Improving the design accuracy of GSM (EDGE) products

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Improving the design accuracy of GSM (EDGE) products [Copy link]

Although the third generation (3G) wireless communication technology has begun to emerge, wireless system designers have not slowed down their efforts to improve the data processing capabilities of existing mobile phones and base stations. This positive spirit has led to the development of the so-called 2.5G technology, which enables wireless communication operators to provide voice and high-speed data services to users without replacing the entire telecommunications infrastructure. This article mainly introduces the EDGE specification in 2.5G technology .

An important technology that has attracted the interest of designers in 2.5G systems is the Enhanced Data Rate for GSM (EDGE) specification. EDGE is a revolutionary technology for current GSM systems, which can provide data transmission rates up to 384kbps , enabling the system to simultaneously provide voice, data, Internet connections and other interconnection solutions.

EDGE has attracted much attention for several reasons. First, it can provide high data rates without building new infrastructure. Another important benefit is the full-rate feature. By providing data rates up to 384kbps , EDGE greatly improves the transmission speed of existing wireless communication systems, which currently have a maximum data rate of only 14.4kbps .

To fit more data traffic into a fixed bandwidth requires the use of more complex signaling formats and receivers, making the design and testing of new systems more complex.

To solve EDGE design problems, system developers turned to digital signal processing technology. Using digital simulation, they can test whether the design meets the requirements before the receiver is manufactured. For receiver testing, the use of DSP software technology can accurately predict typical statistics of complex signals, such as error vector magnitude (EVM) . To better illustrate this point, let's first study digital communication link simulation.

Link Simulation

The most commonly used metric for measuring the performance of digital communication systems is the average bit error rate (BER) . In simple terms, the average bit error rate is the probability that the transmitted data is received incorrectly at the receiving end. Channel interference may change a logical 0 to a logical 1 , or vice versa. Generally speaking, this metric is sufficient for end users to measure the quality of an end-to-end link. Figure 1 is a curve of the average bit error rate versus the signal-to-noise ratio (SNR) , where the signal-to-noise ratio is expressed in E _b /N ₀ (dB) . The figure shows that the signal-to-noise ratio at the receiver output increases as the bit error rate decreases. Figure 1 shows four different types of curves.

Other statistics are also easy to collect and can be used for early evaluation of candidate system architectures. Communications systems are increasingly using more complex algorithms such as error control coding, equalization, multi-user detection, and many other algorithms. Collecting the end-to-end average bit error rate of such systems requires a model of the entire link design. However, you may not know what the model is in the early stages of system development. At the same time, evaluating the entire design may be cumbersome and expensive, so performance tests that can quickly and roughly evaluate candidate system or subsystem designs in the early stages are very necessary.

As an example, coding systems can generally be used to measure the raw symbol error rate at the output of the receiver to infer the average bit error rate at the output of the error correction decoder. Figure 2 shows a simple quadrature phase shift keying (QPSK) system using error correction coding, where the demodulator makes a hard decision on each received symbol to make a best estimate of the original transmitted signal. This bit error rate is sometimes called the symbol error rate or raw BER , as opposed to the coded BER .

The raw BER is shown in the box in Figure 2 , overlaid on the theoretical value curve, where there is an additive white Gaussian noise (AWGN) . Since the system used has no distortion sources, the curve distribution should be within the statistical range.

Estimated Coding BER

In some cases, the code BER can be inferred from the symbol error rate . In the AWGN channel, the code BER limit range is obtained using the symbol error rate and specific error correction code parameters .

As shown in Figure 1, the BER performance limit range of a certain code is the Viterbi algorithm convolutional coding with rate r=1/2 and constraint length k=7 . The limit here is an upper limit ( represented by a purple line ) , and the purple box represents the Monte Carlo simulation result of the actual end-to-end coding system. Note that the curve here is very consistent with the BER value .

Given the code, the receive SNR , and Es /N0 _{, the} type of bounded range shown in Figure 1 can be calculated . If _{Es /} N0 is known or can be measured, the coded BER can be fitted very well . This can sometimes avoid the need for extensive Monte Carlo simulations of end-to-end coded links at the target BER .

In the simulation shown in Figure 2 , the AWGN level can be precisely controlled by adjusting the standard deviation of the Gaussian noise samples added to the sampled data representation of the signal waveform, so the SNR conditions at the receiver output can be obtained and the BER can be tabulated as a function of these conditions . However, this is not generally the case in either software simulation or laboratory testing of communications systems.

If it is a software simulation, there may be many additional noise and distortion sources, which will affect the statistical characteristics of the receiver. Even if we assume that the noise statistics at the output of the receiver conform to the Gaussian distribution, the actual signal-to-noise ratio is generally measured. In the laboratory, we cannot accurately control the role and scale of various subsystems, so the output characteristics of the receiver must be accurately measured.

