Modern communication systems employ digital modulation for a variety of reasons, including improved immunity to noise and channel impairments as well as enhanced security compared to analog modulation. In addition, advances in very large-scale integration (VLSI) and digital signal processing (DSP) technology have made digital modulation more cost effective than analog transmission systems. Digital transmissions accommodate digital error-control codes that detect and/or correct transmission errors, and support complex signal conditioning and processing techniques such as source coding, encryption, and equalization to improve the performance of the overall communication link. By using the MATLAB simulation software from The MathWorks, various digitally modulated systems, including 2-, 4-, and 8-level FSK systems in an additive white Gaussian noise (AWGN) channel, will be analyzed to understand bit-error-rate (BER) performance under different operating conditions.

In digital wireless communication systems, the modulating signal may be represented as a time sequence of symbols or pulses, where each symbol has m finite states. Each symbol represent n bits of information, where n = log2m bits/symbol. Some digital modulation techniques have subtle differences between them, and each technique belongs to a family of related modulation methods. For example, frequency-shift keying (FSK) may be coherently or noncoherently detected, and may have 2, 4, 8, or more levels per symbol.¹

Several factors influence the choice of a digital modulation scheme. A desirable modulation scheme provides low bit error rates at low received signal- to-noise ratios (SNRs), performs well under multipath and fading conditions, occupies a minimum bandwidth, and is easy and cost effective to implement. In reality, depending on the demands of a particular application, tradeoffs must be made when selecting a digital modulation scheme.

The performance of a modulation scheme is often measured in terms of its power efficiency and bandwidth efficiency. Power efficiency describes the ability of a modulation technique to preserve the fidelity of the digital message at low power levels. In a digital communication system, in order to increase noise immunity, it is necessary to increase signal power. However, the amount by which the signal power should be increased to obtain a certain level of fidelity (i.e., an acceptable bit error probability) depends on the particular type of modulation employed. The power efficiency (sometimes called energy efficiency) of a digital modulation scheme is a measure of how favorable this tradeoff between fidelity and signal power, and is often expressed as the ratio of the signal energy per bit to noise power spectral density (E_b/N₀) required at the input of the receiver for a certain probability of error (say 10^-3).

Bandwidth efficiency describes the ability of a modulation scheme to accommodate data within a limited bandwidth. In general, increasing the data rate implies decreasing the pulse width of a digital symbol, which increases the bandwidth of the signal. Thus, there is an unavoidable relationship between data rate and bandwidth occupancy. However, some modulation schemes perform better than others in making this tradeoff. Bandwidth efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the ratio of the throughput data rate per Hertz in a given bandwidth. If R is the data rate in bits per second, and B is the bandwidth occupied by the modulated radio frequency signal, then bandwidth efficiency, η_B, is

In terms of bits per second, the number of bits are conveyed or processed per unit of time.

The system capacity of a digital communication system is directly related to the bandwidth efficiency of the modulation scheme, since a modulation with a greater value of ?_B will transmit more data in a given spectrum allocation. There is a fundamental upper bound on achievable bandwidth efficiency. Shannon’s channel coding theorem states that for an arbitrary small probability or error, the maximum possible bandwidth efficiency is limited by the noise in the channel, and is given by channel capacity formula. The Shannon’s bound for AWGN non-fading channel is given by Eq. 2.

In designing a digital communication system, very often a tradeoff exists between bandwidth efficiency and power efficiency. For example, adding error control coding to a message increases bandwidth occupancy (and, in turn, reduces the bandwidth efficiency), but at the same time reduces the required power for a particular bit error rate, and hence trades bandwidth efficiency for power efficiency. On the other hand, higher level modulation schemes (M-ary keying), except M-ary FSK, decrease bandwidth occupancy but increase the required received power, trading power efficiency for bandwidth efficiency.

While power and bandwidth considerations are very important, other factors also affect the choice of a digital modulation scheme. For example, for all personal communication systems that serve a large user community, the cost and complexity of the subscriber receiver must be minimized, and a modulation that is simple to detect is most attractive. The performance of a modulation scheme under various types of channel impairments such as Rayleigh and Ricean fading and multipath time dispersion, given a particular demodulator implementation, is another key factor in selecting a modulation. In wireless systems where interference is a major issue, the performance of a modulation scheme in an interference environment is extremely important. Sensitivity to detection of time jitter, caused by timevarying channels, is also an important consideration in choosing a particular modulation scheme. In general, the modulation, interference, and implementation of the time-varying effects on a channel as well as the performance of the specific demodulator are simulated as a complete system.^1-8

As its name suggests, an FSK transmitter has its frequency shifted by the message.^1-15 Although there could be more than two frequencies in FSK, this experiment will use a binary bit stream, with only two frequencies. The word ‘keyed’ suggests that the message is of the ‘on-off’ variety, such as one (historically) generated by a binary sequence (Fig. 1).²

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