If the transitions between the constellations shown in Figure 1 are made abruptly, then the harmonics generated will extend beyond the narrow frequency band allocated to each EDGE channel. These out-of-band harmonics would interfere with adjacent radio channels if unchecked. The signal therefore needs to be filtered before transmission using a pulse-shaping filter. In the same way as squeezing a balloon in the middle makes it extend in the other direction, squeezing a signal in the frequency domain makes it extend in the time domain. Now, not only do we have 8 symbols but also they are starting to overlap.

To compound the problem there is also the phenomenon of multipath signals. The radio signals arriving at the phone do not all arrive directly—in most cases direct line of sight to a base station is the exception. Instead signals arrive reflected off objects, having travelled different distances, arriving at different times at the phone. When you add to this noise, interference from neighboring channels, interference from distant users on the same channel, Doppler shift, radio imperfections (noise and DC offset), it's amazing it works at all. The net effect is a noisy signal composed of an amalgam of past symbols, and the nature of this interference is formulated in the channel impulse response (CIR), which can be calculated using:

r_n= 0.5x_n + 0.5 x_n-1 + 0.25x_n-2 + 0.25x_n-3 + 0.1x_n-4

where r_n is the current received signal and x_n is the symbol at time n

To illustrate the effect of the filtering, let's refer back to Figure 1 above. From left-to-right, this figure shows the original constellation diagram, the same diagram after filtering, and then finally as it is received. The last diagram is the one we need to extract useful information.

Initially the mobile phone doesn't know either the nature of the ISI (expressed as a CIR) or the data being transmitted. In fact, it doesn't even know whether the incoming transmission is a GMSK or 8PSK modulated signal.

However at the heart of each transmission is a known training sequence, which is a known sequence of data. From this training sequence the mobile phone can identify the type of modulation used, it can then estimate the CIR, and finally use that CIR estimate to decode the remainder of the transmission.

One tradeoff that must be made by designers lies in the symbols they want to include in the history and therefore in constructing the CIR formula, i.e. how many taps to include in the CIR. The more taps included, the more complete the removal of ISI but the computational requirements rise exponentially. A balance between sufficient complexity to tackle the most severe ISI and low computational is the goal.

Options for Equalization
Equalization is the removal of ISI and noise from the radio transmission. GPRS uses a maximum likelihood sequence estimation (MLSE) approach to equalising the data. All possible sequences of symbols are transformed using the estimated CIR and compared to the received signal. The closest match is assumed to be the transmitted signal. It is evident that this is a non-linear problem, with 2 symbols (0,1) and using the past n symbols, the number of sequences to convolve with the CIR and then compare is 2ⁿ. Using a modest digital signal processor (DSP) or simple co-processor, it is possible to perform these calculations within the time constraints.

When the same method is tried for EDGE, it is clear that another approach is needed. For a system using just 4 taps in the CIR, GPRS requires 2⁴=16 sequences to be compared while an EDGE system with 8 symbols will require 8⁴=4096 sequences.

If a system is to achieve multi-slot class 12 (4 EDGE receive slots), then it needs to perform 4 equalizations, a decode operation, and other tasks all within the 4.2 ms of a GSM frame. Creating 4096 sequences, modifying them with the estimated CIR, and then performing the comparisons would be a tall order even with a system employing a 3.06 GHz Pentium. A mobile phone has just a fraction of that processing power available, thus delivering this level of performance is next to impossible.

So if MLSE cannot work what are the other techniques possible? The reduced state sequence estimation (RSSE) is one alternative.

In an EDGE system, designers can expect the most recent symbols to have the most significant effect on the current symbol, and that those further back in time have less effect. Instead of treating symbols as unique objects, the RSSE method allows designers to group symbols into sets, depending upon their temporal significance. We need to identify the incoming symbol as one of the 8 possible symbols as we need to accurately recover the information it contains. The previous symbol may exert a significant amount of ISI, and so again we might want to treat the 8 symbols as unique. For the symbol prior to that, the influence may start to diminish and two symbols may have very similar effects on the current symbol, and so we can start to group symbols into pairs, and reduce the number of permutations.

Going further back in the symbol history we can continue to group the symbols into larger sets as their effect diminishes further. At each stage we maximize the Euclidean distance between the sets, (or in English, we make sure they are as different as possible from each other).

For example, if the estimated channel response is:

MLSE r_n= 0.5x_n + 0.5 x_n-1 + 0.25x_n-2 + 0.25x_n-3 + 0.1x_n-4

where r_n is the current received signal and x_n is the symbol at time n. And:

RSSE r_n= 0.5x_n + 0.5 x_n-1 + 0.25x'_n-2 + 0.25x'_n-3 + 0.1x''_n-4

where x''_n is the set of symbols at time n.

designers might consider grouping the symbols in to sets of 8, 8, 4 ,4, 2. The reduction in complexity is down from 8⁵=32768 to 2048. By trading off the number of CIR taps (i.e. how many past symbols we include) and the grouping of symbols into sets against the performance requirements the complexity and processing requirements can be managed.

