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Today's digital cellular standards put a lot of pressure on the analog-to-digital converter in terms of dynamic-range capabilities. That has limited the choice of A/Ds to only a handful, and selecting among them requires careful estimation of their dynamic-range capabilities. The most important factors that lead to a complete dynamic-range estimation are the required baseband signal-to-noise ratio, the total harmonic distortion of the radio IF sample stream, the radio noise figure and the gain in power between the worst-case interferer and the wanted signal.
Figure 1 shows the basic radio block diagram for noise and dynamic-range estimation. The noise sources are partitioned into radio noise and converter noise. Because base transceiver station (BTS) radio spectrum is issued in "blocks" of 20 to 60 MHz of spectrum, BTS radio designers will design a "block radio" that can tune to any of many carriers inside a block of spectrum on the order of 15- to 40-MHz wide. A single A/D samples some or all of the spectrum block. Tuning and filtering is then done by a digital downconverter, which can process separate carriers out of the sampled spectrum block.
For a single-carrier design, each A/D samples only a single carrier. The overall effect of the IF filter in the single-carrier design is to reduce the difference in power between the strongest signal interferer and the wanted signal.
A multicarrier architecture has more dynamic-range requirements than a single-carrier design, since some of the strongest interferers in addition to the wanted signal are sampled by the IF A/D.
To estimate the effects of A/D noise and distortion, it is necessary to make some assumptions:
1. When the A/D must sample an interferer or adjacent channel, and the interferer or adjacent channel is 30 dB or greater above the wanted signal, then the total IF power will be approximately equal to the interferer or adjacent-channel power sampled by the IF A/D.
2. Based on this first assumption, the gain, either fixed or adjusted by an automatic gain-control circuit, will be adjusted so that the maximum IF signal energy will equal the nominal full-scale value of the IF A/D converter, so that the A/D will not saturate. Also from assumption 1, the gain will be scaled to accommodate the energy of the worst-case interferer or adjacent channel.
3. With a large interferer, the wanted signal at the digital output of the A/D will equal the nominal full-scale output value minus the difference in decibels between the specified interferer or adjacent-channel power and the wanted signal.
Estimating noise margin
To estimate the baseband bit error rate, it is important to calculate the ratio of the signal energy per bit to the noise energy per bit. In the case where the bandwidth is equal to 1/symbol-rate and there is no intersymbol interference, this is referred to as Eb/N0, where Eb = the energy per bit and N0 is the noise spectral density in the baseband spectrum.
In some cases such as GMSK modulation, which is used in GSM, the bandwidth of the baseband signal can be smaller than the symbol rate. As an example, the bit rate for GSM is 270 kbits/second while the bandwidth is only 200 kHz. This is possible because the phase of the transmit signal for GMSK modulation changes only 90 degrees for each bit. A more general formulation for noise energy per bit is expressed below:
Eb = S/R; En = (N0 x B)/R
so...
Eb/En = (Eb/N0) x (R/B) = S/(N0 x B)
Where R = bit rate, S = signal power, N0 = in-band noise spectral density, Eb = energy per bit and B = bandwidth.
In the general case where the baseband bandwidth is equal to 1/chip rate and there is one chip per bit (a chip is a single-phase transition pulse in a phase-shift keying system), Eb/N0 = (signal power)/(noise spectral density x bandwidth).
In the case of the code-division multiple access (CDMA) standards, there is an additional baseband process gain equal to the number of signal-phase transitions, or chips, per bit. Ec/N0, the energy per chip divided by N0, must be calculated first. In the case of CDMA, Ec/N0 = (signal power)/(noise spectral density x bandwidth). The Eb/N0 then equals Ec/N0 + 10Log(chips per bit) + 3.06. The additional 3 dB of process gain comes from CDMA's I/Q spreading. The number of chips per bit is also known as the spreading factor.
The cellular standards specify minimum bit error rates (BER) under certain operating conditions. When the protected or decoded BER is specified, then Eb/N0 must be evaluated as Es/N0 x 1/r where Es is the transmitted symbol energy and 1/r equals the number of transmitted bits (symbols) per information bit. The required Eb/N0 is then ascertained from standard curves that plot either the coded or uncoded BER as a function of Eb/N0. The actual Eb/N0 of the system is estimated and the difference between the actual and required Eb/N0, also known as the noise margin, is then calculated.
Estimating Eb/N0
In the noise-estimation process, we assume that the IF signal with interference is scaled to a nominal converter full-scale value. The thermal noise is first calculated at the antenna, over the bandwidth of a single carrier, and then compared with the wanted signal level to calculate the radio input signal-to-noise ratio (S/N). After the signal plus interferer is amplified to the appropriate full-scale value, the radio has added its own thermal noise. The radio noise figure is subtracted from the input S/N to reveal the S/N relative to the wanted signal. The radio noise figure is equal to the input S/N divided by the output S/N.
The in-band converter noise is ascertained in the following manner. The full-scale S/N specification of the converter is indicated for quantization noise, clock jitter noise and thermal noise, whose energy is evenly distributed over the band 0 MHz to Fs/2 MHz, where Fs is equal to the sampling rate. A process gain is incurred in the baseband filter by reducing the noise bandwidth from Fs/2 to the bandwidth of a single carrier. For a given reduction in noise bandwidth, a proportionate increase in S/N is incurred, which is the ratio of the signal to the level of in-band noise (in the single carrier).
