Optimum Noise Figure Specification

Transcription

1 Chameleonic Radio Technical Memo No. 20 Optimum Noise Figure Specification S.M. Shajedul Hasan and S.W. Ellingson April 25, 2007 Bradley Dept. of Electrical & Computer Engineering Virginia Polytechnic Institute & State University Blacksburg, VA 24061

2 Optimum Noise Figure Specification S.M. Shajedul Hasan and S.W. Ellingson Abstract: The sensitivity of receivers operating at frequencies below 1 GHz can easily be limited by external sources of noise. Presently there is no simple standard way to take this into account when specifying the noise figure of receivers which must tune over a large fraction of this frequency range. Here, we present specification for optimal noise figure which serves this purpose and should be especially useful in the design of the next generation of directconversion receivers for software-defined and cognitive radio systems. Introduction: Receivers that are required to cover large tuning ranges, or which are required to cover multiple bands spanning large fractional bandwidth, traditionally utilize a divide and conquer strategy in which the tuning range is divided into smaller sections which are processed independently. The recent emergence of high-performance direct conversion receivers in deep-submicron CMOS, combined with advances that facilitate very-broadband front ends (e.g., using inherently wideband techniques or reconfigurability such as that provided by micro-electro mechanical systems (MEMS) technology) have sparked interest in the possibility of simplified receiver architectures which permit the entire tuning range to be processed using a single common signal path; see e.g. [1]. Setting reasonable specifications for sensitivity and linearity for such receivers is a challenge not only because these quantities must typically be traded off against each other 1

3 [2], but also because the degree to which external noise contributes to the noise figure can vary considerably over the tuning range. This is especially true at frequencies below 1 GHz, where external noise can in certain conditions be the dominant contribution. In this letter, we describe a simple method for specifying the noise figure of a receiver that takes these considerations into account, and thus is useful especially for the new generation of single path wideband receivers which are often seen as enabling technology for software-defined and cognitive radio applications [3]. We express these specifications in terms of noise temperature, which is especially convenient for work involving interference temperature analysis [4] and is easily converted into noise figure. Characterization of Environmental Noise: The external noise delivered to the input of a receiver includes an irreducible natural (celestial) contribution, plus additional noise resulting from human activity. These contributions have been measured and characterized in considerable detail, and are conveniently described in [5]. Both natural and man-made noise can be accurately described in terms of Gaussian statistics, in terms of a mean noise temperature T, following a power law b af where f is the frequency in Hz, 2 and a variance with respect to location σ. The total noise temperature is the linear sum of the celestial noise and the applicable category of man-made noise. The values of a and b have been summarized in Table 1, derived from data provided in [5]. Furthermore, [5] describes the variation in noise power as a function of location in terms of decile variations D u and D l ; i.e. the values exceeded percent and 90 percent of the time. Assuming Gaussian 2

4 statistics (consistent with the observation that D u and D l are found in [5] to be symmetric about the mean), it is straightforward to derive σ from these values; these are reported in Table 1. Note two characterizations are provided in [5] for Business environments, one from 0.3 to 250 MHz and another one is from 200 to 900 MHz. These are reconciled by modifying these frequency ranges to 0.3 to 130 MHz and 130 to 900 MHz respectively. Also, we found the characterization of celestial noise in [5] to be inaccurate. Celestial noise is the sum of the radiation from the ubiquitous Galactic synchrotron radiation, plus a 2.7 K contribution from the cosmic microwave background (CMB), which at low frequencies is typically insignificant in comparison. Synchrotron noise is calculated using the method described in the appendix of [7], neglecting the relatively weak extragalactic term. Measurements validating this method are reported in [6]. Noise Temperature Specification: For specification purposes, one should choose the applicable category of man-made noise, determine the associated noise temperature, and subtract from this some margin n representing the confidence with which the designer wishes to be sure this value is not exceeded. Under the assumption that the statistics are Gaussian, n is conveniently described in units σ ; i.e., the square root of the variance. Following an analysis described in detail in [7], the noise power spectral density due to the external noise at the output of a system consisting of an antenna and an amplifier, referenced to the input of the amplifier, Sext 2 ηkt 1 = Γ 3

