Channelization: Structured Channel Sharing

While FDMA divides the spectrum into frequency bands, Time Division Multiple Access (TDMA) takes a fundamentally different approach: it divides time into discrete intervals called time slots. Each user is assigned specific time slots during which they have exclusive access to the entire channel bandwidth.

This paradigm shift has profound implications. Where FDMA users transmit continuously at low power on narrow bands, TDMA users transmit in bursts at higher power using the full bandwidth. Where FDMA requires precise frequency filtering, TDMA requires precise timing synchronization. Each approach has its strengths, and understanding TDMA deeply reveals why it became the foundation for second-generation (2G) digital cellular systems like GSM.

TDMA's elegance lies in its digital nature: it naturally integrates with digital signal processing, enables efficient speech compression, supports encryption, and provides built-in capacity for signaling and control—all while potentially achieving better spectral efficiency than pure FDMA.

The core principle of TDMA is deceptively simple: divide time into repeating cycles called frames, where each frame contains multiple time slots. Each user is assigned one or more slots per frame. During their assigned slot, a user has exclusive access to the entire channel bandwidth; during other slots, they must remain silent.

The Frame Structure:

A TDMA frame is the fundamental timing unit. It repeats continuously, creating a periodic pattern:

$$T_{\text{frame}} = N \times T_{\text{slot}}$$

where $N$ is the number of slots per frame and $T_{\text{slot}}$ is the duration of each slot.

For a system to support $N$ users with equal access, each user transmits once per frame, meaning the frame rate equals the user's transmission opportunity rate:

$$R_{\text{access}} = \frac{1}{T_{\text{frame}}} = \frac{1}{N \times T_{\text{slot}}}$$

Burst Mode Transmission:

The key characteristic of TDMA is burst transmission. Consider a voice call that generates data continuously at rate $R_v$. In FDMA, this data is transmitted continuously. In TDMA, the same data must be:

1. Buffered during the frame until the user's slot arrives
2. Transmitted at a higher rate to fit all buffered data into the slot
3. Reconstructed at the receiver from the bursty stream

The burst data rate $R_b$ relates to the continuous rate $R_v$ by:

$$R_b = R_v \times \frac{T_{\text{frame}}}{T_{\text{slot}}} = R_v \times N$$

If $N = 8$ users share a frame, each user must transmit at 8× their continuous data rate during their slot.

TDMA's effectiveness depends entirely on precise synchronization. All users must agree exactly when each time slot begins and ends. If User A's transmission extends into User B's slot, both transmissions are corrupted. This synchronization challenge is TDMA's most demanding requirement.

Timing Advance Mechanism:

To compensate for propagation delay, TDMA systems use timing advance. The base station measures the round-trip delay to each mobile and instructs it to transmit earlier by half that delay. This ensures all mobile signals arrive at the base station synchronized to the frame timing.

$$T_{\text{advance}} = \frac{d}{c} = \frac{\text{distance to base station}}{\text{speed of light}}$$

GSM measures timing advance in units of 0.9615 µs (1/2 of a symbol period), with values from 0 to 63, allowing compensation for distances up to approximately 35 km:

$$d_{\text{max}} = 63 \times 0.9615 \times 10^{-6} \times 3 \times 10^8 \approx 35 \text{ km}$$

Synchronization Sequence:

Each TDMA burst contains a training sequence or midamble—a known bit pattern that the receiver uses to:

1. Verify slot timing — Detect and correct small timing errors
2. Estimate channel response — Characterize multipath and fading for equalization
3. Synchronize demodulator — Align carrier frequency and phase for coherent detection

GSM uses a 26-bit training sequence in the middle of each burst (the midamble position reduces timing uncertainty). There are 8 different training sequences, allowing interference identification in frequency-reuse scenarios.

Just as FDMA requires guard bands between frequency channels, TDMA requires guard times between time slots. Guard times are brief periods of silence that prevent adjacent slot overlap due to timing uncertainties.

Purposes of Guard Times:

Calculating Guard Time Requirements:

The minimum guard time depends on several factors:

$$T_{\text{guard}} \geq \Delta T_{\text{timing}} + T_{\text{ramp}} + \tau_{\text{delay-spread}} + T_{\text{margin}}$$

where:

• $\Delta T_{\text{timing}}$ is residual timing uncertainty after timing advance
• $T_{\text{ramp}}$ is transmitter rise/fall time
• $\tau_{\text{delay-spread}}$ is the channel's delay spread (multipath)
• $T_{\text{margin}}$ is safety margin

GSM Guard Time Example:

GSM normal burst:

• Total slot duration: 156.25 bit periods = 577 µs
• Active data transmission: 148 bits = 546 µs
• Guard period: 8.25 bit periods = 30.5 µs

The 30.5 µs guard time allows for:

• ±5 µs timing uncertainty
• 10 µs transmitter ramping
• 10 µs multipath delay spread (typical urban)
• 5 µs margin

Real TDMA systems use hierarchical frame structures to organize traffic, signaling, and control information. The multiframe and superframe concepts enable allocation of resources for different purposes.

