Cooperative Sensing
How Distributed Radios Fuse a Shared Spectrum View
The motivation for cooperative sensing comes from a single hard physical limit: one radio cannot reliably distinguish an empty channel from an occupied channel it happens to be shadowed from. Outdoor log-normal shadowing routinely reaches a standard deviation of 6 to 12 dB, and a building or terrain feature can attenuate the path to a primary transmitter by 20 to 30 dB. A lone energy detector facing that fade either misses the primary, risking harmful interference if it then transmits, or it raises its threshold so high that it loses sensitivity everywhere. Spreading the sensing job across radios at different locations breaks this deadlock, because the probability that every cooperator is simultaneously shadowed falls quickly when their paths are independent.
Architecturally, cooperative sensing is centralized or distributed. In the centralized form a fusion center, often the cognitive base station or a CBRS Spectrum Access System, collects reports over a low-rate control channel and renders one global decision. In the distributed form radios exchange decisions peer-to-peer and converge through consensus, trading slower settling for resilience to a single point of failure. Either way the design must budget reporting overhead, sensing time, and the correlation between cooperators, since clustered radios within one shadowing correlation distance (often 50 to 100 m) contribute little new information.
Hard Fusion and the k-out-of-N Rule
In hard fusion each radio thresholds its own statistic locally and forwards a single bit. The fusion center declares the primary present if at least k of the N reporting radios voted present. Setting k equal to 1 gives the OR rule, which maximizes detection probability and best protects the primary; k equal to N gives the AND rule, which minimizes false alarms and maximizes secondary throughput; majority voting sits between them. The OR rule is the common default for primary protection because regulatory missed-detection limits dominate the design.
Soft Combining and Sensing Gain
Soft fusion forwards a quantized test statistic instead of one bit. Equal-gain combining simply sums the statistics, while maximal-ratio combining weights each by its local SNR, recovering the full array gain of the cooperating set. Soft combining typically buys 1 to 3 dB of effective SNR over hard fusion at a matched false-alarm rate, at the cost of roughly 6 to 12 quantization bits of reporting per radio per sensing interval.
Governing Detection Equations
Qm = ∏i=1N (1 − Pd,i) → Qm = (1 − Pd)N for identical radios
Network false alarm (OR rule):
Qf = 1 − ∏i=1N (1 − Pf,i) ≈ N × Pf for small Pf
k-out-of-N decision (identical radios):
Qd = Σj=kN C(N,j) × Pdj × (1 − Pd)N−j
Where Pd,i = local detection probability of radio i, Pf,i = local false-alarm probability, N = number of cooperators, k = vote threshold, C(N,j) = binomial coefficient. Example: Pd = 0.6, N = 8, OR rule → Qm ≈ 0.0007 versus 0.4 for a single radio.
Fusion Scheme Comparison
| Scheme | Report per Radio | Reporting Overhead | Relative Sensitivity | Complexity | Best Use |
|---|---|---|---|---|---|
| OR rule (hard) | 1 bit | Lowest | Baseline | Low | Strict primary protection |
| AND rule (hard) | 1 bit | Lowest | Low Pd, low Pf | Low | Maximize secondary throughput |
| Majority vote (hard) | 1 bit | Lowest | Balanced | Low | General-purpose networks |
| Equal-gain (soft) | 6 to 12 bits | Moderate | +1 to 2 dB vs OR | Moderate | Unknown per-radio SNR |
| Maximal-ratio (soft) | 6 to 12 bits | Moderate | +2 to 3 dB vs OR | High | SNR known, low-overhead links |
Frequently Asked Questions
What is the difference between hard and soft decision fusion in cooperative sensing?
In hard fusion each radio sends a single occupancy bit and the fusion center applies an OR, AND, or majority vote, needing only a few control bits but discarding confidence information. In soft fusion each radio reports a quantized test statistic, for example its energy detector output, combined by equal-gain or maximal-ratio combining before one threshold test. Soft fusion typically gains 1 to 3 dB of effective SNR at the same false-alarm rate but costs roughly 6 to 12 quantization bits per radio per interval.
How many cognitive radios are needed for reliable cooperative sensing under shadowing?
It depends on shadowing correlation. With independent log-normal shadowing, missed detection falls geometrically with the number of cooperators: for an OR rule and a per-radio Pd of 0.6, cooperating 5 to 10 radios pushes network missed detection below 0.01. If radios cluster within one shadowing correlation distance (often 50 to 100 m outdoors), the gain flattens, so designs pick geographically diverse radios or censor highly correlated reports.
Why does cooperative sensing solve the hidden-terminal problem?
A radio sitting in a deep shadow behind a building can miss a primary transmitter and then transmit, interfering with a primary receiver it never heard. Because cooperating radios at different sites see uncorrelated fading and shadowing, at least one usually has a clear path to the primary. The fusion center aggregates these views, so even a cooperator shadowed by 20 to 30 dB does not blind the network, which still detects and protects the primary.