cdma waveform generation

FILTRONIC PLC - COMPANY PROPRIETARY

ABSTRACT A design for the generation of wideband code division multiple access (WCDMA) waveforms in digital radios is presented in this paper. An architecture that provides a digital intermediate frequency (IF) eliminates the need for a balanced quadrature modulator. The digital modulator performs pulse shaping on input complex data streams and then interpolates those signals to a multiple of the chip rate. Quarter-band sampling is used to generate a digital IF that is one fourth the final sample rate. Selection of a digital-to-analog converter (DAC) is also covered in the paper. Graphs demonstrate the effect of pulse shaping and CDMA user loading on the transmitted waveform’s peak-to-average power ratio (PAPR).

INTRODUCTION To handle high-speed internet service and real time video applications, the European Telecommunications Standard Institute (ETSI) selected WCDMA for third generation wireless service. The WCDMA format covered in this paper is defined by the 3rd generation Partnership Project (3GPP) [1]. In this paper, we present methods for the generation of WCDMA waveforms through an entirely digital process. Our target system is a single carrier WCDMA base-station, although we will close with extensions to support multi-carrier base-stations. The digital signal is placed at an intermediate frequency eliminating the need for a quadrature modulator. While analyzing the design, elements of WCDMA are also presented. A conventional super-heterodyne design is depicted in Figure 1. In this architecture, the complex baseband data is filtered and promptly converted to an analog signal. After the DAC, the signal is passed through a quadrature modulator which may then continue on to several stages of mixers and filters to reach the desired radio frequency. The performance of the quadrature modulator is especially critical when looking at the error vector magnitude

(EVM) of the transmitted signal. A simple digital correction circuit will remove constant amplitude and phase error. Should the errors vary with frequency, a much more complicated correction system is required. The advantage of this architecture is that the DACs only need to sample at the bandwidth of the signal so higher data rate signals may be generated.

Figure 1. Conventional transmitter architecture. The architecture presented in this paper is shown in Figure 2. Here, the DAC generates the modulated signal at an intermediate frequency that is then converted to the RF. The quadrature modulator has been eliminated although more stages of converters may be necessary to reach the RF.

Figure 2. Digital IF architecture. Continued improvements in DACs should eventually allow the IF to be moved up sufficiently to eliminate an entire mixer stage. Our design uses a 61.44 MHz sample rate which when combined with quarter-band sampling yields an IF of 15.36 MHz. The 61.44 MHz comes from choosing a multiple of the chip rate (preferably one that is a power-of-two multiple).

SYSTEM DESIGN This paper presents some of the design issues when dealing with WCDMA waveforms. The modulator receives digital

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CDMA Waveform Generation for Digital Radios

George Aliftiras - Filtronic Sigtek


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baseband samples from the base-station processor and converts these to an RF signal. The samples must be filtered, interpolated, and then mixed onto an appropriate IF. The two parameters we will use to define the performance of our system will be EVM and adjacent channel leakage ratio (ACLR). Both of these are defined in [2]. The input to the WCDMA modulator is complex baseband data from the digital signal processor

b(k)=ai(k)+jaq(k) (1)

where ai(k) and aq(k) are the in-phase and quadrature components of the baseband signal. The value k represents discrete time samples arriving at a rate of 3.84 MHz, the WCDMA spreading rate. The data ai(k) and aq(k) represents the user data modulated with the spreading sequences for the base-station. The baseband data is the sum of all the individual channelization codes active in the radio. The 3GPP specifications define the test procedures which include a typical user loading. In this paper, we use test model 3 as defined in [2].

PEAK-TO-AVERAGE POWER RATIO One of the unusual elements of the WCDMA format is the variable peak-to-average power ratio (PAPR) which is based on the current user loading. The PAPR is a function of the envelope of the signal b(k)

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Note that equation (2) tracks peak envelope power and not peak instantaneous power as the term b(k) represents a complex signal. PAPR is often proportional to the number of users, however, this function is highly dependent on the user data and the channelization codes assigned to each user. A careful selection of channel codes often results in a lower PAPR than those found in the 3GPP test models. Not only does the channel loading affect the PAPR, but so does the type of filtering

performed on the signal. To minimize the bandwidth occupied by the signals, a root raised cosine filter with an excess bandwidth of 22% is specified for the WCDMA signal. This further increases the PAPR. Table 1 lists the PAPR for different signal types. As a reference, unfiltered QPSK, which has a null-to-null bandwidth equal to twice the symbol rate, has 0 dB PAPR. Filtering a QPSK signal with the WCDMA filter increases the PAPR by more than 5 dB. The unfiltered WCDMA signal already exhibits a PAPR greater than 10 dB. Further filtering the signal only increases the PAPR by 1 dB.

Signal Type PAPR (dB) Filtered QPSK 5.25 Unfiltered WCDMA Test Model 3

10.74

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Complex Gaussian 12.05 Table 1. PAPR for various signal types. Compared to a complex Gaussian signal the PAPR of WCDMA is very similar. This has brought up the comparison of WCDMA to a “noise-like” signal. While the PAPR is similar to that of noise signal, the probability distribution function needs more analysis. The complementary cumulative distribution function (CCDF) of envelope power is used in most types of digital communications test equipment. This function shows the cumulative probability of a particular peak-to-average power occurring.

Figure 3. CCDF of various signals.


