configuration).

Since we are comparing identical secondary memory architectures, we on2y compare k for the two systems. By observing the values of k we arrive at a common basis for comparison of unidirectional and bidirec- tional systems. Incidentally, we are assuming both types of systems receive identical page requests or faults, and since we’re only looking at klrequest, it is unimportant whether such requests are READ’S or WRITE’S.

The simulation was of an Intel 8080 microprocessor system. The simulated memory consisted of a small RAM cache (8 pages, 32 bytes/ page) and a Texas Instruments (TMO101) magnetic bubble secondary memory. A demand paging algorithm was used with LRU replacement. Since k/fault varied only slightly when the number of pages in the cache and the page size were varied, we are only presenting data for a typical cache size and page size. The bubble memories use a major loopminor loop organization. Each device has 144 minor loops avail- able, and each minor loop has 641 shift positions. The system, as simulated, used eight bubble devices to create a byte-parallel memory, Although the bubble devices have 144 minor loops, only 128 were actually used. This means that four 32 byte pages are available in the minor loops at any one time; giving us a capacity of approximately 80K bytes although only 64K bytes are addressable. This organization may not be desirable in a real system, but it did allow for a simpler simulation program. The memory can be thought of as a large page-oriented shift register where each shift brings four new pages to the top of the 128 X 8 = 1024 minor loops. The pages are then transferred to the major loops and the appropriate page is shifted serially out of the memory.

330 PROCEEDINGS OF THE IEEE, VOL. 67, NO. 2, FEBRUARY 1979

Although the minor loops can theoretically be shifted in either direc- tion, once a group of pages is transferred to the major loop, shifting must be in one direction for the bubble detectors to operate properly.

For simulation purposes only READ references (page fetching) to the bubble memory were considered. However, we M y believe that were pages also written back, the bidirectional system would perform even better relative to the unidirectional system. In other words, the klfault of unidirectional to that of bidirectional would be even larger in a real environment. The entire simulator was written in MACRO-11 and run on a PDP-11/40. The simulator used various types of 8080 code. Tfie table lists some of the programs run by the simulator and results for each.

Sice large compute bound 8080 programs were difficult to find, we decided to load the IMSAI BASIC (roughly 8K bytes) interpreter into our simulator and execute a few BASIC programs instead. Though the results for a BASIC execution might be different than for a compiled program, e.g., PL/M, we feel that they are still realistic. If anything, interpreters during function execution probably exhibit less spatial locality than most progragx, leading to more random secondary mem- ory referencing patterns and thus reducing the unidirectional/bidirec- tional ratio.

The first fwe programs were written in BASIC and interpreted by the IMSAI interpreter. Program A created a table using square root and trigonometric functions. Program B was a simple bubble sort Program C consisted of a few matrix operations. Program D was a standard BASIC benchmark program cited by several microprocessor journals. Program E consisted of some on-line editing and Listing in BASIC. Program F was nonBASIC and was an 8080 monitor doing some mem- ory moves and dumps. Program G was a benchmark program written in 8080 assembly code which performs avariety of miscellaneous functions.

111. RESULTS AND CONCLUSIONS The results given in the Table I are persuasive. Programs A through D

show about a factor of 10 improvement of the bidirectional over the unidirectional system. Programs E and F, which perform simpler opera- tions show an even greater improvement. Program G also shows a con- siderable improvement

Due to the spatial locality of secondary memory referencing, bidirec- tional magnetic bubble memories would be far superior to unidirectional. It should be emphasized that we are not recommending this particular system as a superior memory architecture. Consequently, we have done no costlperformance analysis. We have merely used i t as a vehicle to study the behavior of the magnetic bubble memory. Also, one should be careful in extrapolating our results to large complex multiprogram- med systems which use multilevel memory hiemhics. Though with multiprogramming and proper allocation, bidirectional systems may perform even better. Nevertheless, the bidirectional capability of mag- netic bubble memories does make them much more competitive, espe- cially when compared to CCD memories, which shift approximately 20 times faster. Of course C C D ’ s can also, theoretically, be bidirectional, but because of refresh problems such a capability would be of marginal value.

