Measurement and Characterization

Here we focus on the practical matters of how observation of transmitted radar data, particularly observation of inter-pulse timings, may be used to establish key facts about the system under observation.   

 I.          Pulse Quantization 

II.         Signal Formation

III.        Pulse Timing Behavior

IV.       Beamwidth Measurement and Antenna Gain

Quantization and Characterization[1]

I.  Pulse Quantization

     The mechanisms used for measurement of transmitted radio frequency have undergone enormous change since Guglielmo Marconi deployed his first spark-gap-based ship-to-ship radio transmitters. Presumably the construction of his third transceiver brought the realization that 'selectivity' - the capability to adapt operating wavelength, e.g. for interference-mitigation - would be an important characteristic of the future. Selectivity quickly became a significant issue in the MNR domain, too: the wide-spread adoption of the magnetron as the RF power source of choice brought both benefits and consequences. In particular, the magnetron proved relatively easy, and thus inexpensive, to manufacture; its most significant drawback was, and continues to be instability: from a 'cold start', the typical magnetron may exhibit significant drift in its operating frequency - perhaps as much as 0.1% of the nominal center RF.

         For the modern radar receiver, this instability is no great challenge: sampling techniques allow it to obtain pulse-by-pulse RF measurements, from which it synthesizes an offset frequency to be used in translating the microwave input downward, to the VHF band - nowadays, almost universally, centered on 60 MHz. Because the synthesizer tracks the transmitter, the down-conversion results in an RF-independent intermediate frequency, largely eliminating the consequences of transmitter variability. A much greater challenge, not for the receiver but for target-detection processes, lies in population density: the mercantile fleet of the world comprises approximately 30,000 ocean-going merchant vessels with a cargo capacity of 1000 tons or more, the vast majority plying a relatively small number of sea-routes; and on any one day, there may be as many as 170 of these larger ocean-going vessels berthed in major US ports[2] . These figures alone are daunting, and they tell nothing of the countless fishing- , service- and recreational-craft that abound in US coastal waters, a very substantial proportion of which may be using their radars whenever they prepare for sea.  Population density and, more especially, pulse density may represent significant challenges to the radar designer, who may expend considerable effort on mitigation techniques - if only to avoid product-liability issues! With a detached perspective, it is easy to see that bandwidth constraints imposed by the ITU may be less than universally welcomed, since they force a large population to co-exist in a small spectral space[3]. This crowding is exacerbated by IMO regulations defining range resolution; these drive the durations of the transmitted pulse, which in turn affects transmitter and receiver bandwidths: to satisfy the IMO, a radar receiver may require an operating bandwidth of 15-20 MHz, representing 25-30% of the overall MNR band. Operating overlaps and mutual interference are inevitable.

               If modern radar processing is challenged by population density issues, even when the RF used by the transmitter is known, then the challenge for the general-purpose surveillance receiver is enormous: it seeks to measure the RF of every received pulse, without any prior knowledge and throughout its targets' potential range of operation, and to do so with sufficient accuracy that its measurement process does not introduce apparent instability. Perhaps in the early days of surveillance, it may have been feasible to measure the RF of a radar system by manual tuning; it has never been feasible to measure continuously the RF of individual magnetron-generated pulses in this way, even with only one radar system active. Fortunately, the emergence of digital techniques (in particular, the IFM device) has relieved the surveillance-system operator of this Herculean labor; and nowadays, it is perfectly feasible to sustain RF measurement in pulse densities of 500,000 pulses per second. 

            To understand the concept of the Instantaneous Frequency-Measurement device, it is necessary only to consider the relationship between sine and cosine angles. Plotted linearly throughout the 360° rotation of a circle, they depict two sinusoidal magnitude traces that vary with angle, with values ranging from 1.0 to -1.0 and back again. There are two invaluable characteristics to note from this representation:

         first, the phase of the sine plot lags that of the cosine plot by exactly 90° - that is, the magnitude of an angle's cosine is the same magnitude as the sine of the angle minus 90°; and

         that the periodicity of the wave can be determined by measuring the actual distance from any point on the sine curve to the equivalent point on the cosine curve.      

