An instrument for testing North American digital cellular radios - Hewlett-Packard's HP 11846A; includes related article on HP 11846A filtering technique

The HP 11846A is designed to produce filtered [pi]/4 DQPSK modulated I and Q baseband signals needed to test digital cellular radios.

RAPID GROWTH IN THE DEMAND FOR AMPS (Advanced Mobile Phone Service) cellular radios in North America has caused saturation in current analog cellular frequency bands. This has spurred the development of a new digital cellular standard that will increase the spectrum efficiency of cellular radios to allow more users to share the same frequency spectrum. The Telecommunications Industry Association (TIA) has commissioned a group to define this next-generation cellular radio system. Known as the TR 45.3 committee, this group of industry representatives has issued specifications defining the new digital cellular system. The new system requires radios to conform to the old AMPS analog specification as well as the new digital system, hence the name North American Dual-Mode Cellular System (NADMCS). The dual nature of the radios was deemed necessary to ensure compatibility with current cellular systems. These radios will operate as analog AMPS radios in areas that do not require the increased capacity offered by the digital system, and in the digital mode in high-use areas. The new dual-mode radios will require testing for both the analog and digital operating modes. The analog tests can be made with currently available test equipment. The HP 11846A x[pi]/4 DQPSK I-Q generator and the HP 11847A iT/4 DQPSK modulation measurement software are two products designed to test the radios' digital mode.

The NADMCS uses a digital modulation format known as [pi]/4 DQPSK. This system is a time-division multiple-access system that allows up to six users access to a given frequency channel concurrently. Because of the backwards compatibility with the current AMPS cellular system, the channel spacing continues to be 30 kHz. The digital information symbol rate is 24.3 kHz, and to control the spectral energy from the digital transmission, a square root raised cosine filter with a roll-off factor of 0.35 is used to smooth the phase transitions. The HP 11846A [pi]/4 DQPSK I-Q generator is designed to produce filtered I-Q baseband signals needed to create the modulation format used by the NADMCS. The HP 11846A approach for implementing this modulation format yields a simple yet effective technique for generating [pi]/4 DQPSK modulation. When used with an I-Q generator, such as the HP 8780A vector signal generator,(1) the HP 11846A can provide accurate [pi]/4 DQPSK modulated signals for testing North American dual-mode digital receivers. An overall block diagram of the HP 11846A is shown in Fig. 1.

The HP 11847A 77/4 DQPSK modulation measurement software performs accurate verification of the RF performance of cellular transmitters conforming to the TR 45.3 committee recommendations. This software package uses digital signal processing techniques to demodulate the RF signals, recover the data, and measure the modulation accuracy. The HP 11847A digital signal processing techniques result in excellent modulation measurement accuracy and repeatability.

This article provides some background information about digital modulation format and raised cosine filters, and then covers the implementation of the HP 11846A filtered [pi]/4 DQPSK modulation scheme. The HP 11847A measurement software is described in the article on page 73.

Digital Modulation

The modulation format chosen for the NADMCS system is [pi]/4 differential quadrature phase shift keying ([pi]/4 DQPSK). To understand how this modulation format works, we will look at some basic building blocks for digital modulation.

I-Q Diagrams. I-Q diagrams are frequently used to analyze the performance of digital communication systems. The modulation signal has two components, called in-phase (1) and quadrature (Q). The I axis and the Q axis form a coordinate system that presents the magnitude and phase of the signal being analyzed. The length of the vector from the origin represents the magnitude of the signal, and the angle of the vector referenced from the positive I axis indicates the phase of the signal (Fig. 2). To determine the phase and magnitude of a digital signal, a reference signal must be available. On the transmitting side, the reference signal comes from a local stable oscillator. On the receiving side, the reference is usually derived from the incoming phase-modulated signal. Fig. 2b shows four signals of varying phase and their associated I-Q diagram.

Digital communication systems use a combination of RF signals of specific phase and magnitude to represent specific bit patterns. The simplest method of doing this is on/off keying. In this method a digital one is transmitted when the radio carrier is on for one data clock period and a digital zero is transmitted when the carrier is off for one period. The I-Q diagram for on/off keying is shown in Fig. 3. Note in Fig. 3 that there are two states, one for each bit of information transmitted.

QPSK Modulation. QPSK, or quadrature phase shift keying, uses one of four phase states to represent a particular data symbol. An I-Q diagram of QPSK is shown in Fig. 4. The reference chosen for zero degrees is arbitrary. In this system, two bits are required to define the possible phase states, because for any data symbol, there are four potential phase states. As shown in Fig. 4b, determining the phase relationships of digital bit patterns requires a known phase reference for comparison.

