Digital Signal Processing
BER, spectral efficiency, Shannon capacity, and standards based MCS throughput in one workspace. Compare BPSK, QPSK, PSK, QAM up to 4096 QAM, and FSK families against the Shannon limit, and compute peak throughput for LTE, 5G NR, WiFi 6 and 7, DVB T2 and S2, TETRA, DMR, and P25.
Free to use, no sign-up needed.
Walkthrough
Top bar with the three modes (Modulation analysis, Shannon capacity, Standards MCS).
Overview
Digital modulation choice is the lever that converts a noise limited link into a working data circuit. Pick the wrong scheme and you either give up usable throughput by under modulating, or you fail the bit error rate target by over modulating against an SNR that cannot support it. Modern digital standards (LTE, 5G NR, WiFi 6 and 7, DVB T2 and S2) handle this dynamically through Modulation and Coding Scheme (MCS) selection, but the underlying physics still has to be understood. Spectral efficiency, BER versus SNR, the Shannon Hartley bound, and the gap between practical schemes and the Shannon limit are the four numbers that set the achievable performance for any digital link.
The noIM₃ Modulation and Throughput Calculator covers all four together. Modulation analysis selects from any scheme between BPSK and 4096 QAM, with FSK and GMSK families included for narrowband PMR work. Output covers bits per symbol, spectral efficiency in bits per second per Hz (eta equals log base 2 of M times R), symbol rate, gross bit rate, net throughput after overhead, and BER versus SNR in AWGN computed from the exact Q function for PSK, rectangular QAM, and FSK. SNR margin against the Shannon limit is reported alongside a quality classification.
Shannon Hartley channel capacity (C equals B times log base 2 of (1 plus SNR)) is computed at any operating point against configurable bandwidth, SNR, noise figure, and system temperature. A comparison table benchmarks practical modulation schemes against the Shannon limit at the current operating point. Standards based MCS throughput covers the major digital standards in use today. LTE MCS 0 to 15. 5G NR FR1 with 1024 QAM (MCS 0 to 27) and FR2 mmWave. WiFi 5, WiFi 6, and WiFi 7 (including 4096 QAM MCS 13). DVB T2 and DVB S2 MODCOD tables. TETRA, DMR Tier II and III, and P25 Phase 2 for PMR work. Configure channel bandwidth and MIMO layers to compute a first-order modelled peak throughput, calibrated against published 3GPP and IEEE peak data rates.
Select any modulation scheme from BPSK through QPSK, 8 PSK, 16 PSK, 16 QAM, 32 QAM, 64 QAM, 128 QAM, 256 QAM, 512 QAM, 1024 QAM, and 4096 QAM, with BFSK, MSK, and GMSK for narrowband PMR. Output covers bits per symbol, symbol rate, gross bit rate, net throughput after coding rate and overhead, and spectral efficiency in bits per second per Hz.
Bit error rate computed using exact Q function formulas for PSK (Gray coded), rectangular QAM, and FSK families. Curves rendered across the SNR range so you can read the required SNR for a target BER directly. Useful for receiver sensitivity validation, modem specification cross check, and SNR margin work.
Theoretical channel capacity computed using C equals B times log base 2 of (1 plus SNR) with configurable bandwidth, SNR, noise figure, and system temperature. A comparison table benchmarks practical modulation schemes against the Shannon limit at the current operating point, showing percentage of theoretical capacity achieved by each scheme.
Built in MCS tables for LTE (MCS 0 to 15) and LTE Advanced. 5G NR FR1 with 1024 QAM (MCS 0 to 27) and FR2 mmWave. WiFi 5 (802.11ac), WiFi 6 (802.11ax), and WiFi 7 (802.11be) including 4096 QAM MCS 13. DVB T2 and DVB S2 MODCOD tables. TETRA, DMR Tier II and Tier III, and P25 Phase 2 for PMR. Configure channel bandwidth and MIMO layers to compute a first-order modelled peak throughput, calibrated against published 3GPP and IEEE peak data rates.
