SISO: Dual Roles in Comms & Control

• SISO is defined as both a single-input single-output architecture and a soft-input soft-output processing module, critical in various engineering domains.
• Its single-input single-output form uses scalar models for RF links, control systems, and fuzzy reasoning, offering low-cost simplicity but limited capacity.
• In soft-input soft-output applications, SISO modules enhance iterative detection, equalization, and relaying by converting a-priori LLRs into extrinsic information.

SISO denotes either single-input single-output or soft-input soft-output, with the intended meaning determined by domain and notation. In wireless communications, control, sensing, power electronics, and fuzzy systems, it usually denotes a one-input, one-output architecture, such as a 1×1 RF link, a scalar plant, or a single-rule fuzzy system. In iterative receivers, equalization, and cooperative relaying, it instead denotes modules that accept soft information and return soft information, typically in the form of a-priori and extrinsic LLRs. The acronym therefore spans Shannon-capacity analysis, OFDM PHY-security, coarsely quantized receivers, interference channels, RIS-assisted transmission, bistatic ISAC sensing, dead-time root-locus computation, incremental flight control, affine-feedback algebra, sphere decoding, turbo equalization, relay encoding, and fuzzy approximate reasoning (Sengar et al., 2014, 0811.4354).

1. Dual meaning and canonical abstractions

Usage of “SISO”	Canonical object	Representative relation
Single-input single-output	1×1 link, scalar plant, single-rule fuzzy system	$y(t)=h\cdot x(t)+n(t)$; $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$; “If $x$ is $A$ then $y$ is $B$”
Soft-input soft-output	Iterative detector, equalizer, relay encoder	$L^E_{j,b}=L^D_{j,b}-L^A_{j,b}$; $\tilde x_{b_k}(n)=\tanh(l_{b_k}(n)/2)$

In the standard RF single-input single-output channel model, the received complex baseband signal is

$y(t)=h\cdot x(t)+n(t),$

with flat fading, AWGN, perfect CSI at the receiver, and no transmitter-side diversity or beamforming, since there is a single antenna at both ends (Sengar et al., 2014). The same single-input single-output reading appears in dead-time control, where the characteristic equation is written as $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$, and in fuzzy reasoning, where a single rule has the form “If $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$0 is $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$1 then $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$2 is $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$3” (Gumussoy et al., 2020, Son et al., 2020).

Under the soft-input soft-output reading, the canonical objects are LLR-driven iterative modules. In SISO sphere decoding, the detector takes a-priori LLRs

$\Delta(s,K)=1+K\,G(s)e^{-hs}=0$4

and returns extrinsic LLRs

$\Delta(s,K)=1+K\,G(s)e^{-hs}=0$5

while in distributed soft coding each relay forms a soft bit estimate

$\Delta(s,K)=1+K\,G(s)e^{-hs}=0$6

before relay-side SISO encoding (0811.4354, Li et al., 2012). This suggests that acronym resolution is inseparable from the surrounding signal model: antenna cardinality, scalar interconnection, and probabilistic message passing all coexist under the same label.

2. Single-input single-output links and capacity

For a flat-fading RF SISO link with bandwidth $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$7, Shannon’s theorem gives the instantaneous capacity

$\Delta(s,K)=1+K\,G(s)e^{-hs}=0$8

and the normalized capacity

$\Delta(s,K)=1+K\,G(s)e^{-hs}=0$9

The cited capacity analysis emphasizes three facts: capacity scales linearly with bandwidth $x$0, depends logarithmically on SNR, and exhibits diminishing returns at high SNR, so designers often trade bandwidth for SNR or vice versa (Sengar et al., 2014).

The reported MATLAB simulations with $x$1 show, for the 1×1 SISO case, approximately $x$2 at $x$3, $x$4 at $x$5, and $x$6 at $x$7. Figure 1 of the same study places SISO below 2×1 MISO/SIMO and 2×2 MIMO, illustrating its limited spectral efficiency under typical RF conditions (Sengar et al., 2014).

The comparison basis is explicit. For MISO/SIMO with $x$8 antennas on one side,

$x$9

whereas a spatial-multiplexing MIMO system is approximated by

$A$0

The interpretation given in the literature is that SISO has the lowest complexity and the lowest capacity; MISO/SIMO offers diversity or array gain but only logarithmic capacity improvement through increased effective SNR; and MIMO provides approximately linear scaling in bits/s/Hz through multiplexing gain, at the cost of RF/processing complexity and CSI overhead (Sengar et al., 2014).

