GSM Multiplexing Schemes

Step-by-Step Solution:

Why Other Options Are Incorrect:

Option A: Incorrect duplex spacing (20 MHz is wrong; it's 45 MHz). The calculation method is also incorrect—guard channels are already accounted for in the 124 carrier specification.

Option B: While the duplex spacing is correct (45 MHz), the carrier count is wrong. 25/0.2 = 125 mathematically, but GSM specifically defines 124 carriers (ARFCN 1-124) with ARFCN 0 typically unused or used for special purposes.

Option D: Completely incorrect approach. You cannot sum uplink and downlink bandwidths (they are separate frequency bands for FDD). Duplex spacing is 45 MHz, not 20 MHz.

Key Concept:

GSM uses FDD (Frequency Division Duplex) where uplink and downlink operate simultaneously on different frequencies separated by the duplex spacing (45 MHz for GSM 900). This allows full-duplex communication.

Detailed Analysis:

Guard Time Functionality:

The 30.46 μs guard time serves critical functions:

• Propagation Delay Compensation: Allows for different distances between mobile and base station (up to 35 km cell radius)
• Timing Advance: Mobiles closer to base station transmit later; those farther away transmit earlier
• Burst Synchronization: Prevents overlap between consecutive bursts from different mobiles
• Switching Time: Allows transmitter power ramp-up and ramp-down

Why Other Options Are Incorrect:

Option A: The 10% data rate reduction claim is arbitrary. The guard time is essential for system operation, not just overhead.

Option B: While mathematically close, it incorrectly states capacity reduction. The guard time doesn't reduce "capacity"—it's a necessary system design parameter. Also, 5.3% is not the standard metric used.

Option D: Quarter-rate coding (32 users) is not standard GSM. Also, guard time doesn't eliminate ISI "completely" nor allow 100% utilization—this is physically impossible in a TDMA system.

Key Concept:

GSM combines FDMA (200 kHz carriers) with TDMA (8 time slots). This hybrid approach is called Hybrid Multiple Access. The guard time is not wasted capacity but essential infrastructure enabling the cellular concept with variable distances.

Capacity Calculation:

Half-Rate Coding Trade-offs:

While half-rate coding doubles system capacity, it involves significant engineering trade-offs:

Parameter	Full-Rate (FR)	Half-Rate (HR)
Bit Rate	13 kbps	6.5 kbps
Voice Quality (MOS)	~4.0 (toll quality)	~3.5 (noticeable degradation)
Algorithm	RPE-LTP	VSELP or ACELP
Processing Delay	~20 ms	~30-40 ms
Error Sensitivity	Standard	Higher (more compression)

Why Other Options Are Incorrect:

Option A: While the calculation is correct, it oversimplifies the trade-offs by only mentioning MOS score and processing complexity. It misses critical aspects like increased delay and error sensitivity.

Option C: Incorrectly assumes guard bands reduce carrier count in this context. The 4.8 MHz allocation is the usable spectrum; guard bands are typically at band edges, not within the operator's allocation. Also, coverage reduction is not a direct trade-off of half-rate coding.

Option D: Fundamentally flawed. Channel spacing remains 200 kHz regardless of coding rate. Half-rate doesn't change the physical layer channel spacing—it only changes how time slots are assigned to users.

Engineering Insight:

Half-rate coding was introduced in GSM Phase 2+ primarily for capacity enhancement in dense urban areas or during events. However, with the advent of AMR (Adaptive Multi-Rate) coding in 3GPP, network operators can dynamically adjust coding rates based on channel conditions, making static half-rate assignment largely obsolete in modern networks.

The trade-off between spectral efficiency and quality of service is a fundamental concept in wireless engineering, directly impacting customer satisfaction and network planning.