Noise Power Density Research Articles

On Signal and Noise Level Estimation in a Coherent PCM Channel

Joint maximum likelihood estimators are presented for the signal amplitude and noise power density in a coherent PCM channel with white Gaussian noise and a correlation receiver. The estimates are based upon the correlation coefficient outputs of the receiver. From these estimators, an estimator for the quantity (received signal energy)/bit/,(noise power)/(unit bandwidth) upon which the error probabilities depend, is derived. This estimator is shown to be useful as 1) a point estimator for the signal-to-noise ratio for the higher values of this ratio (about 4 dB or greater), and 2) an easily calculated statistic upon which to base data acceptance or rejection criteria. The acceptance or rejection levels are obtained by the use of confidence interval curves in conjunction with word error probability data.

Atmospheric-Noise FSK Error Probabilities for an Envelope-Detection Receiver

A useful expression for FSK error probability with atmospheric noise interference, equal to one half the probability that the noise envelope exceeds the signal envelope, previously derived for a bandpass-filter discriminator FSK receiver applies as well to a matched-filter envelope-detection receiver. This error probability for Gaussian noise interference is equivalent to a more common expression defined in terms of signal energy and noise power density.

Signal-Power Comparison of Coded and Tone Ranging Systems for Spacecraft Vehicles

This paper describes the operation of two spaceranging systems. It evaluates and compares some fundamental capabilities of the two systems described, based upon performance as a function of the ratio of received ranging signal power to noise power density. The characteristics compared are 1) time required for signal acquisition, 2) range measurement accuracy, and 3) maximum range capability. Although no conclusions are drawn as to the preference of one generic type over the other, the results indicate that the described coded system provides greater accuracy and some acquisition advantage compared with the described tone system. Both systems have approximately equivalent threshold capabilities.

Factors influencing the design and performance of mars entry vehicles

reference area planetary miss distance, rp (1 + 2/i/rpFco), in Fig. 2, ft (or km) receiver bandwidth [Eq. (1) and Fig. 4], cps drag coefficient lift curve slope pitch damping coefficient diameter, ft receiver noise figure [Eq. (1)] frequency, cps total antenna gain gravitational acceleration; gc at Mars surface = 12.3 ft/sec atmosphere scale height, ft (or km) noise power density, w-sec/cycle atmospheric losses (Earth + Mars, if direct link) total circuit loss free space loss reference length, ft molecular weight mass, slug transmitted power, w pressure; psurf = surface pressure on Mars, psf (or mb, if stated) stagnation pressure, psf integrated heat load during entry, Btu/ft heat flux; Qc = convective flux at stagnation point; Qr = radiative flux, Btu/ft-sec q R Re RX Rsnt rp S

Multiple Access to a Hard-Limiting Communication-Satellite Repeater

This paper analyzes the communication capability of a hard-limiting satellite repeater when spread-spectrum signals are used for asynchronous access multiplexing. It derives formal results which indicate the most suitable system bandwidth and the resulting maximum number of simultaneous users as a function of the ratio of the received signal power (over the entire system bandwidth) from the satellite to the available noise power density at the ground station receiver. Equally important, the paper sets forth the assumptions and approximations necessary to achieve the formal results and examines their weaknesses.

Signal detection under noise interference in a game situation

With application to radar and data transmission, a game situation is studied where one player selects a suitable receiving filter, and the other a function describing the noise power density under restriction of a fixed total amount of power. The payoff function is a signal to noise ratio. The information the players have about each others' choice defines two extreme situations of practical interest. The fundamental relation of game theory holds for pure strategies.

Performance of Error-Correcting Codes

Binary decoding of relatively short codes corrupted by Gaussian noise or pulse interference has been considered in applications for which the minimum useful information block length is unity, equal to the information bit capacity of a code, or equal to an integral multiple of the information capacity of a code. The following results pertain to applications which are further characterized by the performance criterion of minimizing error rate and transmitter power, with only minor restrictions on transmission bandwidth and none on channel efficiency (no credit given for error detection): [1] The word error probability for any group error-correcting code is never exceeded by its corresponding bit error probability (for either Gaussian noise or pulse interference). [2] Relatively short codes (10 to 50 information bits) of moderate redundancy (40 to 50 per cent) are available which can reduce bit error rates by factors of 10 to 400, or equivalently, permit 1 to 3 db reductions in transmitter power, when the coded system bit error rate is 10-6(Gaussian noise). [3] These same codes can alternatively reduce word error rates by factors of 10 to 104, or equivalently, permit reductions of 1.5 to 3.7 db in transmitter power, for average word error rates corresponding to values of the quantity E/N_{o} (signal energy per information bit/Gaussian noise power density) in the neighborhood of 8 db for the coded systems. [4] Under worst-case pulse interference, these codes permit 4 to 7 db reductions in transmitter power for average word error rates less than 20 per cent. (Considerably greater improvements result for the pulse interference expected.) [5] All of these codes are easily encoded and decoded.