The practical balance is correspondingly asymmetric. Advantages attributed to SISO are low hardware cost, minimal signal processing, and a simple RF chain. Its limitations are no spatial diversity, vulnerability to deep fades and multipath nulls, and inability to exploit spatial multiplexing gains that are described as essential for 4G/5G throughput targets. Deployment scenarios identified as still viable include low-data-rate IoT, legacy systems such as narrowband IoT and certain machine-type communications, and devices with severe size, cost, or power constraints. The same source states that LTE and 5G NR mandate at least 2×2 MIMO at the base station, with pure SISO used sparingly and typically on the uplink in very low-complexity devices (Sengar et al., 2014).

3. Contemporary single-input single-output wireless research

Recent SISO wireless work does not treat the 1×1 architecture as synonymous with an unstructured baseline. In SISO-OFDM PHY-security, FD time-reversal precoding multiplies each subcarrier by the conjugate of Bob’s channel,

$A$1

to produce a focusing gain at Bob, while Eve sees the non-focused coefficient $A$2. Artificial noise is then chosen in the null space of Bob’s effective channel,

$A$3

so that Bob is unaffected while Eve is jammed. For $A$4 subcarriers, 4-QAM, uncorrelated Rayleigh taps, $A$5, and $A$6, the paper reports that with AN and $A$7 the secrecy rate can roughly double, for example from approximately $A$8 to approximately $A$9 at $y$0 (Golstein et al., 2019).

Capacity enhancement is also pursued by front-end reconfiguration. In pixel-antenna SISO-OFDM, the equivalent scalar channel on subcarrier $y$1 under code $y$2 is

$y$3

and the joint capacity-maximization problem couples Boolean antenna coding with WF power allocation across subcarriers. The exact approach combines SEBO with WF, while a codebook-based alternative reduces online complexity. For a $y$4 pixel aperture at $y$5 with $y$6, effective rank $y$7, $y$8 taps, $y$9, and training set $B$0, the reported capacity gain over a fixed conventional antenna is up to $B$1 at $B$2 and $B$3 at $B$4. With a codebook of size $B$5, the approach achieves about $B$6 of the SEBO gain at $B$7 and about $B$8 at $B$9 (Qiao et al., 18 Mar 2026).

A different line of work inserts nonlinear analog operators ahead of coarse ADCs. The end-to-end model is

$L^E_{j,b}=L^D_{j,b}-L^A_{j,b}$0

with $L^E_{j,b}=L^D_{j,b}-L^A_{j,b}$1 drawn from polynomials of degree at most $L^E_{j,b}=L^D_{j,b}-L^A_{j,b}$2 and $L^E_{j,b}=L^D_{j,b}-L^A_{j,b}$3 an $L^E_{j,b}=L^D_{j,b}-L^A_{j,b}$4-level quantizer with $L^E_{j,b}=L^D_{j,b}-L^A_{j,b}$5 parallel branches. The capacity is written as

$L^E_{j,b}=L^D_{j,b}-L^A_{j,b}$6

For one-bit ADCs and quadratic preprocessing, the high-SNR asymptote is reported as $L^E_{j,b}=L^D_{j,b}-L^A_{j,b}$7 bits/use, versus $L^E_{j,b}=L^D_{j,b}-L^A_{j,b}$8 for linear preprocessing, and with $L^E_{j,b}=L^D_{j,b}-L^A_{j,b}$9 one-bit ADCs and $\tilde x_{b_k}(n)=\tanh(l_{b_k}(n)/2)$0 the sample numerical curve reaches approximately $\tilde x_{b_k}(n)=\tanh(l_{b_k}(n)/2)$1 at high SNR versus $\tilde x_{b_k}(n)=\tanh(l_{b_k}(n)/2)$2 for linear processing (Shirani et al., 2022).

