Matlab Simulation Results

The Matlab simulation was performed. The most important data present in the datasheets of the components that were used, namely, mixers, muxes, attenuators and amplifiers, was inserted on the Matlab script developed. The whole LTE filter chain has been simulated. The biggest values of attenuation possible were considered (minimum gains and maximum values of attenuation in the attenuators). The analog filters were simulated as having their optimum case component values. The

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signal was selected to be centered at 2585 MHz. Snapshots of the signal along the entire downconcersion, FPGA and upconversion chains will now be displayed sequentially. Those will be commented upon. It is advised that, for visualization purposes, the reader consults figures 2.1, 2.2, in section 2 and figures 4 and 4.1 in section 4. At the beginning of block A the signal assumed to be received by the antenna has a power spectrum resembling the one present in figure 5.2.

Figure 5.2 – Power spectrum at the entrance of block A.

White noise was generated with such a power that it’s spectral power density is similar (but slighly lower for visualization purposes) to that of the signal. The goal is to simulate an unknown spectra except for the signal to be filtered. The spectra might be filled by all sort of signal types in all kinds of frequency bands and to emulate this, white gaussian noise was generated in the fashion just illustrated.

The signal is centered on ∓ 2585 MHz and can be spotted by the vertical traces below the noise. The sinc shaped spectra of the signal power density rises above the noise. A zoom of figure 5.2 is exhibited in figure 5.3. The sinc shape can be identified in that last picture.

Figure 5.3 – Zoom in of power spectrum of signal at the entrance of block A.

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Signal Received By The Antenna fc=2585 MHZ, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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Signal Received By The Antenna fc=2585 MHZ, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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The signal power density varies between -76.5dBW and -77.4 dBW. The signal then passes through a Mux 2<->4 and encounters HP Band 3. The results are exposed in figure 5.4.

Figure 5.4 – Power spectrum after HP Band 3.

Again the signal can be identified by the vertical traces in the picture. Once more, a zoom in of the signal is presented, this time in figure 5.5.

Figure 5.5 – Zoom in of power spectrum of the signal after HP Band 3.

Note that the maximum power of the signal is around -90 dBW. This equates to -76.5dBW – 7dB from the Mux – 6.5 dB from HP Band 3. Next, after Mux 1->2, Mux 2->1 and Mux 4<->2, the first Down conversion step is performed. The results are displayed in figure 5.6.

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Power Spectrum after FRI1 fc=2585 MHZ, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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Power Spectrum after FRI1 fc=2585 MHZ, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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Figure 5.6 – Power spectrum after the Down Conversion first mixing step.

It is apparent the leaked LO tone power is way higher than the signal power density level. The signal can be spotted by the vertical traces in the bottom of the picture and is predictably centered at 600 MHz. It still rises slightly above the white noise.

A zoom in of the LO leaked tone is illustrated in figure 5.7.

Figure 5.7 – Power spectrum of the LO Isolation error after the 1^st mixing step of the Downconversion.

The LO leaked tone has a power around -54.29 dBW. It has a frequency of 1985 MHz.

A zoom in of the signal at the IF is shown in figure 5.8.

To note that the IP3 error after each downconversion or upconversion step is displayed and discussed in the appendix, section 5.3.

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Power Spectrum after Down Conversion to 600 MHz fc=2585 MHZ, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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-55 -54.5 -54

LO Isolation error after Down Conversion to 600MHz

Frequency [MHz]

Power Spectrum [dBW]

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Figure 5.8 – Zoom in of power spectrum of the signal after Down Conversion 1st mixing step.

The maximum power density of the signal is near -106 dBW/Hz. This is approximately equal to -90 dBW/Hz – 9 dB of insertion losses from the muxes and -7dB from the mixer’s insertion loss.

Then the signal goes through an amplifier and reaches FRI2. The power spectrum after this is exposed in figure 5.9.

Figure 5.9 – Power spectrum after second Image band Rejection Filter , FRI2.

The signal can be spotted at the edges right before the filter starts to increase its attenuation in a very steep fashion. The LO tone power is still very high and and it (LO) is thus, easily identifiable. A zoom in of the signal is presented in figure 5.10.

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Signal at IF after Down Conversion to 600 MHz fc=2585 MHZ, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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Power Spectrum after FRI2 Downconversion, fc=2585 MHZ, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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The signal has a maximum power density of -96.75 dBW/Hz. This is equal to -106dBW/Hz +15.7dB of the gain of the amplifier minus 6.45 dB of attenuation in FRI2. There is a 0.7 dB (−97.3 − (− 98) ) deformation that happens in the left side of the spectrum of signal. This is very hard to avoid. Note that this filter is the most stringent of the entire chain, having an order of 11, whereas the most demanding filters excluding this one, have an order of 9.

