Author: Frank W. Raffaeli
Abstract:With the advent of digital broadcasting, radio manufacturers are seeking solutions that integrate AM, FM and digital demodulation capability in one low-cost package. The Direct I.F. sampling or DIF method yields the best performance and flexibility. Usual DIF sampling techniques require a DSP or DSP core to process the I.F. signal. Dedicated hardware can provide a smaller and more cost-effective solution over the DSP methods. By applying several advanced techniques, a dedicated, mixed signal IC can remain flexible enough to satisfy a variety of system requirements, including reception of conventional AM and FM broadcasts, yet at a far lower cost than other solutions with comparable performance.
Digital Broadcast and Digital Demodulation
The word `digital` is unfortunately all encompassing and is used to describe a variety of processes. Within the context of this report, the word `digital` will refer to one of the following two processes:
Demodulation refers to the means whereby the information is extracted or recovered from the radio carrier. The original information (commonly termed baseband) may be either in analog or digital format. Demodulation can be accomplished by analog or by digital processing. Typical analog FM demodulation circuits include the following:
Digital Modulation for Broadcast
A baseband signal may include, either in whole or in part, some form of digital information. Bandwidth utilization efficiency can be improved by taking advantage of the correlated properties within music or speech programming. In digital format, an audio program may be compressed many times through the use of a transform coding technique such as those used in MPEG audio formats. Versions 2 and 3 are in common usage at the time of this writing. The encoded, compressed information is broadcast, and a reverse coding process is necessary in the receiver to recover the original program. This report does not address the compression and decompression aspects of the receiver hardware, but rather the recovery of the baseband information from the radio signal.
Radio Receiver Architecture Fundamentals
Figure 1 shows a block diagram of a generic radio receiver capable of demodulating an analog or digitally encoded radio carrier.
Figure 1 - Generic radio receiver
The R.F. input amplifier, oscillator and mixer comprise
a system referred to as the down converter. The down converter tunes
the incoming signal, and translates the frequency to a common value known
as the intermediate frequency or I.F. The use of an I.F. allows
for a more efficient design, because most of the selectivity and gain is
within this stage - at a single frequency. When the intermediate frequency
is zero, the architecture is known as zero IF. In a zero IF receiver, the
variable bandpass filter in figure 1 becomes a variable lowpass filter,
and the conjugate quadrature (I and Q) components of the signal are processed
within the demodulator to extract phase and amplitude information.
Radio Broadcast Methods
Radio broadcasts use one of the following methods:
Frequency modulation is an effective method for transmitting reasonable fidelity. The parameters, such as modulation index and channel spacing, vary depending upon the specific government standard; however, the basic method for demodulation remains consistent. Adaptive filtering of the I.F. bandwidth is required to achieve optimum fidelity and selectivity.
Amplitude modulation is used normally on more narrow-band information. The bandwidth may be restricted to 4 kHz or less, and the channel spacing varies from 8 to 10 kHz. The key to good AM receiver performance is good selectivity.
DAB (Digital Audio Broadcast)
An emerging broadcast standard known as the Eureka 147 system broadcasts a digitally modulated carrier at 1.47 GHz. Multiple digital audio data streams are time-division multiplexed after a transform coding has been applied. The Eureka signal is phase-coherent and can be demodulated provided correlated amplitude and phase information is extracted from the carrier.
The CD radio and XM audio satellite systems are both subscription services that offer Digitally modulated program information. Although the details of the modulation technique are proprietary, the overall method requires that the correlated phase and amplitude information be extracted from the carrier, as in the Eureka 147 system.
This form of digital broadcast includes a digital signal that co-exists with the analog AM or FM channel. The modulation technique, like the satellite system, is proprietary, and each radio station is capable of only a single digital program channel.
Direct I.F. Sampling and Digital Demodulation
The premise of a digital, direct I.F. sampled radio is relatively simple. Either the I.F or baseband signal may be sampled directly by a high performance A/D converter. The sampled signal is then processed in real time while it is in digital form. By applying a combination of algorithms, the information contained within the radio signal is extracted. Although the concept of a software radio began as an idyllic goal, successful design and applications of high performance A/D converters and low-cost DSP engines have made this theory a basic reality.
DSP without the DSP
Typical architecture of a direct I.F. radio includes a DSP IC as a core processor. The DSP performs tasks such as I.F. sample to quadrature vector conversion, decimation filtering, low-pass filtering, and trigonometric functions required for phase demodulation. Since the functions of a direct I.F. demodulator are well understood, it may be worthwhile to consider dedicating the hardware for these tasks in order to eliminate the DSP. Figure 2 shows a block diagram of the direct I.F. system architecture. Carrier phase information is recovered from the In-phase and Quadrature (I and Q) components of the signal after a trigonometric transform is applied. Taking the derivative of the phase difference with respect to time can extract FM. Amplitude information can be calculated by the absolute magnitude of the IQ vector.
