•   Digital Modulation

Digital modulation techniques can be classified as either single carrier or multiple carrier (i.e., OFDM, Discrete Multitone (DMT)) techniques.  Furthermore, the various schemes fall into either Linear or Non-Linear families depending upon how the amplitude of the transmitted signal varies with the modulated waveform. The I/Q (in-phase and quadrature) plane is a convenient way to represent these signals as almost any modulated signal can be expressed as a summation of in-phase and quadrature components as follows:

s(t)=I(t) cos(2 ¶ f₀ t + Ø₀) + Q(t) sin(2 ¶ f₀ t + Ø₀)

where:

s(t) is the transmitted signal

I(t) is the in-phase component

Q(t) is the quadrature component

f₀ is the carrier frequency

and Ø₀ is the carrier phase

The in-phase and quadrature components are called the baseband components of the signal in that their bandwidth extends from 0 Hz. to the (relatively) lower message bandwidth.

An example of a non-linear digital modulation technique is the Gaussian Minimum Shift Keying (GMSK) scheme.  An example of a linear digital modulation technique is the Phase Shift Keying (PSK) scheme and it's variations.

• Bandwidth Efficiency / Power Efficiency

The performance of a given digital modulation scheme is a function of the operating channel (i.e., AWGN or Fast, Frequency Selective Fading).   While there are many design tradeoffs to consider, it is always desirable to provide a robust link at the lowest possible SNR necessary to achieve the target BER.   Depending upon the application, cost, size and battery life also are major design factors.

It is common to study and compare digital modulation schemes in the bandwidth/power efficiency plane.  Bandwidth efficiency can be considered the degree to which a given modulation scheme can accommodate information (data rate) within a specified transmitted bandwidth.  Increasing the data rate usually means increasing the transmitted bandwidth.  Bandwidth efficiency can be expressed in the units of bps/Hz.  The overall system capacity of a communication link is dependent upon the bandwidth efficiency of the chosen modulation scheme.  Power efficiency can be considered the degree to which a given modulation scheme can maintain an acceptable BER at low power levels (SNR).

Shannon bounded the maximum possible bandwidth efficiency for an arbitrarily small probability of error as follows:

C/W = log₂(1+SNR)

See "Digital Communications, Fundamentals and Applications", by Bernard Sklar, pp. 385.

You can use our simple graphing calculator to explore Shannon's Capacity bound as follows:

Hit Add Function.

Plug in Log(1+ x) / Log(2).

• Performance Metrics

Power Spectral Density (PSD).  PSD could be used as a performance indicator of Bandwidth efficiency.

Probability of Error (P_error).  P_error (BER or SER) could be used as a performance indicator of Power Efficiency.

Under AWGN and using Coherent Detection, the Probability of Bit Errors (not Symbol Errors) for several popular digital modulation schemes are shown below:

These performance curves can be simulated in any of the commercially available technical computing environments.

It is interesting to note that while BPSK (2-PSK) has slightly superior BER performance than MSK using coherent detection, MSK is sometimes preferable due to the fact that it can be detected non-coherently (limiter/discriminator type detection) which reduces the cost of implementation.

For a very nice summary of many types of digital modulation techniques with their associated P_error see "Digital Radio Modulation: A Wireless Reference Guide", by Peter Okrah, Communication Systems Design, November 1997, pp. 50.

•   Detection Schemes

The performance of a given digital modulation scheme in a specified channel (i.e., AWGN or Fast, Frequency Selective Fading) is also heavily dependent upon the type of detection employed.  For example, if a stable, synchronized carrier reference is available at the receiver, then coherent detection can be used.  Otherwise, non-coherent detection with differential encoding can be employed.   In the later case, it is the phase difference between successive symbols that is used rather than knowledge of the absolute phase.  While non-coherent detection is less complex to implement, over most modulation schemes and channel types, coherent detection delivers superior P_error performance.

For an excellent paper on the performance of various types of digital modulation techniques over different types of channels and detection schemes see, "A Unified Approach to the Performance Analysis of Digital Communication over Generalized Fading Channels", by Simon and Alouini, Proceedings of the IEEE, September 1998, pp. 1860.

• Generic Receiver Architecture

There are many different ways to implement these functional blocks as a function of cost constraints, size, operating channel conditions, frequency plan, receiver architecture, process technology, etc. The following is a generic receiver summary illustrating how digital modulation techniques can be combined with other digital processing schemes to implement high capacity, high fidelity wireless systems.

The first downconverter is employed to mix the received RF signal down to the intermediate frequency. The second downconverter is employed to mix the IF signal down to baseband. Sometimes a PLL can be used to synthesize the LO reference frequency for the mixer. In a direct conversion (or Zero-IF) architecture, the RF signal is mixed right down to baseband where all of the processing takes place.

The digital demodulator is responsible for carrier extraction exposing the (coded) (spread) (scrambled)
(encrypted) message information available for further processing.

An equalizer can be employed to compensate for channel distortions. Most equalizers are adaptive, as they
need to compensate for changing channel conditions. If the output of the equalizer is fed back to the input
and used for further computations, then it is called a non-linear equalizer.

The detector is responsible for symbol sampling (test statistic formation) and estimation (decision logic). A detector that minimizes the error probability of detecting a wrong symbol is called a Maximum Likelihood Detector.

An Optimal Detector uses all available information to make decisions by exploiting the information across bits.

A detector that makes decisions on a bit by bit basis is sub-optimal but less complex and less expensive. Equalizers mitigate the ISI and make bit by bit detection possible, if desired.

If an interleaver was used at the transmitter to ensure that the data stream into the convolutional decoder
was uncorrelated, then a de-interleaver must be employed at the receiver. As opposed to block codes, the data in a convolutional code consists of a continuous stream of inputs and outputs. Convolutional codes tend to perform better if the continuous data stream coming in is uncorrelated. Hence, the need for interleavers. Of course, use of interleavers introduces an undesirable delay in proportion to the interleaver depth.

Interleavers tend to perform better at higher mobile velocities (ie. Doppler Spread is higher). This is because the fading is faster and thus does not cover the whole block of data. At higher mobile velocities, interleavers can compensate for some of the poorer performance of power control (which does not do as well for higher mobile velocities). Conversely, at the slower mobile velocities, where interleavers have more trouble because the fading covers the entire block of data, power control works better.

The decoder recovers the user information from within the covered codewords. The decoding function is partitioned into several blocks, including Channel Decoding and Source Decoding. Channel codes are usually bandwidth expanding and are used to improve the robustness of the link (BER vs.SNR). These FEC codes can be of the block (Reed Solomon, Hamming, BCH, Cyclic, Linear) family, or convolutional family (with Viterbi decoders). Source codes are employed to remove as much information as possible (bandwidth conservation) from the transmitted message while still maintaining acceptable fidelity at the decoder.

If the symbol decision is made at the demodulator / detector stage, then it is called a Hard Decision.  If the symbol decision is made at the decoder, based upon a continuous stream of quantized symbols (and other information), then it is called a Soft Decision.

The next installment in this series will explore some of the tradeoffs associated with digital modulation circuit impairments.