**February 9, 2017**

Ensuring 4G networks perform to carrier specifications is an everyday challenge for field technicians. To achieve high-speed operation and reach established KPIs, interference must be mitigated. Time Difference of Arrival (TDOA), a technique for geo-locating RF sources, is a highly effective method to efficiently achieve this goal by making it easier to locate – and subsequently correct – interference.

TDOA can provide a very accurate location estimate (< 100 m) in a short period. To successfully use TDOA, it is essential to understand the type of signals that can be used, how the results depend on the geometry of the measurement, what the sources of uncertainty are and how to mitigate them, and how to know if the answer is meaningful.

To most accurately locate the interference source using TDOA, wireless field technicians must consider multiple factors. Of course, high-accuracy spectrum monitoring tools and advanced software are paramount. There are other key variables, which we will now explain.

**Modulated Signals –** To time-align the received signal at each probe used, the signal must contain a non-random, non-repeating structure. Many interference sources emit white noise, which lacks the structure necessary to align the signal. Simple sources, such as a sine wave generator, produce a repeating pattern that has structure, but does not allow for a unique time-alignment.

Modulated signals, such as FM radio broadcasts and cell phone signals, contain internal structures that can be aligned in time. For this reason, TDOA is typically used to locate rogue broadcast signals, and other communication signals that are out-of-band or otherwise unexpected.

**Reflections and Signal Strength –** Usually, signal strength is not an issue, if the signal is clearly present. Field technicians need to get a discernable I/Q diagram. Typically, 10 dB to 15 dB above background is required to eliminate any noise. The capture bandwidth also needs to be narrow enough so that other modulated signals are excluded. Be aware that higher signal strength will not necessarily produce a better answer.

Multipath signals will tend to broaden the I/Q pattern and make it more difficult to find the proper time-alignment. If the strongest component of the signal is a reflection off a nearby surface, then the distance calculation will be the reflected signal path, not the direct straight-line path between the probe and source. The test software cannot know this, so the result is a systematic offset to the distance calculation, equal in magnitude to the reflected distance of the signal.

**Probe Synchronization –** To calculate the TDOA wherein each data stream is shifted in time to find the optimal signal alignment, the same signal must be captured at each probe location. To make this as efficient as possible, it is best to have short capture times, perhaps 10s of milliseconds. To capture the same signal at each location, however, the probes must start collecting signals simultaneously. Further, the precise timing of each I/Q pair is required in the data stream so that once aligned, the time shift can be accurately calculated.

A good TDOA system will produce location estimates within 100 meters of the source location. An RF signal travels 100 meters in about 300 nanoseconds. Therefore, the timing of the signal must be known with very high precision.

**Hyperbolic Lines –** A TDOA measurement reveals a time difference in the arrival of the interested signal at two or more probes. The time difference is multiplied by the speed of light to give a change in distance between each set of probes and the RF source. For a set of two probes, the distance does not specify a specific location, but rather a hyperbolic line centered between the two probes (figure 1). Therefore, a successful TDOA measurement on two probes does not give a unique solution, but a continuous set of solutions along a hyperbolic curve.

**Triangulation –** A three-probe TDOA measurement will produce three hyperbola, the intersections of which yield possible locations for the RF emitter, as shown in figure 1. If the source is inside the triangle formed by the three probes, the result may be a single intersection point. It is not unusual to have a few intersection points for the three curved lines, especially if the source is very far outside the probe triangle. It is usually possible to use the relative receive powers at the probes to determine which intersection is the right location.

**Sample Rate –** The number of I/Q data pairs collected per second is the sample rate. The time separation is multiplied by the speed of light to get the distance separation, so the spatial resolution is directly proportional to the temporal resolution. It is tempting to just increase the sample rate to increase the spatial resolution, however, there is a practical limit to how much the spatial resolution can be increased by raising the sampling rate.

Figure 2 shows data from two probes, one slightly ahead of the other. The dots represent sample points. There are not enough data points to accurately reproduce the shape of the curve, so the green and blue lines represent the best guess at the peak position for each set. Because the sample rate is too low, a large error is introduced. In Figure 3, the sample rate has increased and the peak positions are accurately found. Increasing the sampling rate further is not necessarily going to increase the accuracy.

Figure 3

**Cable Length -** The typical transmission speed in a coaxial cable is about 2/3 the speed of light. For every 20 meters difference in cable length, a 30-meter offset in position is introduced. Because this error in location cannot be reduced by averaging, it may be necessary to enter cable lengths into the geo-location algorithm for each probe. Cable length may not be a significant concern if the cables are uniform, or if the differences are small compared with the expected spatial resolution.

**Time Delays –** Another concern is internal delay in the probe hardware and the analog and digital paths used to capture, process, and store the I/Q data stream. This internal delay adds a systematic error that cannot be removed with signal averaging. The I/Q data pairs must be time stamped in the data stream to do time-alignment. Most remote probes will use a GPS signal to synchronize both the start time of the captures and the clocks used to add the time stamps. GPS chips produce a pulse-per-second (PPS) signal that is very reliable and precise. An internal clock ticks at a very high and stable frequency, and time stamps are inserted into the data stream at regular intervals based the clock tick count.

**Emitter Location –** If the RF source is inside the triangle formed by the three probes, the accuracy is expected to be high. When the emitter is behind one of the probes, even if still close to the probe triangle, the uncertainty is higher. Also, for probes far away, the angle of incidence of the hyperbolic lines makes the area of uncertainty larger.

**Signal Averaging –** A good way to reduce random uncertainties in measurements is through averaging. With TDOA this is accomplished by repeating the measurement several times and averaging the distance differences found for each probe pair. This number will vary from measurement to measurement due to statistical noise and uncertainty in the measurement data.

**Intermittent Signals –** With TDOA, intermittent signals are a particular problem. The probes must begin capturing at the same time, and each must capture a long enough data set that the overlap of the signal will be significant. To accomplish this, Anritsu implements proprietary algorithms to capture and time align each bursty signal.

An application note entitled Time Difference of Arrival (TDOA) has just been published and is available for a free download.

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