DQPSK Modulation. DQPSK, or differential quadrature phase shift keying, is a modification of QPSK modulation. This format also has four potential phase states, which require two bits per data symbol. The difference here is that the phase states are defined relative to the last phase state. This means that the absolute phase of the system is not required because the phase of the current symbol is determined from the phase state of the previous symbol. The phase state of a symbol is determined by the phase transition defined for that symbol. For example, consider the phase transitions defined for the following symbols.

  Symbol                DQPSK Phase Transition
           00                             0[deg]
           01                            90[deg]
           10                            90[deg]
           11                           180[deg]

Based on these definitions, symbols arriving in the following order would have the associated phase states, assuming an initial state of 0'.

Thus, the phase state of the current symbol is dependent on the phase state of the previous symbol and the phase transition defined for the current symbol. [pi]/4 DQPSK Modulation. The ir /4 DQPSK modulation system is very similar to DQPSK, in that it is a differential quadrature phase shift system. The difference is that in the I-Q plane, the possible phase states rotate 45 degrees for each symbol. Table I compares the phase transitions for DQPSK and [pi]/4 DQPSK.

The constellation of points on the I-Q diagram now has a total of eight points, but only four are possible for any given symbol. Fig. 5 shows the possible constellation of points for [pi]/4 DQPSK. If the initial phase is at 0 degrees, the possible phase states could be 45, 135, 225, and 315 degrees. For the next symbol, the possible phase states would be 0, 90, 180, and 270 degrees. This pattern continues, allowing a total of 8 phase states for [pi]/4 DQPSK.

The key advantage of [pi]/4 DQPSK modulation is that the spectral energy can be contained to a fairly small bandwidth for a given data rate compared to other modulation formats. In [pi]/4 DQPSK modulation, in which the phase transitions are [+ or -]45 degrees and [+ or -]135 degrees, spectral energy can be controlled by keeping the phase transition per symbol low, and also by reducing the signal amplitude during large phase transitions. Fig. 6 shows unfiltered phase transition trajectories for [pi]/4 DQPSK. The [+ or -]5-degree rotations have small amounts of phase rotation, so the amplitude remains virtually constant. During the larger -135-degree transitions, however, the amplitude is significantly reduced, which helps control the spectral energy. Filtering

The unfiltered phase transitions for 1T/4 DQPSK shown in Fig. 6 produce sharp trajectories in the I-Q plane, which result in a large amount of spectral splatter during phase transitions. To control the spectral splatter, filtering is applied to the baseband I-Q signals. The filter used in the NADMCS is a square root raised cosine filter with an [alpha] (roll-off factor) of 0.35. The raised cosine filter not only minimizes spectral splatter, but also reduces intersymbol interference. Intersymbol interference is caused by the effects of all the filtering at various locations (transmitter, channel, and receiver) throughout a typical baseband digital system (see Fig. 7). This makes data detection more difficult, and filtering is applied to reduce intersymbol interference.

The theoretical minimum system bandwidth needed to detect 1/T symbols/s without intersymbol interference can be shown to be 1/2T Hz. For this case, a rectangular filter shape in the frequency domain is required. This type of filter is difficult to approximate, but if the filter bandwidth is increased, the approximation task is made much easier. This modification to the filter bandwidth is defined by a term called the filter roll-off factor, or [alpha]. Let W[.sub.o] represent the theoretical minimum bandwidth, 1/2T Hz. Let W represent the bandwidth of the filter. The roll-off factor is defined to be [alpha] = (W - W[.sub.o])/W[.sub.o]. The roll-off factor specifies the required excess bandwidth divided by the filter's - 6dB bandwidth. Fig. 8a shows the frequency response of a raised cosine filter for several values of [alpha]. Notice how the amplitude response is 6 dB down at the theoretical minimum bandwidth point, regardless of the value of [alpha].

Fig. 9 shows the impulse response of a raised cosine filter with an [alpha] of 0.35. By examining this response, one can see that the impulse response crosses through nulls at symbol decision points.* This implies no intersymbol interference when this filter is used.

To achieve optimum signal-to-noise ratio, a matched filter situation must be used. This implies a similar filter in the transmitter and receiver. To accomplish this, the raised cosine filter frequency response is modified by taking the square root of this function. This yields a square root raised cosine filter. The et of the filter is the same as the original raised cosine filter. Fig. 10 shows the impulse response of a square root raised cosine filter with an a of 0.35. Notice that this impulse response does not have nulls at symbol decision points. This indicates that there will be intersymbol interference for this filter characteristic. The intersymbol interference problem is rectified because the receiver has another square root raised cosine filter. When the transmitted data is filtered by the receiver's square root raised cosine filter, the received data should have no intersymbol interference. This is the filter arrangement chosen for the NADMCS. Fig. 1 1 shows a better comparison of the impulse response of the raised cosine and square root raised cosine filters.