After this, the signal encounters an attenuator followed by a mixer that will execute the second mixing step of the down conversion. The spectrum after this is exhibited in figure 5.11.

Figure 5.11 - Power spectrum after the Down Conversion second mixing step.

The previous LO tone, LO1, got mixed, which gave origin to two LO tones instead of one. These have a spectral power density of -56.4 dB. The frequencies are 1985 ∓540 which means, 1445 MHz and 2525 MHz.

Note that -56.4 dBW = -54.29 dBW + 15.7 dBW from the amplifier – 6.46 dB from FRI2 – 5.2 dB from the attenuator – 6.15 dB from the insertion loss of the mixer.

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Power Spectrum after FRI2 Downconversion, fc=2585 MHZ, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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Power Spectrum after Down Conversion to 60 MHz fc=2585 MHZ, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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A new leaked LO tone, LO2, is introduced with a frequency of 540 MHz. It has a power of -54.29 dBW, as was to be expected. The signal is centered at 60 MHz and is near the gap around DC (0 Hz), caused by FRI2. A zoom in of the signal is depicted in figure 5.12.

Figure 5.12 – Zoom in of power spectrum of the signal after Down Conversion 2nd mixing step.

The maximum power density of the signal is near -108 dBW. This is approximately equal to - 96.75 dBW – 5.2 dB from the attenuator – 6.15 dB from the insertion loss of the mixer.

Next, the signal passes through an attenuator (with 5.5 dB attenuation) and an amplifier (with a gain of 17.4 dB) and arrives at the Band Pass Filter.

Figure 5.13 - Power spectrum after the Pre Processing Band Pass Filter.

The signal power density varies between -104.6 dBW/Hz and -102.4 dBW/Hz. This can be seen in figure 5.14 where there is a zoom in view of the signal spectra. The LO in 540 MHz has a power of - 162.8 dBW and it is 58.2 dB below the signal. The LO at 1445 MHz has a power of -170.6 dBW and is thus 66 dB below the signal. Finally the LO tone at 2525 MHz has a power of -175.2 dBW and is 70.6 dB more attenuated than the signal.

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Signal at IF after Down Conversion to 60 MHZ fc=2585 MHZ, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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Power Spectrum after Band Pass Filter fc=2585 MHZ, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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Figure 5.14 – Zoom in of the power spectrum of the signal after the Band Pass Filter.

Once again the signal traverses an attenuator (with 12.4 dB attenuation) and then an amplifier (with a gain of 15.4 dB) and then finds the Low Pass Filter, the last filter in the Downconversion Block. The

resultant spectra can be consulted in figure 5.15.

Figure 5.15 - Power spectrum after the Pre Processing Low Pass Filter.

The signal power density varies between -108.3 dBW/Hz and -105.45 dBW/Hz.

This can be seen in figure 5.24 where there is a zoom in view of the signal spectrum. The LO at 540 MHz has a power of -221.59 dBW and is therefore 113.29 dB more attenuated than the signal.

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Power Spectrum after Band Pass Filter fc=2585 MHZ, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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Power Spectrum After Low Pass Filter fc=2585 MHZ, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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Figure 5.16 – Zoom in of power spectrum of the signal after the Low Pass Filter.

Considering that the signal that leaves the LP filter is exactly the one that enters the ADC, the output of the frequency domain simulation of the signal after the ADC, is exhibited in figure 5.17.

Figure 5.17 - Power spectrum after the Analog to Digital Converter.

The signal power density varies approximately between -138.65 dBW/Hz and -136 dBW/Hz. The signal went down roughly 30 dB by the ADC (analog to digital converting) process. This was due to the time sampling of 250 MSPS (mega samples per second). Now, on 45 MHz the power spectrum is around -147.7 dBW and on 75 MHz it is around -145.5 dB.

After the time sampling, the absolute values of the samples are taken. Those are normalized to an interval from 0 to 0.857. This is due to the FPGA digital filter + equalizer that will amplify the values of some samples. The samples’ values are mandatory to be between 0 and 1, at any point inside the FPGA. The power spectrum after this procedure can be consulted in figure 5.18.

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Power Spectrum After Low Pass Filter fc=2585 MHZ, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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Power Spectrum after ADC fc=2585 MHz, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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Figure 5.18 - Power spectrum after Normalization and before the FPGA Digital Filter.

