Field Guide · term

Also known as: bandwidth efficiency, bits/s/Hz

Spectral efficiency (also bandwidth efficiency) is the net information rate a communication channel carries per unit of bandwidth, measured in bits per second per hertz (bits/s/Hz).1 It answers the question every radio engineer faces when spectrum is scarce and expensive: how many bits can you push through a given slice of frequency? Its ceiling is set by the Shannon capacity theorem, which no coding or modulation scheme can exceed.

bits/s/Hz SNR (dB) → Shannon limit BPSK ~1 QPSK ~2 16-QAM ~4 64-QAM ~6
The Shannon curve caps spectral efficiency at each SNR; real modulations sit below it, climbing in bits/s/Hz as SNR and constellation order rise.

How it works

For a single carrier, spectral efficiency is the product of two factors: how many bits each symbol encodes, and how many symbols per second fit in the bandwidth. A modulation of order M carries log₂(M) bits per symbol — BPSK 1, QPSK 2, 16-QAM 4, 64-QAM 6, 256-QAM 8 — and the symbol rate that fits in a band is limited by the Nyquist criterion and the pulse-shaping roll-off. Multiply, then subtract the overhead spent on forward error correction and framing, and you have the net spectral efficiency.

There is no free lunch. Packing more bits per symbol crowds constellation points closer together, so higher-order schemes demand a higher SNR (equivalently, higher Eb/N0) to keep the bit error rate acceptable. The Shannon–Hartley theorem pins the absolute ceiling at η_max = log₂(1 + SNR) bits/s/Hz — you can trade power for bandwidth and vice versa, but never cross that line.

In practice

  • Adaptive modulation and coding exploits the SNR trade directly: LTE, 5G NR, Wi-Fi, and DVB pick a higher-order constellation and lighter coding when the link is strong, dropping to robust QPSK when it is weak — maximizing bits/s/Hz moment to moment.
  • Multicarrier and MIMO raise system-level efficiency: OFDM packs orthogonal subcarriers tightly with minimal guard band, while MIMO reuses the same bandwidth over multiple spatial streams, pushing effective efficiency beyond the single-channel Shannon curve.
  • Narrowband land-mobile systems optimize the opposite way — for channel density and robustness rather than peak bits/s/Hz — which is why their spectral efficiencies look modest next to broadband data systems.

Relevance to SDR

Spectral efficiency explains the design choices behind the systems a scanner meets. DMR and P25 Phase 2 use two-slot TDMA to double voice capacity in the same 12.5 kHz channel, roughly doubling spectral efficiency over a single-carrier equivalent; TETRA fits four timeslots in 25 kHz. These are all bandwidth-efficiency decisions traded against required SNR and equipment cost. GopherTrunk does not compute a spectral-efficiency figure — it is a design property of the protocols GT decodes, not a runtime measurement — but understanding it clarifies why a denser mode needs a cleaner signal to lock, and why capacity-oriented systems demand better link quality than their robust predecessors.

Sources

  1. Spectral efficiency — Wikipedia, definition, units, and the link to Shannon capacity and modulation order. ↩

See also