5 where η is the efficiency associated with ground loss (significantly <1 only for f < 0 MHz), k is Boltzmann's constant ( 1.38 J/K), and Γ is the voltage reflection coefficient at the antenna terminals looking into the amplifier. The optimal amplifier temperature T amp is that which is sufficiently small to make S ext dominant over internally generated noise. If we express this in terms of the ratio γ = S /( kt ), then this is achieved by γ on the ext amp order of. However, smaller γ perhaps even γ <1 might be appropriate depending on the application and the need to trade off sensitivity for improved linearity or reduced cost. The corresponding noise factor is computed from noise temperature using F opt Topt = + 1 T 0 where T opt S kγ ext = is the optimal value of amp T. Example and Results: To illustrate the methodology we present an example here for the frequency ranges of 3 MHz to 3 GHz. Figure 1 shows the noise figure log ( F opt ) for γ = and n = 2σ in various environments. The specification shown in Figure 1 is the linear sum of celestial noise temperature plus that of the most relevant man-made noise category, minus the specified margin. Concluding remarks: It should be noted that the specification described here does not take into account radio frequency interference and impulsive noise; these are separate considerations. Also, values in Table 1 are based on the 4

6 measurements reported in [5], which may not be universally valid or representative of new sources of man-made noise. Corrective measures might include increasing n, making site-specific measurements and extracting from them applicable values of a and b, or using noise measurements reported by others, such as Rogers et. al. (2005) [4]. 5

7 References 1 Bagheri, R. et al.: 'Software-Defined Radio Receiver: Dream to Reality', IEEE Communications Magazine, Aug. 2006, pp Rohde, U. and Whitaker, J.: 'Communications Receivers: DSP, Software Radios, and Design' (McGraw-Hill, 2000). 3 Reed, J.H.: 'Software Radio: A Modern Approach to Radio Engineering' (Prentice Hall, 2002). 4 Rogers, A. E. E. et al.: 'Interference temperature measurements from 70 to 1500 MHz in suburban and rural environments of the Northeast', Proc. IEEE DySPAN 2005, Bultimore, MD, Nov. 2005, pp ITU-R: Radio Noise, P.372-8, Ellingson, S.W., Simonetti, J.H., and Patterson, C.D.: 'Design and Evaluation of an Active Antenna for a MHz Radio Telescope Array', IEEE Transactions on Antennas and Propagation, Mar. 2007, vol. 55, no. 3, pp Ellingson, S.W.: 'Antennas for the Next Generation of Low-Frequency Radio Telescopes, IEEE Transactions on Antennas and Propagation, Aug. 2005, vol. 53, no. 8, pp Authors affiliations: S.M. Shajedul Hasan and S.W. Ellingson (Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, 432 Durham Hall (0350), Blacksburg, VA 24061, USA.) address of corresponding author: hasan@vt.edu 6

8 Figure captions: 2 Fig. 1 Noise figure specification for γ =, n = 2σ, assuming η 1 Γ = 1 (i.e., perfectly matched antenna with no ground loss). Expected value of Galactic+CMB" noise is shown for comparison. 7

9 Figure 1 8

10 Table captions: Table 1 Parameters for mean noise temperature T = af b [K]. 9

11 Table 1 Frequency (MHz) Quiet Rural Rural Residential Business A/B Celestial a b a b a b a b a b a b σ 5.3 db db 4.5 db 6.6 db Add 2.7 K to account for CMB. 2 Decile values not available from [5], using D = D = 6.8 db as for Rural. 3 Decile values not available from [5], using Dl = Du = 8.4 db as for Business B. 4 Varies over about 2 db depending on time of day; see [6]. l u