Filtered [pi]/4 DQPSK Modulation

The HP 11846A generates a square root raised cosine filtered I-Q output using an FIR finite impulse response) type of digital filter. The HP 11846A implementation uses a ROM-based FIR filter, which allows a fairly simple hardware design. The block diagram of a conventional ROM-based filter for [pi]/4 DQPSK is shown in Fig. 12. The incoming data bits are input to the serial-to-parallel converter which separates the first and second bit of each symbol into separate data paths. The symbol data is then differentially encoded and enters a shift register. The length of the shift register is determined by the FIR filter length. In the case of the HP 11846A, the FIR filter length is eight, making the output of the shift registers eight-bit parallel data. Outputs from both shift register banks are applied to the ROM address lines, giving 16 address bits. The ROMs perform a convolution of the input data with the filter's impulse response to produce the I-Q output data. The box on page 71 provides more detail about the ROMS' convolution operation.

The HP 11846A updates the I-Q outputs at a rate 16 times the NADMCS symbol rate. This allows the HP 11846A to generate a smooth I-Q trajectory between symbol decision points, which is necessary to control unwanted spectral energy. For 16 subintervals per symbol, four address bits are required to be presented to the ROM address line. Adding the 16 address bits mentioned above, this implies a total ROM address space of 20 bits, or 1M bytes of address space. For 16-bit-output ROMS, this implies 16M bytes of storage for both the I and Q ROMS, for a total of 32M bytes of ROM storage. This amount of ROM was impractical, so a different approach to a ROM-based filter was implemented.

Fig. 13 shows the filter block diagram used in the HP 11846A. The key difference is that the I and Q ROMs have been replaced by cosine and sine ROMS. The I and Q outputs are now generated by an addition and subtraction of the sine and cosine ROM data. The key to being able to use this type of approach was recognizing that a/4 DQPSK can be generated from DQPSK by a 45-degree rotation every symbol. By using a coordinate transformation technique, the I and Q outputs are broken down into their cosine and sine components (see the box on page 71). The result is that the address bits required for any of the ROMs in this implementation are:

  Number of Bits                Description
           8           Bits from shift register, either
                       the first or second bit per symbol.
           3           Bit counter. This counts the
                       45-degree rotation modulo 8.
           4           Subinterval counter.

The number of address bits to any given ROM is therefore 15. In this implementation, four ROMs (two ROMs for the I channel and two ROMs for the Q channel) are required, compared to the two ROMs in the conventional filter implementation. The overall result is a reduction by a factor of 16* in the memory required to implement the FIR filter. This reduction of memory not only saves cost, but significant printed circuit board area. In addition, since all of the filter information is stored in ROM, as new communication systems come on line, potentially with different filter characteristics, only a ROM change is required to meet the needs of these systems.

Measurement Specifications

The [pi]/4 DQPSK modulation format required a new method for measuring modulation accuracy. In conventional analog modulation, FM for instance, the figures of merit are distortion and deviation. Therefore, if the deviation, rate, and distortion can be precisely measured, the transmitter is accurately characterized.

In digital modulation systems, such as the NADMCS, phase accuracy at the decision points is the main figure of merit. However, since [pi]/4 DQPSK is not a constant-amplitude system, both the amplitude accuracy and the phase accuracy are important. The TR 45.3 committee has recommended that this modulation be measured in terms of magnitude of vector error. In an I-Q diagram, the vector error is measured by plotting the desired decision point and the measured value at the decision point. The vector error is computed by measuring the vector length between the two points (see Fig. 14). In the NADMCS, the phase of the vector error is not deemed to be important, but only the magnitude of the vector. The HP 11846A has typically less than 1% vector error magnitude for its I-Q outputs. This compares with the NADMCS system modulation accuracy specification of less than 12.5%.

Conclusion

The HP 11846A provides a highly accurate and efficient implementation of [pi]4 DQPSK modulation. This I-Q source can be used to verify the performance of the new NADMCS radio receivers. The HP 11847A analysis software allows characterization of the NADMCS transmitters for modulation accuracy. Additional test equipment is required to characterize NADMCS radios fully, but these two products test the heart of this new system. The NADMCS system provides almost a six-to-one improvement in capacity over the current analog AMPS cellular system. Because of the increased spectral use, digital modulation formats such as the NADMCS system will be the communication systems of choice for the future.

Acknowledgments

The author would like to thank Ray Bergenheier, who developed the mathematical approach used for the HP 11846A ROM lookup data, and Al Tarbutton, who sat in on the TR 45.3 committee and assisted in the design of the HP 11846A digital filter. Thanks also to Ken Thompson and Bob Garner who contributed to writing this article.