Unlike random noise, whose level is reduced by lowering the noise bandwidth, harmonic noise generated in a converter tends to alias back into the wanted signal and third-order intermodulation distortion is also mostly in-band. Therefore, no process gain is applied to the harmonic noise. The harmonic distortion is added to the in-band noise to create a new in-band Sinad, or signal to noise and distortion.
The S/N of the wanted signal relative to the converter noise is simply equal to the full-scale converter S/N in decibels minus the difference in dB of the interferer and the wanted signal (Figure 2). This is because the full-scale power of the converter approximately equals the power of the interferer, and the wanted signal will be scaled down from full scale to a level equal to the specified difference between the interferer and the wanted signal.
The IF in-band noise from the radio and the A/D are added together to create a total-noise sum, which is then used to estimate the Eb/N0. The resultant S/N from adding the radio and A/D converter noise is equal to the linear product of the S/Ns divided by the linear sum of the S/Ns. In the case of CDMA, the S/N first calculated over the bandwidth of a single carrier is then increased by the spreading factor to provide additional process gain.
The specifications in Universal Mobile Telecommunications System (UMTS) with the greatest impact on the digital radio and A/D converter dynamic-range requirements are the interference specifications-namely, 3G TS 25.104 version 3.3.0, sections 7.4.1 and 7.5.1. For the speech mode, the spreading factor is 64 chips per bit, and the chip rate is 3.84 Mchips/s. A rate 1/3 convolutional encoder is used in the transmitter and a rate 1/3 Viterbi decoder is used in the receiver for error correction.
The UMTS standard specifies an interferer that is 100 dB above the wanted signal and within 20 MHz of the UMTS band. For this condition, we expect analog SAW filters in the radio to attenuate signals 20 MHz or less outside the band edge to a negligible amount relative to the 10-MHz offset interferer described below. The worst-case dynamic-range requirement is where the wanted signal is at -115 dBm, and is 75 dB below a UMTS signal whose power level is at -40 dBm and whose center frequency is 10 MHz, or two carriers more away from the wanted signal. With no interference, the minimum BER should be met with the signal at -121 dBm at the basestation receiver antenna. For all of the above test conditions, only a single user or code channel is active within the UMTS wanted signal. In UMTS, the signal bandwidth is 3.84 MHz. Each carrier's center frequency is 5 MHz from an adjacent carrier.
Because the interfering signal dominates the total signal power, we are concerned only with the peak-to-average power ratio of the -40-dBm channel. We can see from Figure 3 that the interferer has only a single code channel turned on, which produces a signal with a peak-to-average power ratio (PAPR) of 5 dB.
If we do not wish to require dynamic automatic gain control (gain control during active communication), and meet the 0.001-BER requirement at -121-dBm signal strength, with no interferers, then we must add an extra 6 dB of dynamic range to the A/D dynamic-range requirement, needed for the worst-case blocker conditions mentioned above.
For all intents and purposes, we will then stretch the worst-case blocker condition such that the wanted signal is at -121 dBm and the blocker is 81 dB above the wanted signal, at -40 dBm. We will now proceed with the noise-margin estimation.
The UMTS chip rate is 3.84 Mchips/s. For speech data, a rate 1/3, constraint-length = 9 convolutional coder is employed. For speech data, the spreading factor is 64 chips per bit with 3 dB of I/Q spreading gain, for a total baseband process gain of 21 dB.
The BER performance is specified for the 12.2-kHz speech data mode after interleaving and Viterbi decoding. A chart in the book CDMA by Andrew Viterbi (Figure 4) shows the "protected" BER for various Viterbi-decoding schemes as a function of Eb/N0 in a binary symmetric channel. The required BER for voice data, under the above conditions, is specified to be 10-3. It can be seen from that figure that the minimum required Eb/N0 is 2.7 dB.
Since Eb/N0 = Es/(N0 x r), Eb/N0 is derived from the in-band S/N by first calculating the coded symbol energy-to-noise density ratio, or Es/N0. Es/N0 equals the in-band S/N, plus the 64-chip/bit process gain of 18 dB, plus the 3 dB of process gain that results from I/Q spreading. Because a rate r = 1/3 coder is used by the UMTS reverse channel, we add another 4.77 dB to Es/N0 to arrive at the uncoded Eb/N0.
For example, we choose the A/D nominal-power level to be 5 dB below full scale to account for the 5-dB PAPR of the interferer. We see from the table (Fig. 3 again) that the resulting noise margin for a 5-dB NF radio, whose output is sampled by the ADS5410, operating at a nominal power level of -5 dBFS (relative full scale) with the interferer, is more approximately 5 dB.
From Fig. 4, we can observe:
For a -124-dBm UMTS signal with a -40-dB interferer and a relaxed radio noise figure of 5 dB, the required A/D S/N, commonly specified over the band Fs/2, is approximately 9 dB to 5 dB, or 4 dB lower than the required in-band distortion; for UMTS, we exceed the dynamic-range requirements with in-band noise and distortion that is only 70 dB or more down from the analog-to-digital converters' nominal full-scale value; the BER performance in the UMTS basestation receiver is more dominated by the analog radio noise; and BER performance does not improve much with reduced in-band A/D converter noise and distortion levels when the sum of this distortion is already more than 70 dB down off nominal full scale.
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For more on this subject see:
1. "Low-Voltage LDOs Juggle Loads and Power Savings"; www.CommsDesign.com/story/OEG20020709S0018.
Richard Cesar (r-cesari@ti.com) is a senior wireless-comms system engineer for Texas Instruments Inc. He holds BSEE and MSEE degrees from Tufts University (Medford, Mass.).