From Figure 3, the CCDF of our WCDMA waveform follows that of a Gaussian signal up to a 6 dB PAPR. Beyond that the WCDMA waveform experiences a higher probability of occurrence for larger PAPR values. For PAPR values above 10 dB, the probability of occurrence is an order of magnitude greater. As the occurrence of large peaks is common in WCDMA waveforms, it is critical that the modulator and power amplifier minimize the clipping. Excessive clipping will result in reduced signal quality and spectral regrowth.

FILTER DESIGN The pulse shaping filter in WCDMA is a root raised cosine filter with an alpha of .22. When combined with a matched filter at the receiver, the resulting waveform will have zero intersymbol interference at the ideal symbol sampling instants. To ensure transmitter quality 3GPP specifies EVM at the sampling instants. One subtlety of the pulse shaping filter is that it also performs bandwidth shaping. For WCDMA, not only must the in-band signal meet the EVM requirement, it must also meet an adjacent channel power requirement to minimize interference with other base-stations. A simple modulator design would use a pulse shaping filter that has been interpolated to the final output rate (61.44 MHz for this design). There is a large complexity cost with this method. The number of taps required for a particular transition bandwidth is proportional to the sampling rate, i.e., a filter with 16x oversampling will require eight times as many taps as a filter that is 2x oversampled. To avoid this, the presented architecture uses half-band filters. Half-band filters are excellent interpolate by two filters where only (S+1)/2+1 coefficients in an S-tap FIR filter are non-zero [3]. If the pulse-shaping filter interpolates by two, then the design requires three cascaded half-band filters to achieve the additional 8x interpolation.

Figure 4. Cascaded pulse shaping and half-band filters for modulator.

By reducing the interpolation factor of the pulse shaping filter, a more effective filter may be constructed. To reduce the ACLR, the passband energy must be maximized while minimizing the stopband energy. A technique was given in [4] that performed this optimization for a root raised cosine filter shape. In this design, the half-band filters provide sufficient stopband attenuation combined with the root-raised cosine filter.

FREQUENCY CONVERSION There are several options available for digital upconversion. One is to use a look-up table based sine wave generator and mix the signal much the same way as an analog modulator. Another method is to use the CORDIC algorithm to rotate the signal vector. The CORDIC is more bit efficient in that less truncation occurs than that of the multipliers in the sine wave generation. For this paper, a modified form of the sine wave generator is used, see Figure 5(a). By limiting the intermediate frequency to be a quarter of the sampling rate, the sine wave may be reduced to a simple series of {+1, 0, -1, 0…}. The disadvantage of this quarter-band mixer is the lack of frequency agility. However, the reduced logic complexity is a large advantage as is the elimination of truncation errors. The multipliers can be replaced by a simple adder/subtractor that flips the sign of the incoming data stream, as shown in Figure 5(b). No information is lost by multiplying and truncating thereby improving the transmit signal quality.

Figure 5. (a) Quarter-band upconverter. (b) Efficient digital implementation.

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DAC ISSUES The DAC is the bridge between the analog and digital sections of the modulator. The DAC must have a sufficiently high sample rate and bit resolution to meet the requirements. The bit resolution is often the most complicated issue. Using the presented modulator design, different DAC resolutions were simulated for ACLR. The results are shown in Table 2. At 14 bits and higher, the DAC is no longer the limiting feature of the modulator. To take advantage of a higher performance DAC, it would be necessary to improve the digital stopband rejection for the 5 MHz channel offset.

DAC Resolution

ACLR 5 MHz offset

ACLR 10 MHz offset

10 bits 58 dB 59 dB 12 bits 67 dB 70 dB 14 bits 70 dB 81 dB 16 bits 70 dB 88 dB

Table 2. ACLR versus DAC resolution. The zero-order hold of the DAC introduces a sin(x)/x distortion in the signal. For a single carrier, this distortion is approximately .5 dB across the bandwidth. A seven-tap FIR inverse sinc filter without multipliers from [5] corrects this to less than 0.05 dB. The final spectral output of the system is shown in Figure 6. The nearest DAC

Figure 6. Spectral output of the DAC. image is centered at 46.08 MHz and is 10 dB lower than the signal of interest. The

analog low-pass filter should be designed to eliminate this image.

CONCLUSION In this paper, we have presented a design for a WCDMA base-station. Signal specific aspects of WCDMA such as PAPR have been reviewed. Filter design from pulse shaping to interpolation has been presented. A simple and efficient digital upconverter translated the signal to a digital IF. A 14 bit DAC was selected to match the digital filter performance. The design in this paper can be further extended to a WCDMA multi-carrier modulator by replacing the quarter-band converter with a more frequency agile converter.

REFERENCES [1] 3rd Generation Partnership Project; “UE Radio Transmission and Reception (FDD)”, 3G TS 25.101 v3.5.0, Dec. 2000. [2] 3rd Generation Partnership Project; “Base Station Conformance Testing”, 3G TS 25.141, v4.0.0, Mar. 2001. [3] Lyons, Richard G., Understanding Digital Signal Processing. Reading, MA: Addison-Wesley, 1997. [4] Vankka J. et al., “A Multicarrier QAM Modulator,” IEEE Transaction on Circuits and Systems II, vol. 47, no. 1, Jan. 2000. [5] Samueli, H, “The Design of Multiplierless FIR Filters for Compensating D/A Converter Frequency Response Distortion,” IEEE Transasction on Circuits and Systems, vol. 35, pp. 1064-1066, Aug. 1988.

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cdma waveform generation

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