Reference

1. Hewlett-Packard journal, Vol. 38, no. 11, December 1988, pp. 4-52.

HP 11846A Filtering Technique

The implementation of the digital filtering scheme for the HP 11846A is shown in the detailed block diagram shown in Fig. 1. The input bit stream a, for the U.S. cellular system is at 48.6 kbits/s. The [pi]/4 DQPSK modulation has two bits/symbol, so the serial-to-parallel block separates the first and second bits. The differential encoder block performs phase rotations of the input symbol relative to the current phase state, The differential encoder block is implemented for DQPSK modulation, not [pi]/4 DQPSK modulation, Transfer to unit circle is a scaling operation that translates the I-Q phase states to a unit circle. Before the phase rotation block the modulation is strictly DQPSK and after phase rotation it becomes DQPSK modulation. The final operation is to take the desired filter characteristic, which is a square root raised cosine filter, convolve the input data with the filter impulse response, and generate the desired I and outputs.

To help understand the symmetry used for this modulation format, refer to Table I on page 67 which compares the effect on a given input symbol for the two modulation formats. Related to regular DQPSK, the [pi]l4 shift represents a coordinate shift of [pi]/4 radians every symbol period. This rotation is described as a modulo 8 characteristic, since after eight symbols the shifts have increased the phase 360 degrees.

To generate 7T/4 DQPSK, the following coordinate transformation is performed on the DQPSK formatted data (C[.sub.k] and in Fig. 1).

I[.sub.k] = C[.sub.k]cos(k[pi]/4) - D[.sub.k]sin(k[pi]/4)

Q[.sub.k] = C[.sub.k](k[pi]/4) + D[.sub.k]cos(k[pi]/4).

where C[.sub.k] and D[.sub.k] represent the I and components of the DQPSK modulation, and represent the I and components of [pi]/4 DQPSK modulation, and k represents the kth symbol. These two equations show a rotation of [pi]/4 radians per symbol. The argument k[pi]/4 repeats every eight symbols, since at this point a rotation of 2[pi] radians has occurred.

Generating ROM Lookup Data

To generate the ROM lookup data and thus the desired output data, the input data must be convolved with the impulse response of the desired filter. A standard equation for this process is:

[FORMULA OMITTED]

where X(k) is the discrete data input stream, h(n - k) is the impulse response of the desired filter, and Y(n) is the output at the time of the nth sample.

For the following discussion g(t) represents the square root raised cosine impulse response, which is the IT/4 DQPSK filter's impulse response. A plot of this impulse response is shown in Fig, 1 0 on page 69. Note that for convenience, the impulse response has been shifted in time to go from zero to the filter length. This choice prevents having any negative time representations for the filter impulse response equations. Given this choice the continuous time outputs for the I and Q channels are: where T is the sample time and k is the kth element of or Substituting in the expressions for the coordinate transformation from DQPSK to DQPSK yields.

[FORMULA OMITTED]

where k = (t/T - L + 1)[equal to or less than]k[equal to or less than](t/T) and L is the length of the filter response in symbols.

When these limits of summation are referred to the impulse response then g(t - kT) has limits of g((L - 1)T) to g(O). These limits agree with Fig. 10, which has the impulse response defined from 0 to L. From these equations, we can determine the minimum information needed to compute the I and filter outputs. The information needed is:

* The time relative to the last data symbol clock time (i.e., the subinterval position with each data bit)

* The past L data bits, C[.sub.n],C[.sub.n] 1,...,C[.sub.n] L 1, and D[.sub.n],D[.sub.n] 1,..., D[.sub.n-L-1]

* k[pi]/4 modulo (2n).

If we let t = t[.sub.1] + nT, 0 < t, < T, the resolution of t is determined by the desired number of subintervals that should be computed. In the case of the HP 1 1 846A, we chose to implement 16 subintervals per symbol. The benefit of computing subinterval points is that the phase transition between symbol intervals can be smoothed and the spectral energy controlled. Sixteen subintervals has proven to allow a very smooth transition between symbol phase states.

With the above definition for t[.sub.1], we can state the following for the first term of i(t).

[FORMULA OMITTED]

summed over m=O to m= L- 1 +

The information needed to compute this term includes:

* t[.sub.1], which is the time from the most recent data symbol occurring at t=nT. Since we are using 16 subintervals, four bits are required for the lookup ROM address.

* C[.sub.n], which is the most recent input bit. C[.sub.n] L-1 is the input bit the farthest in the past. We are using a total of L values of C[.sub.n-m] in this computation.

* n, which is the input bit counter. Since cos((n-m)[pi]/4) has a

period of eight, the input bit counter can be counted modulo

8. This implies that three address bits are required for the

ROM address.

The HP 11846A uses 16 subintervals and a filter length of eight, which results in requiring 15 address bits for the lookup ROMs.

From the above discussion, the final design equations for the lookup ROMs are:

[FORMULA OMITTED]

where t, = t - nT and nT < t < (n 1)T. T is the symbol period and n is a bit counter.

The sine and cosine ROMs shown in Fig. 1 contain the summation terms for the I and equations described above.

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