1.4 Wireless communications background  (Page 4/4)

Similarly, the required $\frac{E_b}{N_0}$ for a modem operating at a channel capacity of 28.8 kbps in an AWGN bandwidth of 3.4 kHz will be approximately 16.3 dB.

Bandwidth and power constraints

The design of a digital communication system begins with the channel description, received power, available bandwidth, noise statistics, and definition of system requirements such as data rate and error performance. Two primary communication criteria are the received power and available bandwidth. In bandwidth-limited systems, spectrally efficient schemes can save bandwidth at the expense of power. In power-limited systems, power-efficient schemes can be used at expense of bandwidth.

For any digital communication system, the relationship between received power to noise-power spectral density $\frac{P_r}{N_0}$ and received $\frac{E_b}{N_0}$ is given by Equation 10:

$\frac{P_r}{N_0}=\frac{E_b}{N_0}R$

Where $N_0=\frac{N}{B}$ . This relationship is frequently used in designing and evaluating digital communication systems.

Bandwidth-limited systems

Bandwidth efficiency increases as $B{T}_b$ product decreases. Therefore, signals with small $B{T}_b$ products are employed in bandwidth-limited systems. In uncoded systems, the objective is to maximize the information rate within the allowable bandwidth at the expense of $\frac{E_b}{N_0}$ while maintaining a required $P_b$ . MPSK and MQAM are examples of bandwidth-efficient modulation schemes with bandwidth efficiency (Equation 11):

$\frac{R}{B}={\log }_2(M)bits/sec/Hz$

Suppose you have to choose between MFSK and MPSK for the following parameters: bandwidth = 4 kHz, data rate = 10 kbps and $\frac{P_r}{N_0}$ = 60 dB-Hz. First you find that the received $\frac{E_b}{N_0}$ = 55 – 10*log10(10000) = 15 dB. Since the required data rate exceeds the bandwidth required, the best choice is MPSK. Next, decide on the value of M that will give a symbol rate closest to the bandwidth of 4 kHz. From M = 8, you know that the symbol rate is 3.2 kHz. Next, you'll see that for $P_b$ of less than 10e-5, the required bandwidth is around 13 (from BER curves) which is less than the received, so the best choice is 8PSK.

Power-limited systems

For this type of system, where power is limited but bandwidth is abundant, the following trade-offs are possible:

1. Improved $P_b$ at the expense of bandwidth for fixed $\frac{E_b}{N_0}$ .

2. Reduction in $\frac{E_b}{N_0}$ at the expense of bandwidth for fixed $P_b$ .

MFSK is an orthogonal signaling technique used in power-limited systems. It has a bandwidth efficiency of noncoherent MFSK given by Equation 12:

$\frac{R}{B}=\frac{{\log }_2\mathrm{(M)}}{M}bits/sec/Hz$

Suppose you have an available bandwidth of 45 kHz and $\frac{P_r}{N_0}$ = 50 dB-Hz. Again the goal is to choose a modulation scheme to meet the same BER performance. The received $\frac{E_b}{N_0}$ = 50 – 10log(10000) = 10 dB. Since you have plenty of bandwidth compared to the data rate, the best modulation scheme would be MFSK. In an effort to conserve power, you should look for the largest M such that the minimum bandwidth for MFSK doesn’t exceed 45 kHz. For M = 16, the required $\frac{E_b}{N_0}$ to keep $P_b$ less than 10e-5 is around 8 dB (from BER curves), which is below 8.2 dB.

References

1. Sklar, Bernard. Digital Communications: Fundamentals and Applications. Prentice Hall, 2001. http://books.google.com/books/about/Digital_communications.html?id=Bh4fAQAAIAAJ

2. Molisch, Andreas F. Wireless Communications. John Wiley and Sons, 2010. http://books.google.com/books/about/Wireless_Communications.html?id=vASyH5-jfMYC

3. Johnson, C. Richard, and Sethares, William A. Telecommunication Breakdown: Concepts of Communication Transmitted Via Software-Defined Radio. Prentice Hall, 2004.

4. Gu, Qizheng. RF System Design of Transceivers for Wireless Communications. Springer, 2005. http://books.google.com/books?id=fuUwM1Hiu24C