The signal power density goes nearly between 6 dBW/Hz and 8.9 dBW/Hz, which shows a jump of about 130 dB in the signal power density due to the normalization procedure alone.

What follows is the crossing of this signal with the FPGA Digital Filter. The frequency domain output of that filter, after a renormalization, is presented in figure 5.25.

Figure 5.19 - Power spectrum after FPGA Digital Filter, after Renormalization.

After the signal being digitally filtered in the FPGA, it is renormalized back to its original value range so that it can be compared with the signal present before the ADC. The signal now varies between - 138.86 dBW and -135.44 dBW. The 1 dB ripple introduced clearly took its toll.

This figure (5.19) must be compared with figure 5.18. Note the impact of the filtering. The edges on the outer frequencies of the signal band are now much steeper, smoother and thinner. For instance, on 45 MHz or below the power spectrum density is now, at maximum, -234.2 dBW and on 75 MHz or above, the power spectrum density is always equal or below of -227.9 dBW. This means, 95 dB attenuation on the left edge of the signal and 88.7 dB attenuation on the right edge of the signal, were reached, after the respective 5 MHz transition bands. The 80 dB attenuation intended was exceeded and the digital filtering was a success. The noisefloor is sensitively around -245 dB.

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Power Spectrum After Normalization fc=2585 MHz, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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Power Spectrum After FPGA Filter fc=2585 MHz, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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After passing through the FPGA digital filter, the signal is going to be equalized. This is to nullify the effect of a big part of the ripple induced in the signal in the whole Downconversion and Upconversion chains. Finally, a simulation gain is applied to the signal, to simulate the power level adapter that exists after the DAC. The resultant power spectrum is exposed in figure 5.20.

Figure 5.20 - Power spectrum after FPGA Equalizer and after power adaptation before the signal encounters the first Upconversion mixer.

The signal power density has values roughly between -95.54 and -93.38 dBW/Hz. To note that the spectrum of the signal is evidently higher on the lower frequencies. This is to counter the effects of the filters ahead that attenuate more the lower frequencies than the higher ones.

It is of the utmost importance to call the reader’s attention to something that has happened. After the equalization was performed, all the samples were rounded so that only the 12 most significant bits of each sample were used to represent them. This is because, after the DAC, only the 12 most significant bits will be error free from the DAC operation itself.

The noisefloor has consequentially gone up a lot, being now around -167 dB. The SNR is now near 71.25 dB. This is the single bottleneck of the system performance. If a better, accessible DAC, is put on the market, it shall be used instead. The signal to noise ratio, will, at this stage in the chain, increase 6.02 dB (20 log 2) if one error free bit added in the resolution the DAC can handle. If 2 additional error free resolution bits are available, the DAC will no longer be an impairment to the minimum quality of filtering of 80 dB guaranteed by the remaining system developed.

Next, the signal crosses the DAC. The DAC is simulated just as explained in the OFDM signal generation sub section (sub section 5.1.1). It is therefore, an ideal DAC, comprised of an oversampling, a sample and hold and finally an ideal low pass filter. The spectrum after each of these three phases of the digital to analog conversion is shown respectively in figures 5.21, 5.22 and 5.23.

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Power Spectrum After Equalization And After Simulation Gain fc=2585 MHz, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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Figure 5.21 - Power spectrum after Oversampling. The replicas have appeared exactly as expected. See figure 2.28 in section 2.5.3. The signal power density is the same as in figure 5.20 (last figure).

Figure 5.22 - Power spectrum after the Sample and Hold. The replicas have been multiplied by a sinc shape. The signal power density has slighly changed. This is better visible in the next figure, figure 5.23, where only the 60 MHz replica remains, all other replicas having been rejected by the ideal low pass filter.

Figure 5.23 - Power spectrum after DAC ideal Low Pass Filter. The signal power density varies approximately between -97.58 dBW/Hz and -94.88 dBW/Hz. At this stage, there is, thus, a temporary ripple of around 2.7 dB in the signal.

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Power Spectrum After Oversampling fc=2585 MHz, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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Power Spectrum After Oversampling and Sample & Hold fc=2585 MHz, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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Power Spectrum after DAC Low Pass Filter fc=2585 MHz, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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This noise (in the worst case, lower frequencies than the signal spectra) is frequently composed of tones with a power of -169 dBW, which is only 71.42 dB below the signal minimum level of power spectral density. This can be observed in figure 5.22.

Then the signal goes into the mixer that performs the first upconversion step. It can be inspected in figure 5.23 that the power density average, of the signal spectra delivered to the mixer, is below -96 dBm. This means, said signal has a power under 7 dBm, which is 3dB away from saturating the mixer.

