Digital Signal Processing

Constellation Diagram Analyser

Multi impairment IQ constellation workbench from BPSK to 4096 QAM including the 128 and 512 QAM cross constellations used by microwave backhaul, plus the land mobile radio and narrowband waveforms: pi over 4 DQPSK (TETRA), pi over 8 D8PSK (TETRA TEDS), 4FSK (DMR, P25 C4FM, NXDN), and 2FSK (POCSAG, MPT 1327, RTTY). Apply AWGN, phase noise, IQ imbalance, AM AM and AM PM nonlinearity, carrier frequency offset, OFDM PAPR clipping, and inter carrier interference, with automatic impairment diagnosis and a paired eye diagram view.

Free forever on a Standard account. No credit card.

Overview

Every RF impairment leaves a fingerprint on the IQ constellation. AWGN noise produces a circular blur around each ideal symbol point. Phase noise smears symbols along arcs centred on the origin. IQ amplitude imbalance compresses one axis. IQ phase imbalance skews the grid. Carrier frequency offset rotates the entire constellation, with the rotation rate proportional to the offset. AM AM nonlinearity compresses outer symbols radially. AM PM rotates outer symbols. DC offset shifts the centre. Each pattern is recognisable to a trained eye, but the recognition takes practice and the design discussion is faster when the tool can name the impairment for you.

The noIM₃ Constellation Diagram Analyser is a complete IQ signal quality workbench that renders constellations for BPSK, QPSK, 8 PSK, and QAM 16 through QAM 4096, applies nine independent RF impairments in a physically motivated cascade, and automatically diagnoses the dominant degradation mechanism. The impairments map directly to the hardware blocks they originate from. AM AM compression from the power amplifier. AM PM phase shift from the same amplifier nonlinearity. OFDM PAPR clipping from the transmit chain. IQ amplitude and phase imbalance from the modulator. Carrier phase rotation from the synthesiser. Per symbol phase noise from the local oscillator. AWGN from the receive chain. DC offset on each axis.

EVM contributions from each source are computed analytically and combined via root sum of squares. AWGN gives EVM equals 100 divided by square root of SNR linear, expressed as percentage. Phase noise gives EVM equals sin of phi rms in radians times 100 per cent. IQ amplitude imbalance gives EVM equals magnitude of (10 to the G over 20 minus 1) divided by square root of 2 times 100 per cent. IQ phase imbalance gives EVM equals magnitude of sin of theta over 2 times 100 per cent. A horizontal bar chart shows each source as a percentage of total EVM power, identifying the dominant impairment. A separate eye diagram panel applies a raised cosine matched filter at configurable rolloff and overlays 200 traces, providing the canonical timing margin and ISI view alongside the constellation.

Capabilities

Fifteen modulation formats

BPSK, QPSK, and 8 PSK from the PSK family. Pi over 4 DQPSK (TETRA, P25 CQPSK heritage) and pi over 8 D8PSK (TETRA TEDS) from the differential PSK family, rendered as the full 8 and 16 point visible symbol unions. 2FSK (POCSAG paging, MPT 1327 FFSK control channels, RTTY) and 4FSK (DMR, P25 C4FM, NXDN) rendered in the deviation domain, the convention used by land mobile radio test sets. 16 QAM, 64 QAM, 256 QAM, 1024 QAM, and 4096 QAM from the rectangular QAM family plus the 32, 128, and 512 QAM cross constellations (square grids with corner blocks removed) used by point to point microwave backhaul radios. Ideal points rendered in red and received impaired symbols in blue.

Nine impairment chain

AM AM radial compression r prime equals r over square root of (1 plus beta r squared). AM PM phase rotation delta phi equals alpha r squared. OFDM PAPR hard clip at configurable dB above RMS. IQ amplitude imbalance with I and Q arms scaled inversely. IQ phase imbalance with the Q axis rotated from 90 degrees. Carrier phase rotation. DC offset on I and Q independently. Per symbol phase noise as Gaussian phase rotation. AWGN. Applied in a physically motivated cascade matching the hardware order.

Carrier frequency offset (CFO)

CFO specified in Hz or ppm and converted to a phase increment per symbol. Each rendered symbol accumulates the phase, producing the characteristic arc or ring pattern of uncompensated frequency offset. In animated mode the symbols stream in with cumulative phase, showing the rotation rate visually. Normalised CFO epsilon equals f CFO divided by f sym is displayed for AFC loop budget assessment.