In summary, the purpose of this correspondence was to demonstrate the rather high difference in shift latency that is possible between uni- directional and bidirectional magnetic bubble memories. This ratio was typically an order of magnitude and often more. We feel that this is an important consideration for memory device and system designers. It is a rare thing indeed in the field of computer engineering that over an order of magnitude improvement in performance can be had for so little cost.

REFERENCES

[ l ] S. H. Fuller and P. F. McGehearty, “Minimizing latency in CCD memories,”IEEE Trans. Compuf., vvl. C-27, no. 3, pp. 252-256,

[2] D. P. Bhandarkar, “On the,,wformance of magnetic bubble mem- Mar. 1978.

ories m computer systems, EEE f i n s . Compuf., vol. C-24, no.

[ 31 D. P. Bhandarkar and J. E. Julinssen, “Tutorial: Computer system advantages of magnetic bubble memories,” Computer, vol. 8 , no.

[4] H.’S. Stone, “The organization of electronic cyclic memories,”

[ 5 1 R. R. Martin and H. D. Frankel, “Electronic disks in the 19803,’’ Compufer,vol. 9 no. 3, pp. 45-50,Mar. 1976.

Compufer,wl. 8 , no. 2, pp. 24-30, Feb. 1975.

1 1 , ~ ~ . 1125-1129,Nov. 1975.

11 Pp. 35-40, NOV. 1975.

A Uniform Power Spectral Density Jamming Signal

F. CASSARA, E. N T H , AND D. GETTYS

Abstmct-In this work a technique is descnied for generating a jam- ming signal with a continuous uniform-power-spectral density band- limited over any desired frequency band. Experimental results demon- strating the technique are presented.

I. INTRODUCTION It is often useful in electronic countermeasures to transmit high-

power noise over some prescribed band of frequencies in an attempt to interfere with transmissions from an unfriendly source. Since we do not know with any certitude the frequencies at which the source transmits and/or receives, it is desirable to use a high-power signal with a continuous uniform-power-spectral density bandlimited over some frequency band for the noise jammer. In this work a technique is described for generating such a signal with flexibility in designing for its center frequency and bandwidth.

The technique employed utilizes Woodward’s Theorem [ 11 which states that the spectrum of an FM signal with large modulation index Ca,, 2 10) takes on the same shape as the probability density func- tion (PDF) of the amplitude of the modulating waveform.

A block diagram of the system used to generate the noise jammer is shown in Fig. 1. A nonlinear network is used to transform Gaussian noise into a stochastic signal whose amplitude has a uniform PDF. The resultant signal is then used to frequency modulate a carrier with large 8. The spectrum of the transmitted signal will ,then be uniform and continuous centered around the carrier frequency with bandwidth (BW) approximately equal to twice the peak-frequency deviation (Carson’s Rule). The power contained in the transmitted s i g n a l can be made large by using a high-power FM modulator or by using efficient nonlinear RF power amplifers following the modulator.

11. NONLINEAR NETWORK The nonlinear network required in Fig. 1 is readily determined using

the techniques relating to transformation of a random variable. If x (see Fig. 1) is assumed to be a zero-memstationaryCaussian random process with variance u i , and we desire y to be a zeromean- uniformly distributed process over the normalized interval [ -1/2, 1/21, then the transfer function of the nonlinear network can be shown [ 21 to take on the form

\“x J where the error function

is well tabulated [ 31 . Although a broad-band nonlinear diode waveshaping network could

be designed with transfer function proportional to Erf(x/u,), for sim- plicity the constant current biased bipolar junction transistor differen- tial pair configuration [4] was employed.

For such a network the transfer characteristic relating the output col- lector voltage y and the applied input differential base s i g n a l x is given by 141

where k denotes Boltzmann’s constant, q is the charge of an electron, kT/q = 26 mV at room temperature (T = 300°K),Zk isthemagnitude of

Manuscript received August 4 , 1978;revised October 4, 1978. Thii work was supported in part by NSF under Grant ENG 76 24468

and ARO under Grant DAAG 29 77 G 0232 made to the Polytechnic Institute of New York.

NY 11735. F. Cassara is with Polytechnic Institute of New York, Farmingdale.

E. Muth and D. Gettys, were with Polytechnic Institute of New York

07733. Farmingdale, NY. They are now with Bell Laboratories, Holmdel, NJ

0018-9219/79/0200-0330$00.75 0 1979 IEEE