Up to 32 spatial streams supported (5G NR FR2 maximum). MIMO multiplies the spectral efficiency of the underlying modulation, so the throughput output reflects the per layer modulation scheme, the spatial multiplexing gain, and any antenna configuration constraints set by the standard.
Compares the configured operating SNR against the minimum required SNR for the chosen modulation scheme and BER target. Reports the margin in dB alongside a quality classification (excellent, good, marginal, insufficient). Useful for fast feasibility decisions during link budget development.
Chart based output covering BER versus SNR curves for each modulation family, throughput versus SNR comparison across schemes, spectral efficiency bar charts by coding rate, Shannon capacity curves with operating point overlay, and MCS throughput and minimum SNR bar charts for the selected standard.
Runs entirely in your browser. No modulation parameters, MCS configurations, or design data are submitted to a server. Useful for commercially confidential infrastructure work and environments where information security policy prohibits sending engineering data to third party services.
Inputs and outputs
Inputs 10
Outputs 14
Use cases
BPSK, QPSK, 8 PSK, 16 PSK, 16 QAM, 32 QAM, 64 QAM, 128 QAM, 256 QAM, 512 QAM, 1024 QAM, and 4096 QAM. BFSK, MSK, and GMSK are also covered for narrowband PMR work. BER versus SNR is computed from exact Q function formulas for PSK (Gray coded), rectangular QAM, and FSK (non coherent) families.
The Shannon Hartley channel capacity C equals B times log base 2 of (1 plus SNR) gives the theoretical maximum data rate at a given bandwidth and signal to noise ratio. The calculator computes C at the operating point and benchmarks every practical modulation scheme against it as a percentage. A 50 per cent of Shannon link is a competitive design. A 90 per cent of Shannon link is at the practical edge of what coding can achieve. Useful for understanding how much headroom is left in the channel before considering bandwidth or SNR upgrades.
Spectral efficiency in bits per second per Hz is the data rate per Hz of channel bandwidth. Eta equals log base 2 of M times R, where M is the modulation order and R is the coding rate. BPSK at full rate is 1 b per s per Hz. 64 QAM at 5 over 6 coding rate is 5 b per s per Hz. 256 QAM at 3 over 4 coding rate is 6 b per s per Hz. 1024 QAM at 5 over 6 coding rate is 8.33 b per s per Hz. The calculator surfaces eta directly so dense modulation modes can be compared on a like for like basis.
LTE MCS 0 to 15 and LTE Advanced. 5G NR FR1 with 1024 QAM (MCS 0 to 27) and FR2 mmWave. WiFi 5 (802.11ac), WiFi 6 (802.11ax), and WiFi 7 (802.11be including 4096 QAM MCS 13). DVB T2 and DVB S2 MODCOD tables. TETRA, DMR Tier II, DMR Tier III, and P25 Phase 2. Configure channel bandwidth and MIMO layers to compute a first-order modelled peak throughput, calibrated against published 3GPP and IEEE peak data rates.
Up to 32 spatial streams are supported, matching the maximum specified by 5G NR FR2. MIMO scales the spectral efficiency of the underlying modulation linearly under ideal channel conditions, so peak throughput equals per layer modulation throughput times the number of spatial layers. Real world MIMO efficiency depends on channel conditions, antenna correlation, and processing capability, but the peak number is what 3GPP and IEEE peak throughput claims reference.
Gross bit rate is the total bit rate transmitted including coding and protocol overhead. Net throughput is what the application actually receives after coding rate is applied (subtracting forward error correction redundancy) and protocol overhead is removed (control, pilot, framing). Net throughput is the number that actually matters for capacity planning and end user performance.
The required SNR for a chosen modulation and BER target feeds directly into the link budget as the receiver sensitivity threshold. The noIM₃ Link Budget Calculator consumes the required SNR and computes the link margin against the received power. Use the Modulation and Throughput Calculator to choose the scheme and identify the required SNR. Use the Link Budget Calculator to confirm whether the link delivers enough received power and SNR to support that scheme.
No. The calculator runs entirely in your browser. No modulation parameters, MCS configurations, or design data are submitted to a server. Useful for commercially confidential infrastructure work and environments where information security policy prohibits sending engineering data to third party services.
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