Hybrid Access Networks
6.2. Agnostic digitizing of radio signals
The scope of this section is to explain how radio carriers (at intermediate or at broadcasting frequencies) can be digitized in an almost agnostic way to the radio standards.
Once a radio signal is digitized and the samples encapsulated into packets, the final digital flow no longer depends on the transported radio standard. Also the dependency on the radio standard is reduced to the digitizing and reconstruction stages.
6.2.1. Techniques scope
Practical limitations of directly applying the Shannon theorem
A first glance, the Shannon Theorem requires to sample the RF signal at a frequency at least the double of the highest frequency contained in the spectrum of the signal that is to be digitized. The resulting information bandwidth contains all frequencies from DC to half of the sampling frequency. A processor, via software, is then expected to digitally filter, decimate, and operate further baseband functions.
Figure 6.2.: Direct digitization front-end, (picture from [96])
For instance the upper bound of the UMTS Band I is 2170MHz, and would require a sampling frequency of at least 4340MHz. Then assuming a 9-bit resolution1 —provided that such an ADC exists— the resulting bit stream would be 39.06Gbit/s. Hence the digitizing at the RF carrier frequency using Shannon’s theorem, as in Fig. 6.2, is not practical.
Remaining Techniques
Currently two digitizing techniques of the complex base-band envelope2 exist. They differ by the frequency shifting requirements prior to digitizing:
1. frequency shifting the signal to a lower intermediate frequency (as close as possible to 0Hz frequency as shown in Fig. 6.3), and then use legacy digitizing techniques (Shannon)
2. digitizing the radio signal at its carrier frequency using the Band Pass Sampling (BPS) technique
Of course the latter can also handle signals that are frequency-shifted lower than their initial carrier frequency, yet it is not its main interest.
1for a target SNR of 50dB since for anideal ADC:𝑆𝑁 𝑅𝑑𝐵= 6.02·𝑁+ 1.72, where 𝑁 is the resolution
2in the sense that the I and Q components are mixed and indiscernible
6.2.2. Digitizing using Shannon on frequency-shifted signals
Figure 6.3.: Traditional digitization front-end, (picture from [96])
As far as 1993, [97] suggests to build digital radio over fiber networks by digitizing down-mixed radio signals in order to fit the sampling capabilities of the ADCs.
Example of a commercial product
The ADC company proposes such a system that digitizes portions of spectrum, and uses legacy digital transceivers for meeting optical budgets of 25dB.
The maximum bit stream resulting of the digitizing, and that can be handled by the system, values 3.072Gbit/s and allows to carry approximately 60MHz of spectrum, when using UMTS signals. Thus we can assume each 5MHz portion of spectrum i.e. each UMTS carrier to represent 1/12th of the bit stream (256Mbit/s). Assuming a 9-bit precision for the Analog to Digital Converter (ADC), the sampling frequency values 28.4MHz. Given the spectral occupancy of an UMTS carrier to be 4.68MHz, the oversampling factor values roughly 6.
Despite the fact that carrying a UMTS carrier only requires one twelfth of the link’s capacity, the used protocol’s bit rate does not adapt to the payload, and therefore requires a 3.072Gbit/s data flow to transport a single UMTS carrier. Hence this solution limits its integration into current PON’s digital flows (2.5Gbit/s in the downlink). As a result, a separated and dedicated wavelength is required.
The main drawback of this technique is the required Local Oscillator (LO) for down- and up converting the radio signal in order to fit the sampling bandwidth of the ADC.
6.2.3. The Band Pass Sampling concept
A digitizing technique that allows to get rid of the carrier frequency issue when digitizing is the BPS theorem [98]. It consists undersampling a modulated signal to achieve frequency translation by intentionally aliasing of the information bandwidth of the signal [97].
Thus the sampling frequency requirement is no longer based on the frequency of the RF carrier, but on the occupied information bandwidth of the signal. As we will see the resulting sampling rate can be significantly reduced.