The lower right side of FIG. 2 is a statistical curve at the output of the receiving device. This is a typical distribution diagram drawn according to the integral and in-phase demodulator output. 256 code element outputs are covered on the curve.

Figure 2 has adjusted the AWGN to a level where the received E _b /N ₀ is 30 dB . When Es _/ N ₀ is at this level, even the original BER coherent detection result is very small. Under this condition, the received Es _/ N ₀ estimate can be obtained by simply subtracting the corresponding constellation point of the hard judgment of the receiving device from the normal judgment statistic .

"Normal" means adjusting the receiver output to give _Es = 0dB . Because _the system model used here is linear, the result is simply a sequence of complex Gaussian variables with variance N0 /2 . An estimate _of N0 can be obtained by averaging the squares of these complex numbers over a large enough number of symbols to remove any statistics of random phenomena inherent in the system or channel ( in this case AWGN) , which may require hundreds, thousands, or even millions of symbols.

The deviation of the complex statistical value of the receiving device output from the ideal signal set point is called EVM , and EVM has been shown to be helpful in describing the distortion effects of nonlinear circuit components ( such as amplifiers ) .

EDGE Signal Basics

The GSM mobile communication standard is now almost universal. It was developed in the mid-1980s and is a mature communication technology that provides reliable service. The GSM system operates using Gaussian Minimum Shift Keying (GMSK) modulation circuits, in which the envelope is constant.

In order to provide more effective bandwidth signals for high-speed applications, the EDGE signaling format was developed as an upgrade to the existing GSM system. The EDGE format is an octal MPSK signal that uses a special pulse shaping filter to achieve linear I&Q modulation. The EDGE signaling format is designed to make its spectrum and other characteristics compatible with the current GSM and TDMA systems using GMSK , and is suitable for coverage on existing systems.

However, the phase modulation in EDGE is a linear function of the input coefficients, while GMSK continuous phase modulation (CPM) is nonlinearly related to these coefficients. Depending on the GMSK demodulation / detection method, different types of precoding and transmission bit interleaving may be used. Here we only focus on how to describe the transmission output waveform characteristics.

Signal composition

EDGE signals are generated by mapping the incoming data bits into octal symbols, which are equivalent to the constellation points of a normal 8- level phase shift keying (8PSK) signal. These signal points are used as I&Q modulation coefficients and input to the corresponding channels in the I&Q modulator . EDGE modulation also adds a step, which is to rotate the subsequent symbols by 3π /8 .

Figure 3 shows the simulated transmitter output waveforms for GMSK and EDGE signals. The simulation is represented by a complex envelope, and the RF signal I&Q envelope is shown in the lower left corner. Sampled data approximation is used for the transmit simulation waveform, with 8 samples taken per channel signaling interval . Note that both the GMSK and EDGE waveforms are relatively smooth.

The symbol conversion of EDGE and GMSK signals is performed step by step, resulting in a dense spectrum. The spectral characteristics of the modulation circuits used in the two systems are very similar, as shown in the spectrum coverage trace in the lower part of the figure, where the spectral characteristics are averaged from more than 10,000 randomly generated symbols .

The final graph in Figure 3 is the I&Q trace for both modulations . The GMSK trace has a constant envelope, and since the EDGE signal does not necessarily have a constant envelope, the amplitude and phase in the I&Q trace vary, and this signaling format places more stringent requirements on amplifier linearity.

ISI Effect

Like the GMSK signaling used in GSM , EDGE signals use modulated pulses with leading and trailing edges that extend into adjacent symbol intervals. Unless special measures are taken, such pulses will cause statistical interference between consecutive received symbols at the receiver output , causing one symbol to affect the voltage levels of the symbols before and after it.

However, it is possible to achieve independence between the receiver output signals with so-called Nyquist pulses, which can cause the tail and beginning regions of successive pulses to cancel each other out, even if the pulses extend beyond one symbol. This principle has been exploited in the context of linear modulation types such as EDGE .

When considering the pulse shape characteristics of linear modulation, the modulation and demodulation filter cascade must be considered; the demodulation filter should also be matched to the modulation filter in order to optimize Es /N0 _at the receiver output . To meet both objectives, Nyquist filters with a square root frequency response must be used in the modulator and demodulator, and it is better to improve _the cascaded cosine response so that the square root of the cosine terminal filter response is also improved.

Unfortunately, the principle of selecting the EDGE modulation pulse filter must be compatible with the existing GMSK signal, not based on Nyquist filter considerations. Obviously, the EDGE pulse shape does not match the square root of the Nyquist filter, so it is impossible to choose a demodulation filter that does not generate inter-symbol interference (ISI) and matches the modulation filter.

