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Chapter 5: Problem 14

A cellular radio system uses a frequency reuse plan with 12 cells per cluster. If ideal 8 -PSK modulation is used, what is the system spectral efficiency in terms of bit/s/Hz/cell?

Short Answer

Expert verified
The system spectral efficiency is 0.25 bit/s/Hz/cell.

Step by step solution

01

- Understand Frequency Reuse

Frequency reuse is the concept of using the same frequency channels in different cells within a cellular network to optimize the use of the available spectrum. In this case, 12 cells per cluster means that each frequency channel is reused every 12 cells.
02

- Determine System Modulation

The problem states that 8-PSK (Phase Shift Keying) modulation is used. 8-PSK can encode 3 bits per symbol since \[ 2^3 = 8 \].
03

- Calculate Frequency Channels Per Cell

With 12 cells per cluster, each cell gets \[ \frac{1}{12} \] of the total available frequency spectrum.
04

- Compute Spectral Efficiency

Spectral efficiency is calculated by multiplying the number of bits per symbol by the fraction of the spectrum assigned to each cell. The spectral efficiency in bit/s/Hz/cell for 8-PSK with 12 cells per cluster is \[ \frac{3 \text{ bits/symbol}}{12} = 0.25 \text{ bit/s/Hz/cell} \].

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Key Concepts

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

Understanding Frequency Reuse
Frequency reuse is an essential concept in cellular systems. It aims to maximize spectrum efficiency by using the same frequency channels in different cells within a network. For our exercise, there's a frequency reuse pattern of 12 cells per cluster. This means each frequency channel can be reused every twelve cells, allowing the network to cover more area with the limited spectrum. This reuse plan helps to minimize interference between cells operating on the same frequency, thus optimizing the performance while conserving spectral resources.
8-PSK Modulation Simplified
8-PSK, or 8-Phase Shift Keying, is a modulation scheme that can transmit 3 bits per symbol. Modulation is the process of varying a signal to encode information. In the case of 8-PSK, the signal can occupy one of eight distinct phase positions. Because there are 8 possible positions, we use three bits to represent each phase: \( 2^3 = 8 \). Therefore, each symbol in 8-PSK modulation carries 3 bits of information. This makes 8-PSK more efficient than simpler modulation schemes like BPSK, which only carries 1 bit per symbol, or QPSK, which carries 2 bits.
Spectral Efficiency Calculation Steps
Calculating spectral efficiency involves determining how efficiently a system uses its available frequency spectrum. For our problem, the calculation requires combining the frequency reuse factor and the modulation level. In a scenario with 12 cells per cluster, each cell gets \( \frac{1}{12} \) of the total frequency spectrum. For 8-PSK modulation, each symbol carries 3 bits. So, the spectral efficiency formula becomes:
\[ \text{Spectral Efficiency} = \frac{\text{Bits per Symbol}}{\text{Number of Cells per Cluster}} \] Applying the provided values:
\[ \frac{3 \text{ bits/symbol}}{12} = 0.25 \text{ bit/s/Hz/cell} \] This shows the spectral efficiency is 0.25 bit/s/Hz/cell.
Understanding Bits Per Symbol
Bits per symbol is a measure of how many bits of information each symbol in a modulation scheme carries. For 8-PSK, we have 8 different phase states, each representing one symbol. To find out how many bits are represented by these 8 symbols, we use the formula: \( 2^n = 8 \), where \( n \) is the number of bits per symbol. Solving for \( n \), we get \[ n = 3 \] bits per symbol. This means each symbol in 8-PSK modulation encodes 3 bits of data. Higher bits per symbol increase data capacity, but often require more complex signal processing and can be more susceptible to noise.

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Most popular questions from this chapter

The L1 band of the global positioning system (GPS), is centered at \(1.57542 \mathrm{GHz}\) and has two overlapping spread-spectrum encoded signals. The stronger of these is the coarse acquisition \((\mathrm{C} / \mathrm{A})\) signal with an information bit rate of 50 bits \(/ \mathrm{s}\) and a transmission rate of 1.023 million chips per second using BPSK modulation with an RF bandwidth of \(2.046 \mathrm{MHz}\). In ideal conditions the \(\mathrm{C} /\) A signal received has a power of \(-130 \mathrm{dBm}\). A GPS receiver has an antenna noise temperature is of \(290 \mathrm{~K}\). (a) What is the processing gain? (b) What is the noise in \(\mathrm{dBm}\) received in the \(2.046 \mathrm{MHz}\) bandwidth? (c) What is the SNR in decibels? (d) If a C/A signal is received from each of 10 satellites (so there are 9 interfering signals), what is the total interference power for one satellite's \(\mathrm{C} / \mathrm{A}\) signal? (e) With respect to just one of the \(\mathrm{C} / \mathrm{A}\) signals, what is the SINR (signal to interference plus noise ratio) at the receiver? (f) If the receiver does not contribute noise, what is the effective SNR of the despread bitstream from each satellite? (g) If the required minimum effective SNR is \(6 \mathrm{~dB}\), what is the minimum acceptable power, in \(\mathrm{dBm}\), of the GPS signal received from one satellite?

A free-space \(2 \mathrm{GHz}\) pulsed monostatic radar system transmits a \(2 \mathrm{~kW}\) pulse and has a minimum detectable received signal power of \(-90 \mathrm{dBm}\). What is the antenna gain required to be able to detect a target with a radar cross section of \(10 \mathrm{~m}^{2}\) at \(10 \mathrm{~km} ?\)

GLONASS is the Russian satellite navigation system with one of two open signals called the L1OF band at \(1600.995 \mathrm{MHz}\). The system uses DSSS encoding and BPSK modulation and each GLONASS satellite transmits on a different frequency. The symbol rate is 511,000 chips \(/ \mathrm{s}\), the bandwith of the transmitted signal is approximately \(540 \mathrm{kHz}\), and there are 50 information bits per second. (a) What is the system's processing gain? (b) What is the noise in \(\mathrm{dBm}\) received in the \(540 \mathrm{kHz}\) bandwidth? (c) If the required system minimum effective SNR is \(6 \mathrm{~dB}\), what is the minimum acceptable power, in \(\mathrm{dBm}\), of the received signal? Assume that the receiver is noiseless.

A \(4 \mathrm{kHz}\) bandwidth voice signal is coded by a vocodor as an 8 kbit/s data stream. Coding increases the data stream to \(64 \mathrm{kbit} / \mathrm{s}\). What is the processing gain that can be achieved at the receiver if QPSK modulation is used with a modulation efficiency of 1.4 bit \(/ \mathrm{s} / \mathrm{Hz}\) ?

A communication system uses a modulation with a modulation efficiency of \(5 \mathrm{bit} / \mathrm{s} / \mathrm{Hz} .\) Ignore coding so that \(R_{b}=R_{c}\). What is the radio spectral efficiency in terms of bit/s/Hz/cell if there are three cells per cluster?
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