Real-Time Digital Equalization: A First Step in the Calibration Process of Element Level Digital Beamforming

As digital control at the subarray and element levels becomes more common in phased array radars, the quality of data received by the radars may be enhanced through methods such as adaptive digital beamforming (ADBF), which are often used to mitigate the effects of interference or clutter at the cost of a little computation. Some of these algorithms even allow users to “request” nulls in specific directions, perhaps where particularly problematic wind turbines are located. For these algorithms to be precise in their steering and thus achieve maximum effectiveness, the channels must be well matched, which may require that an equalizer be used on the raw digital IQ data. While calibration can be used to improve channel matching, the temperature dependence of the frequency responses of some components means that, even with calibration, the channel mismatch may be higher than desired.

Digital equalization can help combat such channel mismatch. Digital equalization is typically performed by taking a least-squares approach to the design of an FIR filter that matches the frequency response of the channels to some reference frequency response. Additionally, because digital equalization can be performed using signals of opportunity, it can be performed in the field; thus, if an FPGA or ASIC equipped with an FPGA routine were incorporated into a radar receiver signal processing chain, a digital equalization calculation routine could be triggered whenever channel mismatch exceeded tolerable levels, allowing an FIR to be designed to bring each channel’s frequency response closer to matching with virtually no pause in operations.

The experiment takes place in two parts:

- In the first part, a simulation environment is designed which is capable of mimicking how a simplified four-channel radar receiver would receive data from multiple sources while suffering from suffering from channel mismatch. The channel mismatch is modeled as an FIR filter with randomly assigned weights. Digital equalization is performed to counteract this simulated channel mismatch, and the performance of the digital equalization in terms of the improvement in the channel pair cancellation ratio (CPCR) and of the change in location and depth of any adaptive digital beamforming nulls are assessed.

- In the second part, data is collected in a loopback setup from the HORUS receiver; a snapshot of this data is shown in Figure 1. This data is a 500 microsecond chirp spanning 124 MHz and suffers from noticeable channel mismatch throughout its bandwidth. To combat this, digital equalization is performed and the subsequent improvement in CPCRs is assessed. Once equalized, an interfering signal of equal power is artificially introduced and adaptive digital beamforming was performed on the resulting data with and without digital equalization, and the impact of equalization on the location and depth of adaptive beamforming nulls and resulting SNR is assessed, as shown in Figure 2.

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Fig. 1: Channel mismatch is noticeable in this four-channel data collected from the HORUS receiver. Digital equalization can be leveraged to reduce the difference in the frequency response of each channel, increasing data quality and beamforming potential.

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Fig. 2: The beampatterns of the 4-channel HORUS data. The LFM signal now appears to come from 30 degrees azimuth (vertical green dashed line); the interferer appears to come from -16 degrees azimuth (vertical red dashed line). The blue beampattern is the default beampattern; the purple is the beampattern after ADBF without equalization; the green is the beampattern after ADBF with equalization. Since the interfering signal’s power is equal to that of the desired signal, the use of equalization before adaptive digital beamforming does improve the overall SNR of the signal.