            Now, consider this representation as an input electromagnetic wave with a known wavelength, divided into two parts of equal magnitude, one of which is delayed by a period that is equal to a quarter of the anticipated wavelength, i.e. 90 degrees. If the magnitude of the delayed channel is expressed as a cosine value, and the other as a sine value, then, in a perfect world, there should be no difference in magnitude. There are undoubtedly many other ways to get nothing from an electrical circuit, but this particular method has a distinct purpose: the zero-difference arises because of the 90-degree phase delay; more precisely, it arises because the physical time-delay represents 90 degrees, for a specific wavelength. For any other wavelength, there will be a real, non-zero difference that is related to the difference between the wavelength of the input signal and the delay path's length. In theory, it's necessary only to filter the input band so that no ambiguities may arise, and to convert the magnitude to a value that corresponds to the illuminating pulse's RF. In reality, of course, the IFM device is substantially more complex than this conceptual description conveys, even in its most basic form.            

            Early IFM system designs fared well with pulsed waveforms but, at worst, might be entirely desensitized in the presence of continuous signals such as from satellite ground terminals; pulse-on-pulse situations, where two or more radars' pulses illuminated the surveillance receiver in the same spectral space, might occasionally result in erroneous quantization;  RF resolution, or quantization, was generally quite coarse; and the shadow time, the interval between successive measurements, could be substantially longer than individual pulses, to name but a few of the issues of the day. However, continual development, over decades, has resulted in a very different situation: the modern IFM system, such as in the Ukrainian Kolchuga, is a precision measurement device capable of characterizing pulses' RF to within 400 KHz, over an extremely wide range; and it is not at all unusual to find systems advertised with the capability to quantize time of arrival, pulse duration and amplitude with resolutions and fidelities that are seemingly unmatched by the MNR designer.  The modern IFM system, or its counterpart, the Digital Frequency Discriminator (DFD), represents the core of modern pulsed-radar surveillance systems, and any understanding of the maritime domain requires some basic grasp of its performance. A good sense of technical capability at any time may be gleaned from the product advertising materials of systems manufacturers such as Rockwell Collins. Nowadays, a typical IFM or equivalent system is capable of quantizing:        

         Radio Frequency in the range 2-18 GHz, to approximately 0.4 MHz;

       Pulse Duration in the range 50 nS to 200 mS, with a resolution of about 10 nS;

       Pulse amplitude over an 80 dB instantaneous dynamic range, with a resolution of around 0.5 dB;

     Time of arrival (TOA,  the time that the pulse is detected), with a resolution of 5 nS,

at a sustained rate of at least 1 million reports per second. These systems may also report other facets, such as the presence of intra-pulse modulation and various aspects of the processing. Familiarity with the surveillance system is important in avoiding misrepresentation during processing of the resultant data.


II. Signal Formation

            The process of associating individual pulses from one radar source among many is often proprietary and, in some circumstances, may even be deemed by national authorities to be classified. The intent here is to avoid such sensitivities, by dealing only in generalities except where specifics are either published or readily deducible. In general, signal formation, also known as de-interleaving, takes place in stages:

