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Chapter 5: Problem 36

An OFDM system with 48 subcarriers carrying data uses 16-QAM modulation of each subcarrier and a coding rate of \(2 / 3\). The actual modulation efficiency for the 16-QAM system here is 2.7 bit \(/ \mathrm{s} / \mathrm{Hz}\). What is the maximum data rate supported in Mbit/s when the bandwidth of each modulated subcarrier is \(312 \mathrm{kHz}\) ?

Short Answer

Expert verified
39.936 Mbit/s

Step by step solution

01

Determine the Bits per Symbol

In an OFDM system using 16-QAM modulation, each symbol carries 4 bits. Given the modulation efficiency of 2.7 bits/Hz, we first confirm that this efficiency fits the modulation scheme. Typically, 16-QAM has an efficiency of 4 bits/symbol. Let's continue with efficiency given.
02

Calculate the Effective Bits per Symbol

The system uses a coding rate of \(\frac{2}{3}\), meaning \(\frac{2}{3}\) of the total bits are useful. Therefore, the effective bits per symbol is \(4 \times \frac{2}{3} = \frac{8}{3} \text{ bits/symbol}\).
03

Calculate the Total Bandwidth

Bandwdith of each subcarrier is \(312 \text{kHz}\). In the system, 48 subcarriers carry data: \(312 \text{kHz} \times 48 = 14,976 \text{kHz} = 14.976 \text{ MHz}\).
04

Calculate Total Data Rate

To find the total data rate, multiply the effective bits per symbol by the number of subcarriers and the bandwidth of each subcarrier.\( \text{Total Data Rate} = \frac{8}{3} \text{ bits/symbol} \times 48 \text{ subcarriers} \times 312 \text{kHz}\)
05

Convert Total Data Rate into Mbit/s

First, compute the product from step 4: \( \frac{8}{3} \times 48 \times 312 \text{kHz} = 39936 \text{kbit/s} = 39.936 \text{Mbit/s} \). This is the maximum data rate supported.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Orthogonal Frequency Division Multiplexing (OFDM)
Orthogonal Frequency Division Multiplexing (OFDM) is a digital multi-carrier modulation method. It efficiently divides a single data stream into multiple smaller streams that are then transmitted simultaneously on different frequencies.
Key characteristics of OFDM include:
  • Orthogonality: Ensures subcarriers are mathematically orthogonal, which means there's no interference among them.
  • Resilience: Highly resilient to signal interference and fading.
  • Efficiency: Maximizes data rate and spectral efficiency, making it widely used in modern wireless systems, such as Wi-Fi and LTE.
Using OFDM helps improve the reliability and speed of data transmission.
16-QAM Modulation
16-QAM stands for 16-Quadrature Amplitude Modulation. It's a modulation technique that carries data by changing (modulating) the amplitude of two carrier waves that are out of phase by 90 degrees.
In 16-QAM:
  • Each symbol represents 4 bits of data. This is higher than simpler modulations like QPSK.
  • The modulation scheme consists of 16 distinct symbols (hence the '16' in 16-QAM).
  • This allows for more efficient data transmission but at the cost of lower signal robustness compared to simpler schemes. Hence, it鈥檚 more suitable when the signal-to-noise ratio (SNR) is high.
In our OFDM system, 16-QAM helps achieve higher data rates by transmitting more bits per symbol.
Coding Rate
The coding rate explains how redundancy is added to the data stream for error correction. A coding rate of \( \frac{2}{3} \) means only \( \frac{2}{3} \) of the data is useful, while the rest is extra data used for error detection and correction.
Considerations:
  • This redundancy helps in correcting errors caused by noise and interference.
  • Low coding rates (more redundancy) improve robustness but reduce efficiency. High coding rates improve efficiency but reduce robustness.
In this example, with a coding rate of \( \frac{2}{3} \), for every 3 transmitted bits, 2 bits represent actual data, and 1 bit is for error correction.
Bandwidth
Bandwidth refers to the width of the frequency band used for transmitting data. In an OFDM system, the bandwidth of each subcarrier is crucial for determining the overall data rate.
Key points:
  • Each subcarrier in our OFDM system uses 312 kHz bandwidth.
  • The total bandwidth used by the system is derived by multiplying this value by the total number of subcarriers. So, for 48 subcarriers the total bandwidth is \( 312 \text{kHz} \times 48 = 14,976 \text{kHz} \text{ or } 14.976 \text{MHz} \).
The allocated bandwidth directly influences the number of bits that can be transmitted and ultimately affects the data rate.
Bits per Symbol
In digital modulation schemes and specifically in OFDM, 'bits per symbol' defines the number of bits each symbol can carry. For example, in 16-QAM, each symbol represents 4 bits.
Steps to calculate effective bits per symbol:
  • Identify the initial bits per symbol from the modulation scheme. For 16-QAM, this is 4 bits.
  • Adjust for coding rate. With a coding rate of \( \frac{2}{3} \), the useful bits are \( 4 \times \frac{2}{3} = \frac{8}{3} \) bits/symbol.
In our example, the coding rate modifies the number of effective bits per symbol, accounting for error correction and ensuring more reliable data transmission.