A method of digital signalling in the presence of additive Gaussian noise

This paper considers the basic problem of transmitting digital information through a noisy channel with minimum probability of error in finite time. The transmitted signals are average-power limited, and the noise is assumed to be additive Gaussian with a power spectrum which may be nonwhite. A theory of so-called efficient codes (minimax, equal separation, and nearly equal separation) is developed. Efficient codes are formed from weighted sums of eigenfunctions generated by an integral equation with its kernel corresponding to the inverse Fourier transform of the Gaussian noise power spectrum. In addition, the theory of equidistant and nearly equidistant codes [1] is extended to the case of nonwhite Gaussian noise. It is shown that efficient codes perform better than equidistant codes if the noise is nonwhite; i.e., properly chosen waveforms are more efficient than binary coding. Performance results are given for several different codes when the interference is white Gaussian noise and when the noise power density increases with increasing frequency. The detection scheme used does not require estimation of the signal or the noise levels at the receiver and is thus independent of fading.

Aural Detection of a Gated Sinusoid as a Function of its Duration

Using the two-interval forced-choice procedure, we conducted detection tests with gated sinusoids of 1000 cps in Gaussian-process noise. The signals varied in duration from 63 msec to 10 sec. We employed four different schedules or patterns of the time intervals within each trial. Duration was a highly significant variable. The temporal pattern was not. The results confirm and extend the findings of Hamilton and of Green, Birdsall, and Tanner [J. Acoust. Soc. Am. 29, 506–511 and 523–531 (1957)]. The ratio of signal energy to noise power density required for 75% correct detection falls from about 12.5 db at 5.0 msec to about 9.5 db at 20 msec (Green), is then constant at 9.5 db out to 160 reset, and then rises to about 13.5 db at 1.0 sec and 24 db at 10 sec. The question, whether or not these results indicate that the auditory parameters are variable and adjust themselves to the task at hand, will be discussed. [This research was supported in part under Air Force Contracts AF 18(600)-1219 and AF 19(604)-2051, monitored by the Operational Applications Laboratory, Air Force Cambridge Research Center, ARDC.]

Detection of Gated Sinusoids in White Noise as a Function of Frequency

Aural detection of 0.1-sec segments of pure tone in white noise was measured at sixteen frequencies, 250, 500, 750,⋯4000 cps, with a two-interval, forced-choice procedure. The measure of the listeners' performance in detecting the signals was the ratio (E/No) of the signal energy to the noise power density that was required for 75% correct response. The results of this experiment with fixed-duration segments of tone are compared with those of other studies which employed tones of indefinite or extended duration. The detection of a compound signal synthesized by adding together the sixteen harmonics of 250 cps was also measured. The individual harmonics were so adjusted in amplitude as to be equally detectable. The results are related to a model of summation over frequency. [This research was done in part under a National Science Foundation Fellowship and in part under Air Force Contract AF 18(600)-1219.]

A NEW TECHNIQUE FOR THE STUDY OF SCATTER PROPAGATION IN THE TROPOSPHERE

The power spectrum of the fluctuations in received signal strength on a near-optical U.H.F. circuit has been measured. The sidebands associated with these fluctuations can overlap the information-carrying sidebands of a communication system. When this happens, these sidebands must be taken into account in determining the signal-to-noise ratio of the system. In other words, the fluctuations then have the characteristics of noise, and therefore they are called propagation noise in the present paper. Experiments at a carrier frequency of 500 Mc. have shown that the propagation noise power density usually varies with sideband frequency ƒ (measured from the carrier) as 1/ƒ2, for f in the range 0.1 to 10 c.p.s. Departures from this law have been observed in the regions near 0.1 c.p.s. and 10 c.p.s. The measurement of the power spectrum directly offers several advantages over the conventional signal strength recording method, and these are discussed herein.

Current Noise in Thermistor Bolometer Flakes

The characteristics of the additional electrical noise generated by iron oxide thermistor bolometer flakes due to direct current passing through the units is investigated. It is found that the noise is similar to the current noise observed in other semiconductors. The current noise power density is observed to depend inversely upon frequency, to be approximately proportional to the direct current, and to be independent of temperature. It is indicated that the major source of the noise is at the electrodes which make electrical contact to the semiconductor. Electrodes produced by evaporated gold applied through a potential difference are found to yield relatively low noise flakes.

A Theory of Contact Noise in Semiconductors

A theory of contact noise is described in which the low-frequency noise is attributed to the random movement of adsorbed ions on the surface of a semiconductor from which an electron current is being drawn. Emission of electrons is assumed to take place only at localized patches on the surface and the adsorbed ions are assumed to give rise to a Schottky barrier layer, in which the potential maximum is linearly related to the concentration of ions. Diffusion of the ions over the surface gives rise to random fluctuations in the concentration of ions in a patch which results in random fluctuations in the height of the potential barrier and the emission current. It is shown that for a circular patch the spectral power density of the noise current varies with mean current J0 and frequency f as j02fx over a small range of frequency and that x varies monotonically from -0.75 at the lowest frequencies to -1.125 at the highest frequencies. It is also shown that for a long thin rectangular patch in index x varies monotonically from -0.5 to -1.5 as the frequency is increased from zero. The dependence of the noise power density on temperature is also discussed.