  • First, it is usual to attempt clustering of pulses that are adjacent in both time and parameter space. Whatever approach is used, the desired outcome is a series of clusters, each representing time-adjacent pulses from a single radar system as it illuminates the surveillance system. Optimally, all pulses will be associated unambiguously and correctly with their "siblings" - an extremely demanding goal. A more reasonable goal is to assure that all radars are detected, with minimal erroneous associations; with MNR systems, this may be attainable in all but the very densest pulse environments. Methods may range from simple binning, to k-means and Mahalanobis distance algorithms, and even the application of so-called "fuzzy logic." These are beyond the scope of this short text.
    • Cluster formation, known also by names such as burst-formation, scan-formation and lobe-formation, is followed by characterization and validation. Characterization will derive higher-order statistics about the localized cluster, for the set's RF and PD; these statistics will almost certainly include sequential behavioral characteristics, such as inter-pulse timings, and may include amplitude-envelope behavior. In the latter context, the typical MNR - which scans its antenna mechanically - is likely to exhibit a pulse-to-pulse amplitude behavior that correlates approximately to a |sin(X)/(X)| behavior, as illustrated below; this behavior may be used in any validation processes that follow cluster formation. Cluster width, or lobe width, may also be characterized, by determining how much of the central lobe exceeds a half-power threshold.
      • Individual clusters, once characterized, may be subjected to post-detection processing which tests the validity of "set membership." In the MNR domain, this may be as simple as testing whether a consistent duty cycle is maintained, or whether apparent inter-pulse timings are "consistent." Some systems may take the post-detection processing of clusters a stage further, exploiting the derived statistics to assess whether the cluster might be extended by using unassociated pulses; this is rarely of value in the MNR domain.
        • As successive clusters are formed, they are subjected to another level of association, sometimes called scan-linking, burst-linking, or lobe-linking. The aim of this stage is to form higher-level representations from multiple illuminations by individual radars, from which yet further information may be distilled. The techniques used are likely to be similar in form to those used in cluster formation, exploiting the higher-order statistics derived from cluster formation and validation.   Yet more statistics, such as cluster-to-cluster timings that equate to the radar's rotational periodicity and that may lead to beamwidth approximations, are likely to be derived; and the cluster-level statistics will certainly be refined.
          • By this point, some attempt will be made to identify the radar system unambiguously, by comparison with parametric and behavioral databases. It is also likely, in a surveillance system, that some form of situational-awareness action will occur, e.g. by tabulating a description or plotting a symbol; and that some form of data-logging activity will be implemented.

                      The preceding description is intentionally superficial in its attempt to synthesize the processes underlying an extensive array of systems, systems that are used routinely for much more than simply maritime domain awareness; the intent is solely to encapsulate common processes that are predictable for any such system. There are, however, two noteworthy wrinkles in these processes, both related to the geometry between pulse source and surveillance system:

                    In some surveillance systems, a complex antenna system and multiple receiver channels may be used to compute the angle-of-arrival of individual pulses. The availability of angle-of-arrival adds a powerful discriminant to associative processing, at all stages of signal formation, and has an especially attractive military attribute: since the discriminant is independent of any radar characteristic, it may be used to associate pulses that might otherwise be discounted, thereby potentially negating attempts at disguise. Such systems, which may use combinations of phase and amplitude comparison between multiple receiver channels, are typically expensive and unlikely to be in routine use for maritime domain awareness.  

                    An extension of this phase-comparison process involves an architecture comprising multiple, dispersed receivers from which a long-baseline interferometer is synthesized. The techniques involved in this have been exploited in surveillance systems since at least the late 1950s, when Czechoslovakian scientist Vlastimil Pech published his work on "the chronometric hyperbolic principle." This principle, which was employed by the erstwhile Warsaw Treaty Organization in its Ramona and Tamara electronic surveillance complexes, involves cluster formation much as described above, but at multiple locations; individual cluster descriptions are forwarded from a surveillance station to a correlating station, where they are compared with descriptions from other stations. The propagation delays from source to sensors (referred to in some literature as TDOA, time-difference-of-arrival) might be used to define a hyperbolic line-of-position for the radar transmitter; and, by extension, they might be used to negate disguise, in much the same way as in angle-of-arrival systems. A prototype system introduced into Czech military service in the mid-1960s, the PRP-1 Correlation Processor, is the forebear of modern equivalents such as the Ukrainian Kolchuga[4].    