Sub-sampling and spectral folding
Figure 6.4.: Frequency shift induced by the BPS technique
In this case a signal of bandwidth 𝐵, within the frequency range𝑓𝑙𝑜𝑤 to 𝑓ℎ𝑖𝑔ℎ can be rebuilt from the samples under the condition that the sample rate 𝑓𝑠 abides with the condition:
𝑓𝑠 ≥2·𝑓ℎ𝑖𝑔ℎ
𝑛 (6.1)
where𝑛 is the greatest integer of the ratio 𝑓ℎ𝑖𝑔ℎ 𝐵 : 𝑛=
⌈︃𝑓ℎ𝑖𝑔ℎ 𝐵
⌉︃
(6.2) Due to the sub-sampling procedure, multiple copies of the sampled frequency band of interest can be found in the spectrum as shown in Fig.6.4. Whether 𝑛 is odd or even, the first occurrence of the side band of interest is respectively located below or beyond the sampling frequency.
The main advantage of BPS is that the information band is acquired without any LO mixing and image filtering. Only a narrow bandpass filter (Fig. 6.2) centered above the carrier frequency attenuating the frequencies outside the information band is required.
However at the re-built stage, a LO is still required.
In a radio environment where several standards exist, the first step is to keep the frequency band of interest isolated (by using standard diplexers), limited, and as narrow as possible in order to lower the specifications of the sampling frequency.
Performances by Nirmalathas [99, 100]
When using the BPS method, according to experiments and formal expressions, the SNR at the output is directly proportional (valid up to 8 bits) to the resolution of the ADC (Fig. 6.5a). Beyond a resolution of 8 bits, the SNR is dominated by the jitter of the ADC.
The digital flow being function of the flow generated by the ADC, it is possible to link the output SNR to the required bit rate of the link (Fig. 6.5b).
However the SNR performance show in Fig. 6.5a is limited to 40dB which is not sufficient for downlink distribution of radio carriers given the ACLR requirements.
(a) (b)
Figure 6.5.: Performances of the BPS-RF technique (a) SNR as a function of the ADC resolution, contribution from the different components; (b) SNR as a function of the link bit rates. (both pictures from [99]).
Performances by Kim [101]
From [101]’s experimental results, we can derive a quick application for UMTS downlink signals. According to the Fig. 6.6, when targeting an output SNR of 50dB, the ADC resolution is to be at least of 9bits, for the different possible rms jitters, the maximum input frequencies are 850, 1080, and 1450MHz.
Thus directly BPS UMTS carriers in the 2100MHz range is not possible. However, let’s assume the RF band of interest can frequency-shifted3 close to the frequency range for which output SNRs of 50dB are achievable.
The goal is to BPS 25MHz of efficient spectrum —3 UMTS carriers spaced by 10MHz for instance. Also as recommended by [98] some guard-band at each side of the band of interest is required. For instance [99] used a 2.5 ratio between the total bandwidth and the effective band of interest, thus let’s target a digitization of a 62.5MHz portion of spectrum.
Applying the formulas of §6.2.3, the minimal sampling rates can be found. Assuming a sampling resolution of 9 bits, then the minimum raw bit streams can be found: 1.15 to 1.17Gbit/s. These bit stream are minimumand are expected to increase due to overhead information and eventual Forward Error Correction (FEC) code.
Given the ACLR and SNR requirements of downlink UMTS signals, band-pass sampling them at their initial central frequencies of 2.1GHz appears to be limited and even impossible.
Yet for central frequencies in the 800MHz range this seems to be possible.
Recently the 832-862MHz band were authorized to be used LTE signals (which has downlink ACLR/SNR requirements of 45dB). Also different operators aim at using the 900MHz band, initially allocated to GSM, for UMTS. Finally this BPS technique could be used for the latter mentioned radio bands on radio signals that do not require to
Figure 6.6.: Effect of jitter, ADC resolution and input frequency on the SNR (Fig. from [101])
Table 6.1.: Minimum raw bit streams using [101]’s BPS results (9-bit resolution) BW BW w/ guard fc fmax n fs min Minimum Raw Bistream
[Mhz] [Mhz] [Mhz] [Mhz] [Mhz] [Mbit/s]
25 62.5 800 831.25 13 127.9 1151
25 62.5 1000 1031.25 16 128.9 1160
25 62.5 1400 1431.25 22 130.1 1171
25 62.5 2140 2171.25 34 127.7 1149
be frequency-shifted. Then however the main advantage of the BPS technique (vs. the Shannon theorem technique using a LO for down-mixing) is lost.