The output spectrum after the first upconversion step is completed, is displayed on figure 5.24.

Figure 5.24 - Power spectrum after first Upconversion mixing step.

A LO tone with a power density of -49.41 dBW was introduced with a frequency of 540 MHz.

The signal is now centered at 600 MHz and its image band, centered in 480 MHz, has appeared with the same power density. In comparison with last figure, the signal has just suffered the effect of a 6.15 dB conversion loss, its power density being now between -103.73 and -101.03 dBW. Next, the signal faces an attenuator (with attenuation equal to 1.9 dB), then an amplifier (with a gain of 15.7 dB) and after that, it crosses FRI2, that will filter the undesired image band created in this upconversion first mixing step. The resulting power spectrum is presented in figure 5.25.

Figure 5.25 - Power spectrum after Upconversion first Image Band Rejection Filter, FRI2.

The signal power density varies between -95.97 and -93.90 dBW/Hz. To note that -93.90 dBW/Hz is equal to -101.03 dBW/Hz – 1.9dB from the attenuator + 15.7 dB from the amplifier

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Power Spectrum after Up Conversion From 60 MHz fc=2585 MHz, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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Power Spectrum after Upconversion FRI2 Upconversion, fc=2585 MHz, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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– 6.67 dB from the FRI2. The ripple in the signal is now only slightly above 2 dB.

The image band of the signal has a maximum power density of -191.35 dBW/Hz. The rejection of the image band was thus successful, since it is now more than 90 dB more attenuated than the signal.

After this, the signal goes through an attenuator (with an attenuation of 10.7 dB), an amplifier (of gain equal to 14.1 dB) and finds a Band Reject Filter that works as a notch to cut the leaked LO tone of frequency 540 MHz. This filter’s response is illustrated in figure 5.26. The power spectrum after crossing this filter, is exhibited in figure 5.27.

Figure 5.26 – Filter response of an order 6, Chebyshev, Band Reject Filter, that functions as a Notch to the 540 MHz frequency.

The attenuation provided by this notch is quite high, exceeding 250 dB in 540 MHz. The result is this good only because closest to ideal component values were used.

Figure 5.27 - Power spectrum after “Notch” at 540 MHz (the filter response is shown in figure 5.26)

The signal power density varies between -99.17 and -97.29 dBW/Hz. -99.17 dBW/Hz is equal to - 95.97 dBW/Hz – 10.7 dB from the attenuator + 14.1 dB from the amplifier – 6.6 dB from the “Notch”.

The ripple in the signal is, at this point in the circuit, slightly below 2 dB.

It is observed in figure 5.27 that the leaked LO tone is more than 120 dB more attenuated than the minimum power density of the signal.

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Band Reject Filter As Notch At 540 MHz fc=2585 MHZ, LB=20MHz

Frequency [MHz]

Filter Response [dB]

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Power Spectrum after "Notch" at 540 MHz fc=2585 MHz, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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After the “Notch”, the signal encounters an attenuator (with an attenuation of 5 dB) and then enters the mixer that will perform the upconversion second mixing step. The output spectrum of that mixer, is depicted on figure 5.28.

Figure 5.28 - Power spectrum after the Upconversion second mixing step.

A new LO tone, LO2, with a frequency of 2585 – 600 = 1985 MHz, was leaked. The power of LO2 is - 49.41 dBW, as was prospective. The signal power density stands approximately between -111.22 and -109.34 dBW/Hz. This is better observed on figure 5.29 that shows a zoomed in view of just the signal and its image band on the positive frequency side of the spectrum.

Figure 5.29 – Zoom in of power spectrum of, signal at IF and respective image band.

Comparing with figure 5.28, it is visible that the signal suffered the effect of the 5 dB attenuation in the attenuator plus 7.05 dB attenuation due to the insertion loss of the mixer.

The signal has already returned to its original center frequency, 2585 MHz.

The image band and leaked LO tone, present in the power spectrum, still have to be rejected in comparison with the signal. The image band issue is tackled first. For this purpose the signal goes through an amplifier (with a gain of 10 dB), a 2<->4 Mux (with an insertion loss of 7 dB) and finally reaches HP Band 3 filter that attenuates the image band of the signal. The output power spectrum is presented on figure 5.30.

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Power Spectrum after Up Conversion From 600 MHz fc=2585 MHz, LB=20MHz

Frequency [MHz]

Power Spectrum [dBW]

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Signal at IF after Up Conversion From 600 MHz fc=2585 MHz, LB=20MHz

Frequency [MHz]

Power Spectrum [dB]

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