           III. Pulse Timing Behavior

                      Beyond any doubt, the most significant characterizations derived from signal formation relate to pulse sequencing, specifically to the intervals between consecutive pulses, usually referred to as the Pulse Repetition Interval or PRI. As noted elsewhere, timing is everything in radar processing, and the MNR design may make use of timing signals at numerous points in the overall architecture, from the triggering of its magnetron to the formation of the IMO-mandated range-rings on the radar's PPI display.  Whenever these are used, timing sources present an opportunity for greater understanding of the design. For the observer, their use is most likely, if at all, to reveal itself in the sequencing of pulses in the transmission cycle. Thus, from an observer perspective, MNRs may be divided into two classes: those whose timing source patently influences the observed waveform; and those in which a timing source is not discernible. For the purposes of this description, a third "category" is ignored: those in which the possible existence of a timing source is screened by insufficient fidelity in the surveillance system, such as may occur when an excessively narrow bandwidth distorts pulse shape and hence quantization.

                      Both classes of MNR, as defined for the purpose of description here, may exhibit similar pulse-sequencing behaviors, behaviors that are usually described as constant, or stagger, or jitter. What distinguishes them is not the basic behavior, but the degree of variation that the individual PRI elements [5] exhibit. It is generally safe to assert that the more complex the behavior and the longer the period of observation, the greater the prospect that statistical processes will distinguish between the two classes. What are these statistical processes? It is usually enough to create a histogram representation of the inter-pulse timings, where the histogram bins are no wider than the resolution of the pulse-timing mechanism in the surveillance system. If individual elements do not emerge, or if elements appear to exhibit substantial variability, then the underlying timing mechanism, if any, will not be revealed; and variabilities greater than approximately one half of the radar's shortest pulse duration should be considered as substantial. Some allowance should perhaps be made for variabilities induced by radar or surveillance-system motion, but if the extent of variability exceeds approximately 50 nS, then it will be increasingly difficult to discern the underlying timing mechanisms.  Here, it is assumed that variabilities greater than 50 nS indicate either that the timing mechanism is concealed by measurement instabilities, or that the behavior is patently not synchronized by a stable reference source.

                      Before moving on to a description of the methods used in this handbook, it may be useful to examine what is meant by the terms used above: constant, stagger and jitter. In general:

          • Constant is used to signify that a sequence of pulses uses a single, repetitive inter-pulse interval that varies by no more than the average pulse duration of the sequence. Note that "constancy" is not necessarily the same as stability: a notionally constant behavior may nonetheless fail to satisfy the variability goal proposed above.  
            • Stagger is used to signify that a sequence of pulses uses multiple inter-pulse intervals, in a manner that is ultimately repetitive and predictable. Fixed-duration intervals, or elements, may occur more than once in a repetitive sequence; their placements within a sequence are referred to as positions. Thus a stagger sequence is a multi-element multi-position sequence. To illustrate, consider a sequence comprising fixed-duration elements of 900, 1000 and 1100 μS, (which are labeled A, B and C for ease of reference): an ABC sequence, or an ACB sequence, would both be described as a three-element, 3-position stagger; in either case, the sequence length remains fixed. By contrast, a sequence in which, say, elements A and C occur multiple times (such as a repetitive AAABCCC behavior) would be described as a three-element seven-position sequence. Clearly, there can never be more elements than positions in a sequence; but there may be many more positions than elements. The sequence may be described as the firing order; it is always repetitive in a stagger sequence. Stagger behaviors may be exhibited by either of the MNR classes defined above.    
              • Jitter is less readily defined, in that the term may be used to embrace many behaviors. At one extent, it may be used to signify pulse sequences that do not satisfy the requirements of a constant waveform, because of an inherent instability. At the other extent, the term could be used to describe sequences where there are multiple, very stable fixed-duration elements such as could be seen in a stagger sequence, but the firing order is not readily discernible (and may even be quasi-random). Clearly, used alone, the term jitter is ambiguous; amplifying terms, such as continuous and discrete, may add clarity when used consistently. In this handbook, a collection of stable fixed-duration elements used in a pattern undetermined from observation is described as discrete jitter; any other usage of jitter implies instability, whether of a single or multiple elements.