OFDM mode and inter carrier interference

Enabling OFDM mode activates PAPR hard clipping at a configurable level (compresses outer QAM symbols and generates out of band splatter) and inter carrier interference from CFO. ICI EVM is modelled as pi times magnitude of epsilon divided by square root of 3 times 100 per cent (flat spectrum approximation), where epsilon equals f CFO divided by subcarrier spacing. Combined with all other impairments via RSS for total EVM.

Automatic impairment diagnosis

The diagnosis engine identifies the dominant impairment from the EVM breakdown and maps it to a recognisable visual pattern (arc shaped elongation for phase noise, skewed grid for IQ phase imbalance, compressed corners for AM AM, rotated outer symbols for AM PM, shifted centre for DC offset). A recommended corrective action is surfaced alongside the diagnosis so the design discussion moves quickly from observation to fix.

EVM breakdown and metrics

Per source EVM contributions surfaced in a horizontal bar chart showing the share of total EVM power. Total EVM displayed in per cent and dBc, with equivalent SNR and MER. BER estimated using Gray coded Q function (PSK and QAM forms). Shannon spectral efficiency and the maximum achievable modulation order at the current EVM are also reported.

Eye diagram with raised cosine matched filter

Generates 600 random symbols, upsamples at 8 times the symbol rate, applies a raised cosine filter with configurable rolloff alpha (0.01 to 0.99), and adds AWGN. The filtered waveform is chopped into 2 symbol period windows and 200 traces are overlaid. The canonical eye diagram for assessing timing margin, noise margin, and inter symbol interference. I or Q channel selectable.

Live animation and presets

Live streaming animation with age bucket alpha fading at 80 symbols per frame. Preset scenes for clean signal, AWGN, CFO, phase noise, IQ imbalance, AM PM, OFDM, eye diagram, TETRA (pi over 4 DQPSK at 18 ksym per second, rolloff 0.35), DMR, P25 C4FM (4FSK at 4.8 ksym per second, rolloff 0.2), and HF Modem (serial tone 8 PSK at 2.4 ksym per second with HF representative noise and phase jitter) accelerate teaching and design exploration. Symbol count selectable from 512 to 4096 for trade off between detail and rendering speed.

Standards compliance

EVM checked in real time against 5G NR (3GPP TS 38.101 to 1), LTE (3GPP TS 36.101), WiFi 6 (IEEE 802.11ax), DOCSIS 3.1, TETRA (ETSI EN 300 392-2, 10 per cent RMS vector error for pi over 4 DQPSK), and P25 (TIA 102.CAAB, 5 per cent Class A modulation fidelity for C4FM). Pass or fail and margin in dB reported per modulation order. ETSI publishes deviation tolerances rather than an EVM style limit for DMR, so 4FSK is benchmarked against the P25 figure. Useful for pre compliance checks during transmitter design and for educational demonstrations of how each standard sets its EVM bar.

Browser only computation

Runs entirely in your browser. No constellation data, impairment configurations, or design parameters are submitted to a server. Useful for commercially confidential transmitter and receiver design work, defence and intelligence radio development, and environments where information security policy prohibits sending engineering data to third party services.

Standards & methodology

  • 3GPP TS 38.101 to 1. 5G NR User Equipment radio transmission and reception
  • 3GPP TS 36.101. LTE User Equipment radio transmission and reception
  • IEEE 802.11ax to 2021. WiFi 6 PHY specification
  • CableLabs DOCSIS 3.1 PHY specification
  • ETSI EN 300 392-2. TETRA air interface, pi over 4 DQPSK vector error limits (RMS 0.1, peak 0.3)
  • TIA 102.CAAB. Project 25 C4FM and CQPSK transceiver performance, modulation fidelity limits
  • ETSI TS 102 361-1. DMR air interface, 4FSK modulation and deviation tolerances
  • Saleh model for AM AM and AM PM nonlinearity
  • Raised cosine matched filter convention for eye diagram

When to use this tool

  • Transmitter IQ impairment characterisation including AM AM, phase noise, and IQ imbalance identification
  • Receiver sensitivity verification with SNR margin against modulation minimum for BER less than or equal to 10 to the minus 3
  • Carrier frequency offset tolerance budget analysis
  • OFDM system design assessment of combined PAPR clipping and ICI effects
  • IQ calibration validation that calibration corrects skew and scale before over the air test
  • Training aid for new RF and digital engineers learning impairment patterns visually
  • Standards pre compliance check against 5G NR, LTE, WiFi 6, DOCSIS 3.1, TETRA, and P25 EVM limits
  • Land mobile radio waveform familiarisation for TETRA pi over 4 DQPSK and DMR or P25 4FSK eye diagrams ahead of test set work
  • Eye diagram analysis for timing margin and matched filter performance with different rolloff values
  • Phase noise budget allocation across local oscillator and synthesiser blocks
  • Power amplifier nonlinearity impact assessment on outer constellation symbols
  • Digital pre distortion algorithm validation against measured AM AM and AM PM curves
  • Producing teaching materials and reference visualisations for RF and DSP courses

Is this the right tool for you?