Figure 2 - Direct I.F. digital processing - block diagram
Digital Processing Advantages
In a digital broadcast, even if the signal is demodulated with analog techniques, it must be available in a digital format to apply the reverse transform coding. If the signal is already in digital format, The high performance A/D converter and the associated conversion losses can be eliminated. For FM demodulation, Digital processing yields perfect linearity, as well as freedom from calibration drift and alignments common to analog quadrature detectors. Freedom from drift is especially important in automotive applications, where vibration and shock can de-tune an analog adjustment over time. Reception of a radio signal from a moving vehicle can be quite tricky. To improve reception, especially with the Eureka system, a diversity antenna is required. A diversity antenna system controls the antenna directivity pattern dynamically, in order minimize multipath and signal fading effects. The diversity control software and hardware requires accurate information about the quality of the radio signal. A digital demodulator can serve as a better complement to a good diversity system than an analog system can because more information is available e.g. amplitude and phase. The optional signal derivatives are also easier to create, such as modulation components within a particular frequency range. One method used for early indication of multipath distortion, for example, uses the demodulated derivative of the signal phase as a primary input to the diversity controller. There are several other applications that are implemented more efficiently with a direct digital interface, as in the case with transform coding. Many receivers now employ digital audio processing for functions such as:
A simple but performance-limited type of digital demodulation is possible simply by recursively sampling the I.F. signal at the right point(s) in time and keeping track of their significance. Figure 3 shows a sinusoidal waveform, such as the I.F. in a receiver, sampled every ¼ cycle. One way to better understand this process is to view the generic modulation operator on the original carrier. A radio signal S(t), phase modulated by a quadrature baseband signals I(t) and Q(t) with frequency w and amplitude As would have the following expression:
(1) S(t) = As· [I·cos(wt) + Q·sin(wt)]Quadrature baseband signals I and Q are conventional representations of the modulus of the In-phase (I) axis, chosen arbitrarily, and the Quadrature (Q) component, which lags the In-phase component of the carrier by 90 degrees. Note that any type of modulation is possible with this expression: phase, frequency and amplitude. For a linear system, the reciprocal case is also true: demodulation of any modulation type is possible simply by recovering the quadrature baseband components.
Figure 3 - a simple I.F. sampling demodulator
The digital sampling demodulator shown in Figure 3 is capable of recovering the baseband I and Q components. Applying convolution theory and assuming an equivalent zero-order hold for the sampling detector yields the relation:
(2) S(t) ® s(w) = S [I(w+ n/T) + Q(w+n/T)]Where T is the sampling period and nth component in the frequency domain occurs at a multiple of the sampling frequency. In the example of figure 3, the signal is aligned with the Q component and has no I component. The vector representation is therefore magnitude of 1 with an angle of p/2 or 90 degrees. Because the choice of the In-phase component is arbitrary, this signal is merely thought of as having a magnitude of 1. The relative angle is measured with respect to the sample timing.
The digital demodulator shown in figure 3 does not necessarily require sampling beyond the Nyquist rate for the I.F., provided the I.F. Bandwidth is sufficiently narrow. Figure 4 illustrates the under-sampling artifacts in the frequency domain which occur as a result of sampling the I.F. at a rate of 1/T:
Figure 4 - effects of under-sampling the I.F.
Direct I.F. – Processing Elements
The direct digital demodulator processing elements as outlined in figure 2 are as follows:
A/D converter / I.F. SamplerA/D converter / I.F. sampler
Digital I.F. sample to I&Q vector conversion
I&Q vector to phase conversion
Phase Differentiator for FM detection
Vector magnitude function for AM detection
Quantization and sampling effects must be considered. A good digital I.F. processor will include some capability for features such as dynamic bandwidth adjustment, amplitude demodulation, AM rejection for FM and PM detection, and dynamic AGC (automatic gain control) of the I.F. amplifier. The converter must also have sufficient bandwidth to pass the I.F. frequency without appreciable amplitude or group delay distortion across the I.F. bandwidth. A reasonable guideline is for the default signal level to occupy the 1/3 of the dynamic range, leaving 2/3 of the total as dynamic headroom.
Digital I.F sample to I/Q vector conversion
The I&Q demodulator example of figure 3 samples the I.F. at 90 degree (p/4) intervals. This is also known as orthogonal sampling. There are significant drawbacks to the orthogonal sampling technique. A p/4 period requires a sampling rate of 4x the I.F., or 4x a sub-multiple of the I.F. as in the case with an under-sampled system. The sampling system, e.g. the A/D converter and A/D clock generator both generate currents within the system at the sampling rate. Because the sample clock harmonics fall directly at the intermediate frequency, it can be tricky to suppress them and they may cause interference with the I.F. Orthogonal sampling is also sensitive to signal distortion because of the correlated nature of the sample timing.