                IV. Beamwidth Measurement and Antenna Gain

                           Antenna beamwidth is a critical aspect of overall radar system gain, as explained in Annex A. When it is known, it can lead to estimations of effective radiated power and hence to an indication of the likely detectability of a radar, given knowledge of an observer's surveillance system. Beamwidths as provided in manufacturer documentation are tabulated in the various case studies of the MNR Handbook; they are also possible to derive from pulse-level data, e.g. from an IFM-based system, provided that pulse amplitudes are measured with sufficient accuracy and resolution. Since the beamwidth of a lobe is defined as the arc bound by the half-power (or -3dB) points of the lobe, all that is required in principle is for the observer to determine:

              • The arc of scan of the radar. Commercial marine radars invariably scan 360°;
              • The duration of the radar's scan; and
              • The time period that separates the pulses where the half-power points are exceeded in amplitude.

                Once these facts are established by measurement, the beamwidth may be calculated:

                                      Beamwidth °   =    Beam Duration : Scan Duration * 360°     

                          In reality, it is somewhat more complex than depicted here. For instance, the observed data is inevitably somewhat grainy compared with the true lobe shape, as the observer's sample interval is defined solely by the transmission of the pulses, and the true half-power points may not be observed (ideally, the impact of this intermittent sampling should be reduced by interpolation). Nonetheless, this approach yields a fairly close approximation.

                          The transition from beamwidth to gain requires that both horizontal and vertical beamwidths be measured; horizontal beamwidth, as depicted above, may be relatively easy to obtain, whereas vertical beamwidth may be exceedingly difficult, for a variety of practical reasons. In the MNR domain, however, we are greatly assisted by the mandates of the IMO, requiring a minimum vertical beamwidth of 20°. In the worst case, then, where vertical beamwidth cannot be defined and only horizontal beamwidth is measured, it is possible to approximate the gain of the MNR antenna from a combination of measured and legally-required characteristics.  There are two approaches to estimation of gain, depending on whether the radiated beam is either approximately circular or approximately rectangular. In the case of the MNR, it is probably safe to assume a rectangular beam shape. To determine gain, as discussed elsewhere, it is necessary only to compare the beam with the theoretical isotropic distribution:

                                      Gain    = Isotropic Area : Radiated Area   

                                                  ≡ 41253 : (BeamwidthHorizontal * BeamwidthVertical)

                                                  ≡ 10 * Log10 (41253 : (BeamwidthHorizontal * BeamwidthVertical)) dBi

              Assuming a 1° horizontal beamwidth and a 25° vertical beamwidth, the gain of an antenna, in dBi, is:

                                                  10 * Log10 (41253 / (1° * 25°) ), or approximately 32.2 dBi.

              The following chart traces changes in gain with horizontal beamwidth, for three vertical beamwidths (20, 25 and 30°):


                          At this point, it is theoretically feasible to extend the characterization of a radar system, by approximating its effective isotropic radiated power, or EIRP, provided mostly that the peak power output of the RF source is known. In many instances, as can be seen from the case studies of the MNR Handbook, MNR manufacturers advertise a notional specification that may be considered as a guide to the maximum attainable power output of the magnetron. In practice, there may be substantial losses, and the real output may differ from this by a very painful amount, but it is nonetheless a useful indicator; by scaling this notional output power, in either dBW or dBmW, and adding the antenna gain factor, an approximation of the EIRP may be obtained. Thus, a magnetron which delivers a peak power of 12 kW to an antenna with a 1° * 25° beam would have a maximum EIRP of:

                                                              10 * Log10 (12,000) + 32.2        dBW

                                                            40.8 + 32.2  ≡ 73 dBW  ≡ 103    dBmW

                      The reality is, of course, rather different, with many potential sources of loss, attenuation and some obvious degradation of performance. Even so, the method is generally viable, even if any of the resulting assumptions are more than a little presumptuous!            


              1. Annex B borrows extensively from earlier writings by Mr. Ian Norman
              2. US Department of Trade, Maritime Administration: Statistics for 2005.
              3. See Section II for details of allowable bands.
              4. This translates to "hauberk" - a chain-mail shirt
              5.     Where multiple fixed-duration intervals are employed in a radar system's pulsing sequence, it  is common practice to refer to the  individual durations as elements.