SISO research also includes interference-limited signaling, RIS-assisted modulation, and sensing. Robust IGS in the two-user SISO IC and Z-IC studies worst-case rates over CSI uncertainty regions, with closed-form designs that are ensured to perform no worse than proper Gaussian signaling and reported worst-case sum-rate gains of up to approximately $\tilde x_{b_k}(n)=\tanh(l_{b_k}(n)/2)$3 over non-robust IGS and up to approximately $\tilde x_{b_k}(n)=\tanh(l_{b_k}(n)/2)$4 over robust PGS in some numerical examples (Soleymani et al., 2019). CIM-RIS embeds bits in Walsh-code indices in addition to $\tilde x_{b_k}(n)=\tanh(l_{b_k}(n)/2)$5-QAM symbols, for a total

$\tilde x_{b_k}(n)=\tanh(l_{b_k}(n)/2)$6

bits per symbol, and reports SNR gains over conventional RIS of $\tilde x_{b_k}(n)=\tanh(l_{b_k}(n)/2)$7 for $\tilde x_{b_k}(n)=\tanh(l_{b_k}(n)/2)$8, $\tilde x_{b_k}(n)=\tanh(l_{b_k}(n)/2)$9 for $y(t)=h\cdot x(t)+n(t),$0, $y(t)=h\cdot x(t)+n(t),$1 for $y(t)=h\cdot x(t)+n(t),$2, and $y(t)=h\cdot x(t)+n(t),$3 for $y(t)=h\cdot x(t)+n(t),$4 under matched spectral efficiency (Cogen et al., 2022). In bistatic ISAC sensing, WiDFS 3.0 models raw CSI as corrupted by TO/CFO-induced random phase, removes that phase via self-referencing cross-correlation,

$y(t)=h\cdot x(t)+n(t),$5

and applies delay-domain MVDR beamforming to suppress Doppler mirroring ambiguity. The resulting delay–Doppler–time tensor is used with MobileViT-XXS with only $y(t)=h\cdot x(t)+n(t),$6M parameters; on three walking trajectories at $y(t)=h\cdot x(t)+n(t),$7 Wi-Fi, median range errors of $y(t)=h\cdot x(t)+n(t),$8, $y(t)=h\cdot x(t)+n(t),$9, and $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$0 are reported for ellipse, linear, and rectangle trajectories, and end-to-end feature generation runs in approximately $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$1 per CPI on a Raspberry Pi 4B (Wang et al., 18 Aug 2025).

4. SISO in control, stability, and affine-feedback algebra

In dead-time control, SISO refers to scalar plants of the form $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$2 and scalar continuation parameters such as controller gain $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$3 or delay $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$4. The root-locus problem is posed on a prescribed right half-plane, with starting points, branch points, and boundary-crossing roots computed first and then traced by a predictor–corrector continuation method using pseudo-arclength parameterization in the augmented space $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$5. The method is described as numerically stable for high-order SISO dead-time systems, with reported timings on the order of $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$6–$\Delta(s,K)=1+K\,G(s)e^{-hs}=0$7 seconds for plants up to order $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$8 and moderate delays (Gumussoy et al., 2020).

Incremental flight control gives a second control-theoretic use of SISO. The plant is modeled as

$\Delta(s,K)=1+K\,G(s)e^{-hs}=0$9

and the modified INDI law introduces gains $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$00 and $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$01, actuator and sensor dynamics, a differentiation filter, transport delays, and pseudo-control hedging. The numerical evaluation on the DA-42 short-period model reports nominal margins and performance metrics of $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$02, $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$03, $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$04, $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$05, $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$06, disturbance RMS error $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$07, noise RMS error $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$08, and robustness STD $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$09. The same analysis stresses that increasing $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$10 or $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$11 improves tracking and disturbance rejection while degrading gain, phase, and time-delay margins and noise attenuation (Lu et al., 2020).

In power-electronic small-signal stability, SISO equivalents are derived from an underlying dq-domain MIMO impedance model of a grid-tied VSC. The accurate positive- and negative-sequence loop impedances eliminate the coupled sequence port in closed form, while the reduced SISO model invokes a strong-grid approximation. The central result is that the accurate SISO model gives identical stability results to the MIMO matrix-based model under Nyquist analysis, whereas the reduced SISO model may lead to wrong results if the PLL bandwidth is large (Zhang et al., 2017).

A more abstract SISO control literature studies affine feedback interconnections of Chen–Fliess series. One paper proves that the affine feedback connection acts as a group action on the plant and is isomorphic to the semidirect product of the shuffle group and the additive group of non-commutative formal power series, which implies that additive and multiplicative feedback loops are structurally non-commutative; reversing their order yields a net additive feedback loop (S., 2024). A companion algebraic study shows that the SISO affine-feedback transformation group is a post-group, and that its infinitesimal structure is a post-Lie algebra whose derived Lie bracket coincides with the Lie algebra of the Grossman–Larson product (Ebrahimi-Fard et al., 2023).

