3 (10 marks) In a QPSK system the bit rate

Ideas for Solving the Problem

1. Symbol Rate in QPSK: In Quadrature Phase Shift Keying (QPSK), each symbol represents two bits. The symbol rate is therefore half the bit rate.
2. Bandwidth Efficiency: Bandwidth efficiency is defined as the bit rate divided by the bandwidth. For QPSK, the bandwidth is approximately twice the symbol rate.
3. Comparison with ASK: Amplitude Shift Keying (ASK) generally requires a larger bandwidth for the same bit rate compared to QPSK. We’ll compare bandwidth efficiencies to illustrate this.

Calculation Steps

Step 1: Calculating the Symbol Rate

Given that the bit rate is 10 Mbps, the symbol rate in QPSK is:

Symbol Rate = Bit Rate / 2 = 10 Mbps / 2 = 5 Mbps

Step 2: Calculating the Bandwidth

The bandwidth (B) of a QPSK signal is approximately twice the symbol rate:

B ≈ 2 * Symbol Rate = 2 * 5 Mbps = 10 MHz

Step 3: Calculating the Bandwidth Efficiency of QPSK

Bandwidth Efficiency (QPSK) = Bit Rate / Bandwidth = 10 Mbps / 10 MHz = 1 bit/s/Hz

Step 4: Comparing with ASK

ASK typically has a bandwidth efficiency of approximately 1 bit/s/Hz. However, this is highly dependent on the specific modulation scheme used. In general, QPSK offers better bandwidth efficiency than ASK for the same bit rate. A more precise comparison would require specifying the exact ASK modulation scheme.

Final Answer

The symbol rate for the QPSK system is 5 Mbps. The bandwidth efficiency is 1 bit/s/Hz. Compared to ASK, QPSK generally offers similar or better bandwidth efficiency. A direct numerical comparison requires specifying the ASK modulation parameters.

Highlights

• QPSK doubles the bit rate compared to BPSK for the same bandwidth.
• The bandwidth of a QPSK signal is approximately twice its symbol rate.
• The bandwidth efficiency comparison between QPSK and ASK is not always straightforward and depends on the specific ASK modulation scheme. QPSK generally offers better spectral efficiency.
• The carrier frequency (2 MHz) is not directly used in calculating the symbol rate or bandwidth efficiency in this problem. It is relevant for other aspects of system design, such as channel selection and filtering.