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Most popular questions from this chapter

An antenna with a gain of \(10 \mathrm{~dB}\) presents an \(\mathrm{RF}\) signal with a power of \(5 \mathrm{dBm}\) to a low-noise amplifier along with noise of \(1 \mathrm{~mW}\) and an interfering signal of \(2 \mathrm{~mW}\). (a) What is the RF SIR? Include both noise and the interfering signal in your calculation. Express your answer in decibels. (b) The modulation format and coding scheme used have a processing gain, \(G_{P}\), of \(7 \mathrm{~dB}\). The modulation scheme has four states. What is the ratio of the energy per bit to the noise per bit, that is, what is the effective \(E_{b} / N_{o}\) after despreading?

The receiver in a digital radio system receives a \(100 \mathrm{pW}\) signal and the interference from other radios at the input of the receiver is \(20 \mathrm{pW}\). The receiver has an overall gain of \(40 \mathrm{~dB}\) and the noise added by the receiver, referred to the out- $$2$$ put of the receiver, is \(100 \mathrm{nW}\). (a) What is the RF SIR at the output of the receiver? (b) If 16-QAM modulation with a modulation efficiency of \(2.98 \mathrm{bit} / \mathrm{s} / \mathrm{Hz}\) is used and the processing gain is \(30 \mathrm{~dB}\), what is the effective SIR after despreading, i.e. what is \(E_{b, \text { eff }} / N_{o, b} ?\)

A proposed modulation format has a modulation efficiency of \(3.5 \mathrm{bit} / \mathrm{s} / \mathrm{Hz}\). Antenna sectoring and required SNR lead to a system with seven cells per cluster. You can ignore the impact of coding so you can assume that \(R_{b}=R_{c}\) What is the radio spectral efficiency in terms of bit/s \(/ \mathrm{Hz} /\) cell modulated signal?

A cellular communication system uses a frequency reuse plan with seven cells per cluster to obtain the required minimum SIR. If a QPSK system is used, what is the radio spectrum efficiency in terms of bit/s/Hz/cell if all transitions on the constellation diagram are allowable? Assume that there is no coding.

Research at Bell Labs in the 1960 s showed that the minimum acceptable SIR for voice communications is \(17 \mathrm{~dB}\). This applies to analog modulated signals, but not digitally modulated signals, where BER is important. Consider a sevencell cluster. If the power falls off as \(1 / d^{3}\), where \(d\) is distance, determine the worst possible SIR considering only interference from other radios. The worst situation will be when a mobile handset is at the edge of its cell. To do this you need to estimate the distance from the handset to the other basestations (in neighboring clusters) that are operating at the same power levels. Consider the cells to be hexagons. Develop a symbolic expression for the total interference signal level at the handset, assuming that all basestations are radiating at the same power level, \(P\). You can use approximate distances. For example, each distance can be expressed in terms of integer multiples of cell radii, \(R\). Is the \(17 \mathrm{~dB}\) SIR achieved using a 7-cell cluster?
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