Simulation Tests to Quantify the Spectral Dynamic Range and Narrowband Interference Robustness of the WIDAR Correlator for the EVLA

In the first memo of this series [1], a number of simulations were performed with the primary goal of quantifying the performance of the proposed WIDAR correlator compared to an ideal correlator operating at the full bandwidth. These simulations demonstrated that the WIDAR correlator yields satisfactory results. It was also stated and demonstrated that the WIDAR correlator could increase the spectral dynamic range and interference robustness in the presence of powerful narrowband interference by causing quantizer-generated harmonics to decorrelate. This memo presents results of a more detailed investigation that more carefully quantifies these interference robustness characteristics. L-band interference spectra from the VLA site is analyzed to show that the correlator is more than capable of operating in its intended environment. Spectral dynamic range tests also yield the important conclusion that only a 3-bit, 8-level, initial quantizer should be required to yield interference-robust performance—even if the interference at the VLA site is an order of magnitude worse than it currently is. This is an important conclusion since 3-bit initial quantization will reduce the cost of the quantizers and the fiber-optic transmission system compared to a 4-bit system. The results of WIDAR correlation of a simulated L-band interference environment including a few +20 dB tones representing satellite interference into the “near-in” sidelobes of the antennas are also presented. Background An extensive discussion of the mechanism whereby the WIDAR correlator can cause narrowband harmonics to decorrelate is presented in [1] and is summarized here. Each quantizer sees the analog signal at a slightly different frequency imposed by offsetting the Local Oscillators in the antennas: when the frequency difference is removed in the correlator, narrowband harmonics—that are at multiples of the fundamental—decorrelate. Unfortunately, the degree of decorrelation is limited by the amplitudes of the harmonics of the digital mixer in the correlator: digital mixer harmonics stop the harmonics generated by the quantizer. A workaround to this problem involving some postcorrelation fringe rotation was discovered and will be presented in this document. NRC-EVLA Memo# 009 2 1DWLRQDO 5HVHDUFK &RXQFLO &DQDGD &RQVHLO QDWLRQDO GH UHFKHUFKHV &DQDGD The major flaw in the interference robustness investigation presented in [1], is that it did not consider the dynamic range limiting impact of intermodulation products that are generated by the quantizer from powerful narrowband interference. The simulations in this memo quantify this effect. Simulation Results A number of simulations were performed using a (software) WIDAR correlator and a full bandwidth correlator (without frequency shifting) where the interference consisted of a narrowband signal generated from a FIR filter and one or more additional tones added to a known quantity of Gaussian noise. The total power of the interference and noise is precisely known from the simulation parameters and so it is possible to precisely quantify the spectral dynamic range in terms of the ratio of total interference power to total power into the quantizer. The spectral dynamic range performance derived from these tests is summarized in Table 1. 2 Signals 3 Signals 4 Signals interf/total power interf/total power interf/total power 25% 50% 90% 25% 50% 90% 25% 50% 90% Ideal/fullband 4-bit n.t. n.t. 35 >50* 42.5 39 >50* 43.5 39 WIDAR 4-bit >55* >55* >55 >50 42.5 39 >50* 43.5 39 WIDAR 3-bit >50* >50* >50 >50 n.t. 38 n.t. n.t. n.t. Table 1 Table summarizing the spectral dynamic range performance (in dB) of an ideal 4-bit (fullband) correlator, a WIDAR 4-bit correlator with 4-bit initial quantization, and a WIDAR 4-bit correlator with 3bit initial quantization. In this case, 4-bit initial quantization is 15 levels (-7, -6, ...-1, 0, 1,...6, 7) with a threshold differential of 0.374σ and 3-bit initial quantization is initially 4-bit/15-level, but shifted by one bit to 8-levels (-4, -3, -2,-1, 0, 1, 2, 3). Quantities with an ‘*’ were derived from other tests within the table, and ‘n.t.’ means that no test was performed. The WIDAR correlator clearly outperforms the fullband correlator when two narrowband signals are present because of the harmonic decorrelation effect. However, in the three signal and four signal cases, the WIDAR correlator does not perform any better strictly in terms of spectral dynamic range. This limitation arises from the fact that some intermodulation products of the fundamental frequencies correlate. For example, if a frequency shift of ε is imposed before quantization, then for three frequencies A, B, and C, the intermodulation product (A+ε)+(B+ε)-(C+ε) (which simplifies to A+B-C+ε) will correlate once the frequency shift of ε is removed in the correlator’s fringe stopper (digital mixer). (A similar effect is possible with two narrowband signals if the quantizer 1 This indicates the number of bits coming out of the initial quantizer. 2 And incorporating the technique which overcomes the digital mixer harmonic correlation effect. NRC-EVLA Memo# 009 3 1DWLRQDO 5HVHDUFK &RXQFLO &DQDGD &RQVHLO QDWLRQDO GH UHFKHUFKHV &DQDGD is too asymmetric and generates even harmonics.) This limitation is fundamental and can only be overcome by using more bits in the quantizer. Despite the above fundamental limitation, the WIDAR technique still reduces the number of intermodulation products to only those that meet the criteria in the above example. Thus, a second metric that is useful in quantifying the performance of the WIDAR correlator is to consider the number of “secondary products” (intermodulation and harmonic products) appearing in the cross-power spectrum. In Table 2, a comparison is made of the number of secondary products for a WIDAR correlator and an ideal fullband 4-bit correlator. These results were obtained experimentally by counting the correlated intermodulation and harmonic products in plots of the simulation results. 2 Signals 3 Signals 4 Signals interf/total power interf/total power interf/total power 25% 50% 90% 25% 50% 90% 25% 50% 90% Ideal/fullband 4-bit n.t. n.t. 15 0* 12 27 0* 31 46 WIDAR 4-bit 0* 0* 0 0 3 6 0* 10 16 WIDAR 3-bit 0* 0* 0 0 n.t. 7 n.t. n.t. n.t. Table 2 Table summarizing the spectral dynamic range performance in terms of number of secondary interference products for an ideal 4-bit (fullband) correlator, a WIDAR 4-bit correlator with 4-bit initial quantization, and a WIDAR 4-bit correlator with 3-bit initial quantization. In this case, 4-bit initial quantization is 15 levels (-7, -6, ...-1, 0, 1,...6, 7) with a threshold differential of 0.374σ and 3-bit initial quantization is initially 4-bit/15-level, but shifted by one bit to 8 levels (-4, -3, -2,-1, 0, 1, 2, 3). Quantities with an ‘*’ were derived from other tests within the table, and ‘n.t.’ means that no test was performed. Several plots of amplitude in dB versus frequency of some of the simulation results used in Tables 1 and 2 are shown in Figures 1 and 2. In Figure 1 plots are shown where the narrowband interference (i.e. the “signals”) power is 90% of the total power in the band. In all cases the WIDAR correlator outperforms the simple 4-bit correlator although the limitation of the correlation of intermodulation products is clear. 3 This indicates the number of bits coming out of the initial quantizer. NRC-EVLA Memo# 009 4 1DWLRQDO 5HVHDUFK &RXQFLO &DQDGD &RQVHLO QDWLRQDO GH UHFKHUFKHV &DQDGD 0 64 128 192 256 320 384 448 512 576 640 704 768 832 896 96