5. Soft-input soft-output detection, equalization, and relaying

In receiver theory, SISO denotes soft-input soft-output rather than single-input single-output. The STS-SD algorithm for MIMO detection extends single-tree-search sphere decoding to the SISO setting by incorporating a-priori LLRs into the branch metrics and clipping extrinsic LLRs during tree search. The detector visits each node at most once, avoids repeated QR decompositions and separate tree searches, and exposes a tunable performance/complexity trade-off through $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$12. The reported result is that, at less than $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$13 from max-log performance, SISO STS-SD can reduce average node visits by approximately $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$14 to $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$15 in typical MIMO-OFDM channels (0811.4354).

Turbo equalization gives a second major SISO meaning. The proposed SISO-DFE formulates extrinsic information in a way that directly accounts for error propagation, and the associated EXIT-chart and BER results indicate superiority to the well-known SISO linear equalizer. The paper explicitly states that this is in contrast with the general understanding that the error propagation effect of the DFE degrades TE performance below that of TE based on a linear equalizer. Its bidirectional extension combines two DFEs running in opposite directions through a correlation-aware LLR combiner; with time-invariant taps, the proposed TIV-BiDFE is reported to remain within $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$16 of MAP while retaining linear per-symbol complexity (Jeong et al., 2011).

In cooperative relaying, a SISO relay encoder is the core of the DISC architecture. Each relay computes SBEs from noisy source observations, then applies a simple SISO encoder in the log domain:

$\Delta(s,K)=1+K\,G(s)e^{-hs}=0$17

Performance depends on the generator-sequence-weight

$\Delta(s,K)=1+K\,G(s)e^{-hs}=0$18

and the code-assignment rule is to pair the largest GSW with the relay having the largest input SNR. The paper states that DISC circumvents error propagation associated with hard detect-and-forward re-encoding and reports, at FER $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$19 in AWGN, gains of approximately $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$20 for DISC(2-state), $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$21 for DISC(4-state), and $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$22 for DISC(8-state) over soft information relaying in a two-relay network, with another $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$23–$\Delta(s,K)=1+K\,G(s)e^{-hs}=0$24 from the sorted pairing rule (Li et al., 2012).

6. Single-input single-output fuzzy systems

In fuzzy approximate reasoning, SISO again means single-input single-output. The system is defined by one rule, “If $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$25 is $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$26 then $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$27 is $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$28,” where the antecedent and consequent are discrete fuzzy sets of dimensions $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$29 and $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$30. The cited work addresses the case $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$31 by embedding both into a common dimension

$\Delta(s,K)=1+K\,G(s)e^{-hs}=0$32

and defining the extended distance measure

$\Delta(s,K)=1+K\,G(s)e^{-hs}=0$33

FMP-EDM and FMT-EDM then construct conclusions by computing the EDM, forming a sign vector, adding an adjustment vector in the embedded space, down-sampling, and normalizing to $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$34 (Son et al., 2020).

A central criterion is the reductive property. The paper proves exact reductivity for both FMP-EDM and FMT-EDM: if $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$35, then $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$36, the adjustment vector vanishes, and the conclusion is exactly $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$37; analogously, if $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$38, the FMT conclusion is exactly $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$39 (Son et al., 2020).

The comparative evaluation spans sixteen fuzzy-reasoning variants and five inference schemes—CRI, TIP, QIP, AARS, and the proposed EDM method—using percentage satisfaction of the reductive property and average CPU time. The reported summary is that EDM-EDM achieves the highest RPCF, approximately $\Delta(s,K)=1+K\,G(s)e^{-hs}=0$40, while AARS is fastest and EDM is next in CPU time. The paper concludes that the EDM-based method is comparatively clear and effective with respect to the reductive property and accords with human thinking better than the alternatives considered (Son et al., 2020).

Across these literatures, SISO is therefore not a single concept but a compact label for two recurrent technical patterns: scalar interconnection structure and soft-information transduction. In one branch it denotes 1×1 channels, scalar plants, and single-rule inference; in the other it denotes modules that map soft priors to soft posteriors. The continuity across the two branches is methodological rather than lexical: both use low-dimensional structure to make rigorous analysis, exact design criteria, and tractable algorithms possible.