Reach for the Constellation Diagram Analyser in any of the following situations.

  • You have a working transmitter that is failing EVM compliance and want to identify which hardware impairment is dominating the EVM budget so design effort targets the right block.
  • You are diagnosing IQ imbalance on a transmitter and need to confirm whether the visible constellation skew is amplitude imbalance, phase imbalance, or a combination, before applying calibration.
  • You are evaluating CFO tolerance for a candidate AFC algorithm and need to see how rapidly the constellation rotates at the worst case CFO before the receiver can lock.
  • You are designing an OFDM system and need to evaluate the combined effect of PAPR clipping and CFO induced inter carrier interference on the achievable EVM.
  • You are validating a digital pre distortion (DPD) algorithm for a power amplifier and need to confirm that AM AM and AM PM correction restores the constellation to within the EVM target.
  • You are evaluating whether a particular phase noise spectrum is acceptable for 1024 QAM operation and want to see the resulting constellation cluster spread.
  • You are training new RF engineers in IQ impairment recognition and want a teaching tool that animates each impairment in isolation so the visual fingerprint becomes intuitive.
  • You are running a standards pre compliance check ahead of a 3GPP type approval test and need real time visual confirmation that the transmitter passes the relevant EVM mask.
  • You are characterising a power amplifier for 256 QAM operation and need to see how AM AM compression squeezes the outer constellation points before backoff is applied.
  • You are designing a matched filter for a candidate symbol shaping pulse and need to inspect the eye diagram across a range of raised cosine rolloff values to choose the right alpha for timing margin.
  • You are validating that an IQ modulator calibration routine has correctly removed amplitude and phase imbalance before over the air verification.
  • You are evaluating the constellation visual signature of a 4096 QAM signal under realistic 5G NR FR2 hardware impairments and need a live demo for an internal design review.
  • You are responding to a customer enquiry about why their high order modulation is failing and need a clear visual that shows the impairment dominating the EVM.
  • You are commissioning a TETRA, DMR, or P25 site and want to brief technicians on what a healthy pi over 4 DQPSK constellation or C4FM deviation eye should look like before they put a test set on the transmitter.
  • You are commissioning a point to point microwave backhaul link running 128 QAM or 512 QAM cross constellations and want to see how much phase noise or PA compression headroom the link has before the constellation degrades.
  • You are operating under a security regime that prohibits sending design data to third party services and need a constellation analyser that runs entirely in your browser.
  • You are producing teaching materials and example constellations for an RF or DSP course and need exportable PNG output across multiple impairment scenarios.

Frequently asked questions

Which modulation formats are supported?

Fifteen modulation formats. BPSK, QPSK, and 8 PSK from the PSK family. Pi over 4 DQPSK and pi over 8 D8PSK from the differential PSK family, rendered as the 8 and 16 point visible symbol unions. 2FSK and 4FSK rendered in the deviation domain. 16 QAM, 64 QAM, 256 QAM, 1024 QAM, and 4096 QAM from the rectangular QAM family, plus the 32, 128, and 512 QAM cross constellations rendered correctly as square grids with the corner blocks removed (6 by 6 minus 1 by 1 corners, 12 by 12 minus 2 by 2, 24 by 24 minus 4 by 4) — the formats point to point microwave backhaul radios actually run. Ideal points are rendered in red and received impaired symbols in blue throughout.

Are TETRA, DMR, and P25 waveforms supported?