GSM Frame Hierarchy:

GSM uses a sophisticated frame hierarchy:

• Time Slot: 577 µs, carries 156.25 bits
• TDMA Frame: 8 slots = 4.615 ms
• Multiframe: 26 frames (traffic) or 51 frames (control) = 120 ms or 235 ms
• Superframe: 26 × 51 = 1326 frames = 6.12 seconds
• Hyperframe: 2048 superframes = 3 hours 28 minutes (used for encryption)

This hierarchy serves multiple purposes:

• Traffic multiframe (26 frames): 24 for voice/data, 1 for signaling, 1 idle
• Control multiframe (51 frames): System synchronization, paging, broadcast

Burst Types:

Different slot usages require different burst structures:

Normal Burst (NB): Used for traffic and most signaling

• 3 tail bits + 58 encrypted bits + 26 training bits + 58 encrypted bits + 3 tail bits + 8.25 guard bits

Access Burst (AB): Used for initial random access (RACH)

• 8 tail bits + 41 sync bits + 36 encrypted bits + 3 tail bits + 68.25 guard bits
• Longer guard time because timing advance is unknown

Frequency Correction Burst (FB): Carries a pure tone for frequency correction

• Enables mobiles to lock to the base station's frequency reference

Synchronization Burst (SB): Provides frame synchronization information

• Contains extended training sequence for timing and synchronization

A key advantage claimed for TDMA over FDMA is improved spectral efficiency. Let's analyze this claim rigorously.

TDMA Channel Capacity:

For a TDMA system with $N$ slots per frame:

$$\text{Users per RF channel} = N$$

If the system has total bandwidth $W$ and each RF carrier occupies bandwidth $B_c$:

$$\text{Total RF channels} = \frac{W}{B_c + B_g}$$

where $B_g$ is the guard band between RF carriers. The total user capacity is:

$$C_{\text{TDMA}} = N \times \frac{W}{B_c + B_g}$$

Comparison with FDMA:

For FDMA with the same total bandwidth, if each user requires bandwidth $B_u$:

$$C_{\text{FDMA}} = \frac{W}{B_u + B_{g,\text{FDMA}}}$$

TDMA can be more efficient if $N \times \frac{1}{B_c + B_g} > \frac{1}{B_u + B_{g,\text{FDMA}}}$

Efficiency Factors:

TDMA efficiency depends on several factors:

1. Slot Overhead: Training sequences, guard times, and signaling reduce effective capacity
2. Compression Efficiency: Digital voice compression enables more users per Hz
3. Statistical Multiplexing: TDMA can dynamically allocate slots based on demand (unlike fixed FDMA)
4. Half-Rate Support: TDMA can double capacity using half-rate codecs when quality tolerance allows

Spectral Efficiency Calculation:

$$\eta_{\text{TDMA}} = \frac{\text{Useful data bits per frame}}{\text{Total bits per frame}} \times \frac{B_{\text{data}}}{B_{\text{total}}}$$

For GSM: $\eta \approx 0.8 \times 0.85 = 0.68$ (68% excluding error correction overhead)

Understanding the trade-offs between TDMA and FDMA is essential for system design. Each approach has distinct characteristics that make it suitable for different applications.

TDMA has been deployed in numerous communication systems, from cellular networks to satellite links. Understanding these applications reveals the technique's versatility.

We've explored TDMA from fundamental concepts through practical system design. Let's consolidate the essential knowledge:

Critical Formulas:

$$T_{\text{frame}} = N \times T_{\text{slot}}$$

$$R_{\text{burst}} = R_{\text{continuous}} \times N$$

$$T_{\text{advance}} = \frac{d}{c}$$

$$C_{\text{TDMA}} = N \times \frac{W}{B_c + B_g}$$

What's Next:

In the next page, we explore CDMA (Code Division Multiple Access), the most sophisticated of the channelization techniques. CDMA allows all users to transmit simultaneously on the same frequency at the same time—distinguished by unique codes. This seemingly impossible feat relies on spread spectrum technology and code orthogonality, achieving remarkable spectral efficiency and graceful capacity degradation.