There are many possible alternatives. When the modulation filter has no empty spots in the spectrum, the demodulation filter can be constructed and cascaded to obtain the Nyquist response, which may compromise the existing E _b /N ₀ but completely eliminates intersymbol interference at the demodulator output.

A matched filter can also be used, however, the matched filter will produce severe inter-symbol interference at the demodulator output , making the unprocessed receiver output signal unusable.

DSP Receiver Technology

In addition to traditional RF methods, DSP technology has also become a major method of filtering in modern receivers. The signal processing used in typical EDGE receiver designs often includes algorithms that provide complex equalization and coding schemes. The algorithms used in these functions can optimize the original received codewords to improve end-to-end BER performance. These algorithms can also be used to implement traditional measurement techniques such as EVM .

However, EVM measurements are difficult for signals with large ISI , in which case the demodulator profile may be very scattered even on a linear channel with negligible noise or distortion.

The ISI caused by matched filtering of EDGE signals is very serious because the EDGE pulse lasts for 5 code elements, and full equalization needs to consider the impact of the first four and last four code elements on the current receiver judgment statistics. The total number of code elements ( 9 in this case ) is sometimes also called the ISI span.

The computational complexity required to perform the maximum likelihood sequence estimator using the Viterbi algorithm is proportional to the size of the modulation alphabet added to the function. Obviously, it is not practical to implement an equalizer that provides full equalization in this case, because we know the original transmitted codewords ( the codewords have already been generated ) , so it becomes extremely simple to build an ideal equalizer to eliminate the adjacent codeword correlation caused by the modulation / demodulation filter cascade.

Ideal Equalizer

In simple terms, the ideal equalizer is a branch delay line, or transversal filter, where all branches except the central branch are connected to the symbol position beyond the ISI variation range. The branch delay line transmits a known symbol stream with ISI coefficients {In} of: n=0 , ± 1 , ± 2, etc. and uses it as the branch gain. At this time, the central branch ( corresponding to n=0) is not connected.

In general, these coefficients are somewhat complicated. To build such an equalizer, the ISI coefficients between symbols at the receiver output must be known . These coefficients can be obtained by calculating the cross-correlation between the transmitted and received pulse shapes. For the case where both terminals use EDGE pulses, the ISI coefficients are {1.1E-11 , 2.5E-07 , 6.63E-04 , 5.65E-02 , 5.13E-01 , 5.65E-02 , 6.63E-04 , 2.50E-07 , 1.1E-11} .

Compromise

Since many ISI coefficients are small, it is possible to take a step back and build a good performing equalizer while reducing complexity, and the ideal equalizer provides a useful performance benchmark against which to compare trade-offs.

The scatter plot in Figure 4 shows the output of a matched filter demodulator for an EDGE signal, with 25,600 symbols overlaid. There are no noise or nonlinear distortion sources in the simulation, and the red stars represent the original or unequalized symbol output. Note that even in such an ideal test the pattern is quite scattered, and the scatter plot is not very useful for qualitatively assessing the effects of distortion.

The small boxes in Figure 4 show the ideal group points collected from the modulator. The symbol values after passing through the ideal equalizer are shown as green dots. Note that these points fall well within the ideal group points. The number of equalizer branches in the example in Figure 4 is limited to five . Including additional branches does not have a significant impact due to the small final ISI coefficient. As can be seen from the scatter plot in Figure 4 , achieving ideal equalization makes the scatter plot an effective tool for predicting system performance, even for communication systems that do not make final bit decisions based solely on the raw symbol values.

After removing the signal drift caused by ISI , the residual drift caused by other distortions can be more clearly shown, which is important for evaluating the noise and distortion effects that may appear in actual system implementations.

Figure 5 shows a simple model of an EDGE system operating in PA mode . The power amplifier can be modeled by describing its AM/AM and AM/PM characteristics, as is done here.

The I&Q plot on the left shows the input signal of the overlaid amplifier and its output signal. The amplifier is not operating in very saturated conditions, but mainly in its linear region, with clipping visible on some signals with large excursions.

The scatter plot on the right shows the scatter of the output signal of the receiving device. The amplifier causes a certain drift of the received calibration group points. The final graph at the bottom of the figure shows the EVM histogram and amplitude probability distribution. From this figure, accurate details about the root mean square (RMS) EVM , level ( expressed as a percentage ) and other statistically useful characteristics can be seen.

With the introduction of EDGE systems, designers need to pay more attention to how to find and eliminate errors in RF signals. By applying DSP technology to traditional RF measurements ( such as EVM technology ) , designers of wireless handsets and base stations can quickly find errors and improve the performance of their 2.5G products.

Author: Kurt Matis , Ph.D.
Director of Systems Research
Applied Wave Research Corp.
Email: kurt@mwoffice.com