Yes. Pi over 4 DQPSK is the TETRA voice plus data waveform (ETSI EN 300 392-2, 18 ksym per second, root raised cosine rolloff 0.35), pi over 8 D8PSK is the TETRA TEDS phase modulation, and 4FSK covers DMR (ETSI TS 102 361-1), P25 Phase 1 C4FM (TIA 102), and NXDN, all at 4.8 ksym per second. 2FSK covers POCSAG paging, MPT 1327 FFSK control channels, and RTTY. FSK formats are rendered in the deviation domain (deviation levels at plus or minus one third and plus or minus full deviation for 4FSK) as land mobile radio test sets display them, and their EVM corresponds to the FSK error or modulation fidelity figure those test sets report. Because an FM transmitter has no IQ modulator, the linear modulator impairments (IQ imbalance, DC offset, carrier phase, AM AM and AM PM, CFO rotation) are disabled for FSK formats — AWGN and phase noise act on the deviation trajectory. Compliance rows cover the TETRA 10 per cent RMS vector error limit and the P25 Class A 5 per cent modulation fidelity limit. ETSI publishes deviation tolerances rather than an EVM style limit for DMR, so no invented DMR limit is shown. Dedicated TETRA, DMR, and P25 C4FM presets load the correct symbol rate, rolloff, and band.

What about HF modem waveforms?

HF serial tone modems (MIL-STD-188-110, STANAG 4285, STANAG 4539) transmit PSK and QAM constellations that are already covered: 8 PSK for the classic 2400 symbol per second serial tone waveforms and 16 QAM through 256 QAM for the wideband appendices. The HF Modem preset loads serial tone 8 PSK at 2.4 ksym per second with HF representative noise and phase jitter. RTTY and SITOR are 2FSK, also covered. ALE (MIL-STD-188-141 8 tone FSK) and FT8 style waveforms are orthogonal multi tone signalling with no IQ symbol constellation to display — they are measured on a spectrum view, so they belong in the FFT Spectrum Analyser rather than a constellation tool, and no invented constellation rendering is offered for them.

How does the impairment chain work?

Nine impairments are applied in a physically motivated cascade matching the hardware signal flow. AM AM radial compression first (from the power amplifier). Then AM PM phase rotation. OFDM PAPR clipping in OFDM mode. IQ amplitude imbalance from the modulator. IQ phase imbalance. Carrier phase rotation. DC offset on each axis. Per symbol phase noise from the local oscillator. AWGN from the receive chain. Each impairment can be enabled or disabled independently so the visual signature of each one can be studied in isolation.

How does automatic diagnosis work?

Per source EVM contributions are computed and surfaced as a percentage of total EVM power. The diagnosis engine identifies the dominant contributor and maps it to the recognisable visual pattern. Phase noise produces arc shaped elongation. IQ phase imbalance produces a skewed grid. AM AM produces compressed outer corners. AM PM produces rotated outer symbols. DC offset produces a shifted centre. The matched pattern and a recommended corrective action are surfaced together.

How is CFO modelled?

Carrier frequency offset is specified in Hz or ppm and converted to a phase increment per symbol delta phi equals 2 pi times f CFO divided by f sym. Each rendered symbol accumulates the phase increment, producing the characteristic arc or ring pattern of uncompensated frequency offset. In OFDM mode, ICI EVM is modelled as pi times magnitude of epsilon divided by square root of 3 times 100 per cent, where epsilon equals f CFO divided by subcarrier spacing.

How does the eye diagram view work?

A separate eye diagram panel generates 600 random symbols at the selected modulation order, upsamples at 8 times the symbol rate, applies a raised cosine matched filter with configurable rolloff alpha (0.01 to 0.99), and adds AWGN at sigma equal to EVM divided by 100. The filtered waveform is chopped into 2 symbol period windows and 200 traces are overlaid to produce the canonical eye diagram. I or Q channel selectable. Useful for assessing timing margin, noise margin, and inter symbol interference alongside the constellation view.

How is BER estimated?

BER is estimated using the Gray coded Q function for PSK and QAM. PSK BER is approximately 2 over k times Q of (square root of 2 Es over N0) times sin of (pi over M). QAM BER is approximately 4 over k times (1 minus 1 over square root of M) times Q of (square root of 3 Es over N0 over (M minus 1)). These are the standard approximations used across the industry for AWGN performance estimation.

How does this relate to the EVM Calculator and FFT Spectrum Analyser?

The EVM Calculator focuses on quantitative EVM with budget allocation and standards compliance. The Constellation Diagram Analyser provides the visual view that shows what each impairment looks like and automatically diagnoses the dominant one. The FFT Spectrum Analyser shows the frequency domain signature alongside. Use the EVM Calculator for budget allocation. Use the Constellation Diagram Analyser to visualise and diagnose impairments. Use the FFT Spectrum Analyser to confirm spectral signature.

Does any data leave my browser?

No. The analyser runs entirely in your browser. No constellation data, impairment configurations, or design parameters are submitted to a server. Useful for commercially confidential transmitter and receiver design work, defence and intelligence radio development, and environments where information security policy prohibits sending engineering data to third party services.