Cellular Radio Erlang Capacity & Sector Blocking Calculator

1. Fundamental Constraints of Wireless Media: Spectrum Boundaries

Unlike wireline PSTN circuits or IP packet backbones where optical fiber transmission paths can be expanded with additional wavelengths, cellular radio networks operate within strictly bounded, licensed radio frequency (RF) spectrum allocations. Every hertz of bandwidth is regulated by international and national authorities (e.g., ITU-R, FCC, ETSI). Consequently, cellular capacity engineering is fundamentally an exercise in allocating scarce time-frequency physical resources among competing signaling overheads, real-time interactive voice calls, and high-throughput mobile broadband (MBB) data streams.

In cellular systems, Grade of Service (GoS) represents the statistical probability that a mobile subscriber attempting to initiate a voice call during the peak busy hour encounters a network rejection or “fast-busy” tone due to resource exhaustion on the radio air interface:

Where m represents the integer quantity of assignable voice bearer channels per sector, and A is the offered busy-hour voice traffic in Erlangs.

2. Hard Blocking vs. Soft Blocking Physics

Cellular radio architectures are broadly classified into two distinct blocking regimes:

• Hard Blocking Systems (TDMA & OFDMA): Utilized in 2G GSM (discrete time-slots per RF carrier) and resource-partitioned 4G LTE / 5G NR (Physical Resource Blocks). In a hard-blocked cell, there exists a rigid, mathematically finite ceiling of discrete channels m. If all m timeslots or PRB voice grants are active, the (m + 1)^th incoming call request is immediately denied connection regardless of RF signal conditions. The standard Erlang B loss formula models hard blocking with exact precision.
• Soft Blocking Systems (CDMA / WCDMA): Historically prevalent in 3G systems using universal frequency reuse. There is no rigid hardware channel ceiling; rather, capacity is interference-limited. Each active mobile transmitter raises the ambient uplink interference floor (measured as Rise over Thermal, RoT). When total interference reaches the target noise threshold, the base station cannot maintain the required Signal-to-Interference-plus-Noise Ratio (SINR). The effective coverage radius of the cell shrinks—a physical phenomenon known as cell breathing—resulting in dropped calls or blocked originations at the cell fringe.

3. 2G GSM Architecture: Timeslots, TRXs, and Signaling Deductions

In GSM cellular networks, each 200 kHz RF carrier (Transceiver / TRX) is structured as a repeating Time Division Multiple Access (TDMA) frame divided into 8 discrete timeslots (TS 0 through TS 7). However, an engineer cannot simply multiply the number of TRXs by 8 to determine voice capacity:

• Timeslot 0 on TRX 1: Exclusively dedicated to broadcast beacon signaling, housing the Broadcast Control Channel (BCCH), Frequency Correction Channel (FCCH), and Synchronization Channel (SCH). No user voice traffic may be scheduled on this slot.
• Timeslot 1 on TRX 1: Typically provisioned as a Standalone Dedicated Control Channel (SDCCH/8), enabling call setup signaling, ciphering negotiation, SMS transmission, and location registration handshakes.
• Remaining Capacity on TRX 1: Only 6 timeslots remain available for user Traffic Channels (TCH/F).
• Subsequent TRXs (TRX 2, TRX 3, TRX 4): Do not require duplicate broadcast beacon channels; all 8 timeslots are fully assignable as traffic channels (unless an additional SDCCH is provisioned to support extreme SMS signaling load).

For a 2-TRX sector, m = (2 × 8) - 2 = 14 TCH channels. At standard 2.0% GoS, 14 channels support 8.20 Erlangs of offered traffic. Enabling Half-Rate coding (TCH/H) doubles the effective timeslot utilization to 28 voice channels, supporting 20.15 Erlangs (a 145% capacity expansion) at the expense of acoustic fidelity.

4. LTE & 5G NR Voice Dimensioning: VoLTE, VoNR, and Semi-Persistent Scheduling (SPS)

In 4G LTE (E-UTRA) and 5G NR (gNodeB), circuit-switched voice channels are completely replaced by packetized Voice over LTE (VoLTE) and Voice over New Radio (VoNR). Voice speech is digitized using the Adaptive Multi-Rate Wideband (AMR-WB) codec or Enhanced Voice Services (EVS) codec, encapsulated inside IP/UDP/RTP packets, and transmitted over the shared time-frequency OFDM resource grid.

The basic unit of radio resource allocation is the Physical Resource Block (PRB), spanning 180 kHz in frequency (12 subcarriers of 15 kHz in LTE or 30 kHz in 5G numerology μ=1) over 1 millisecond.

Because voice generates a small packet every 20 ms, dynamic scheduling would require scheduling grants on the Physical Downlink Control Channel (PDCCH) for every individual packet. With hundreds of active callers, the PDCCH control channel would saturate and collapse long before data PRBs were exhausted.

Semi-Persistent Scheduling (SPS - 3GPP TS 36.321 / 38.321): Overcomes this bottleneck by establishing a deterministic, repeating resource grant every 20 ms. Once initialized, the UE transmits without requiring dynamic PDCCH grants. Combined with Robust Header Compression (ROHC - RFC 3095), which compresses the 40-byte IP/UDP/RTP header down to 2 to 4 bytes, a single HD voice packet occupies only 1 to 1.2 PRBs per transmission instance.

5. Grade of Service (GoS) Standards & Cellular Sectorization Pooling

Wireline toll transit switches historically dimension trunks to strict GoS = P.001 to P.01 (0.1% to 1.0% blocking). In commercial cellular networks, economic trade-offs between expensive RF spectrum and user acceptance dictate a standard operating target of GoS = P.02 (2.0% blocking) during the Time-Consistent Busy Hour (TCBH). During temporary special events (e.g., stadium concerts or stadium Cells-on-Wheels [COW]), operators frequently relax GoS to P.05 (5.0% blocking) to squeeze maximum carried Erlangs from limited carrier assets.

Sectorization and the Erlang Pooling Penalty: Dividing a single 360° omni-directional site into three 120° directional sectors triples frequency reuse and dramatically lowers co-channel interference, multiplying aggregate site throughput. However, splitting a site’s physical voice channels into three independent, non-shared pools incurs a mathematical trunking efficiency loss:

For example, 3 separate sectors of 12 channels each support 3 × 6.61 = 19.84 Erlangs at P.02 GoS. If all 36 channels could be dynamically pooled into a single consolidated trunk group, they would support 27.34 Erlangs. Cellular RF planning engineers must balance this 27% pooling penalty against the massive signal-to-interference (SINR) and spatial reuse advantages of directional sectorization.