Figure 5 - 9p/7 non-orthogonal sampling
A better approach to I&Q vector conversion is to use a non-orthogonal technique. Figure 5 illustrates the vector constellation of a 9p/7 sampling rate. Specifically, a 10.8 MHz I.F. is sampled at 16.8 MHz. Using this technique, sample clock interference is reduced and effective dynamic range is improved. The signal to noise ratio of the recovered I&Q digital baseband information can be calculated for both orthogonal and non-orthogonal cases as a function of A/D effective resolution, I.F. noise floor, and bandwidth as shown in the formula:
(3) S/N =20·log10· [ S (Pn·Ad)/(1/2N + Vnf·ÖHz) ]Where:
Pn = nth IQ 9p/7
or p/4 normalization coefficient
Ad = Fraction of useable dynamic range
N = A/D converter effective binary resolution
Vnf = I.F. noise floor voltage
Normalization coefficients are calculated by:
(4) Pn(I) = cos(1/nT)
(5) Pn(Q) = sin(1/nT)Figure 6 below shows the S/N of the digitally recovered baseband information as a function of A/D converter resolution for both orthogonal and non-orthogonal sampling methods, as calculated by the formulae (3-5). The dynamic range, Ad is 1/3.
Figure 6 - S/N of I&Q vs. A/D resolution
The bandwidth of the recovered data is 384 kHz and the I.F. noise floor is -120 dBc/Ö Hz.
At 7.5 bits of A/D resolution, the non-orthogonal method yields a 10 dB improvement in baseband S/N ratio over the quadrature sampling method. In practice, an even better improvement is found due to the correlated aspects of the distortion and noise on the I.F. signal. If amplitude demodulation is not required, or if strong AM rejection is unimportant, then the Ad coefficient may be increased by as much as 2x, yielding equivalent performance for one less bit of A/D converter resolution.
I&Q vector to phase conversion
Binary IQ to phase vector mapping can be simplified by applying the symmetry of the IQ vector space.
Figure 7 - IQ symmetry & phase demodulation
Figure 7 shows the circle divided into octants, with the resultant first 3 corresponding bits arbitrarily assigned. Note that the angle `wraps` through the zero point from 111 back to 000. First, the circle is divided into quadrants, simply by using the sign of the I&Q vectors to determine the first two bits. Then, the quadrants are bisected by comparing absolute magnitudes of I&Q.
Within the octant, the final result must be determined by estimating the arctangent of I/Q. Figure 8 illustrates the linear approximation and the piece-wise correction factor.
Figure 8 - Linear approximation and correction
Phase Differentiator for FM Detection
Once accurate binary phase has been determined, FM calculation merely requires differentiation with respect to time. If the phase detector output sample rate is 384 kHz, for example, FM baseband information can be extracted by low-pass filtering the phase difference at each sample interval. The best case S/N ratio for strong signal reception can be calculated by:
(6) S/N = 20·log10 · [ SNRbb·(BWIF/2·BWFM) ]
For the text example, using a 7.5 bit A/D for the I.F. sampling, in the non-orthogonal case, and limiting the recovered demodulated bandwidth to approximately 17 kHz, SNR = 67 dB.
Vector Magnitude: AM detection
Absolute magnitude of the I&Q vector sum can be calculated by the sum of squares method. As in the FM case, low-pass filtering is required and the SNR is dependent upon recovered bandwidth.
System Cost Compared to the Soft Radio
Integration of the digital demodulator reduces system
cost by eliminating the DSP and its associated support circuitry. In the
integrated solution, an embedded A/D converter may be used, depending upon
baseband S/N requirements. Imbedding the A/D and other components reduces
the pin count and area as well. The table below details the cost difference
of some of the key blocks common to both types of implementation.
|Block||Integrated cost||DSP cost|
Table 1 - cost of integrated DIF vs. soft DSP
Many have opted for the soft radio solution because of ease of development time and flexibility. Because of the availability of comprehensive and simple design tools, there are fewer obstacles to ASIC development as there once were. Much of the effort and expense is in the design, simulation, and test vector generation. All examples illustrated in this text were built and tested using an FPGA (field programmable gate array) in conjunction with a 6-bit 20MHz A/D converter. The FPGA type is the Altera EPF 6016 with the associated modeling and programming software. The system can be kept soft and flexible, like a programmable breadboard, operating in a live environment, and in real time. At design completion, there are many companies offering the service of ASIC conversion from the FPGA netlist files.
A digital demodulator can be implemented in dedicated hardware to realize all of the performance benefits of a soft DSP system, but at a fraction of the cost. The integrated system described herein is ideal for automotive, as well as other portable applications requiring high performance at reasonable cost.