Hardware vs. Software
Given the complexity of the problem, EDGE equalization is a natural candidate for implementing with co-processor hardware. The latest generation of mobile phone baseband processors are following divergent tracks—one built on a powerful and flexible DSP approach and another that uses a moderately powerful DSP with a co-processor.

Baseband chipsets such as ADI's MSP500, Intel's Manitoba, or Motorola's StarCore have a powerful DSP with a dual MAC architecture and Viterbi instructions to efficiently implement the convolution and correlation and trace-back functions. Using processors such as these, equalization can be performed with about 25 MIPS per slot, thus leaving room for other tasks like blind modulation detection and decoding. The advantages of this hardware implementation include:

• The DSP software (unless housed in ROM) can be modified to take advantage of improvements in algorithms once the baseband processor has been fabricated.
• When not in an EDGE call the resources of the DSP can be utilized for other functions such asMPEG video encoding.
• The challenge is in achieving low power consumption at the same time as utilizing high DSP clock rates, balancing core voltages against leakage, and using the latest silicon geometries and techniques.

The alternative is to move some of the signal processing onto a co-processor. This method can be used to extend the life of an existing GPRS chipset. The computationally intensive tasks can reduce the DSP loading from 25 MIPS/slot on a high-performance DSP to less than 10 MIPS/slot on a much simpler DSP.

Tasks that are candidates for moving to a co-processor include equalization, channel decoding, and Viterbi co-processing. The EDGE equalizer is by far the most obvious candidate for implementing with a co-processor, and the majority of the MIPS reduction can be achieved with a few tens of thousands of gates.

The next candidate is the channel decoding. Moving channel decoding isn't such a cut-and-dry winner. To have a significant effect on reducing MIPS, this move will require more gates on the co-processor, which may prove to be troublesome in some wireless designs.

Radio Headaches
Earlier in the article it was stated that one side-effect of using 8-PSK modulation is that the amplitude of the carrier must be preserved, dictating a linear transmit path. For pure 8PSK modulation, the amplitude of the carrier can drop to zero as it transitions between symbols. Such a wide dynamic range would give severe problems to the radio engineers. To avoid this problem, EDGE systems employ a simple modification to basic 8PSK modulation.

To avoid this situation, EDGE adds a 3π/8 rotation in addition to the symbol transition. As shown in Figure 2, this prevents the carrier passing through the origin and falling to zero amplitude. In the figure the transition from symbol 1 to 5 is shown in both diagrams—lon the left it passes through zero, and on the right it avoids the origin.

For the radio, and especially the power amplifier, the need for a linear transmit path requires changes in the architecture, and has consequences for efficiency.

In GMSK the power amplified is run in saturated mode and can achieve efficiencies of approximately 50%. Running the same power amplifier in linear mode may drop the efficiency down to about 33%, with the consequent increase in thermal management problems. This drop in radio efficiency is often cited as evidence that EDGE products will have a lower battery life than GPRS products. However the data rate has increased three-fold but the efficiency is only reduced by about 1/3. Therefore in terms of energy per bit, EDGE is more efficient.

Another Interesting Challenge
An EDGE-enabled wireless devices product uses GMSK modulation for the control channels, and 8PSK for the data channels. This introduces another interesting challenge. Since EDGE systems uses different modulation schemes for different channels, it would be most efficient to bias the radio into saturated mode for GMSK, and then linear mode for 8PSK. This change in bias needs to be achieved in less than 30 μ s, an extremely difficult challenge especially when there must be no transients that exceed the spectral mask of the narrow frequency channel. The result is that many early EDGE products may opt to bias the radio in linear mode for both GMSK and 8PSK, or may even opt to be EDGE receive only.

To overcome the thermal issues, EDGE products may utilize asymmetric data rates dependent upon form factor. An EDGE mobile phone may be capable of receiving 4-slots of data per frame (240kb/s), but only transmitting two slots to avoid thermal hotspots. In contrast, an EDGE PC-card slotted into a laptop may use a symmetric 4-slot capability in each direction, dumping the heat to the notebook.

Wrap Up
Until the arrival of the new generation of mobile phone chipsets, we didn't have the processing power available to equalize EDGE signals. The cost of tripling the data rate is complexity in the EDGE modem, and changes to the radio. The former has required development of optimized equalization algorithms while the latter has required architectural changes and challenges in thermal management of the radio's power amplifier.