A carrier wave, or, simply, carrier, was a wave of any type, length, and dimension that can transmit anything, such as data, energy, or particles.
Romulan transporters operate on a similar subspace frequency as a Starfleet transporter. With only minor adjustments, a Romulan transporter can be made to simulate a Federation transporter carrier wave. (TNG: "Data's Day")
In 2152, Colonel Grat scrambled his carrier wave while transmitting a message to Enterprise, regarding the imprisonment of Captain Jonathan Archer and Ensign Travis Mayweather. Hoshi Sato speculated Grat did that so his signal would not be traced. (ENT: "Detained")
Later that year, Commander Charles Tucker III tried contacting Lieutenant Malcolm Reed through Enterprise's intercom system after the ship was taken over by the Suliban. However, his transmission was coming out garbled to Reed. Reed suggested that Tucker modulate the sub carrier wave, after which his transmission began coming through more clearly. (ENT: "Shockwave, Part II")
Later on, Reed lost his communicator while undercover on a class M planet with a pre-warp civilization. Ensign Hoshi Sato was able to locate it by transmitting an inverse carrier wave to the communicator so its power signature would be amplified. (ENT: "The Communicator")
While trapped on a planet with Zho'Kaan, Commander Tucker sent a Starfleet carrier wave to Enterprise from an Arkonian transceiver to help the ship locate him and Zho'Kaan before both of them were killed by extreme heat. (ENT: "Dawn")
In the mid-2270s, V'ger transmitted a simple binary code on a carrier wave signal to Earth, with the intention of reaching its Creator. The message was intercepted by Commander Spock on the USS Enterprise, which was within V'ger at the time. (Star Trek: The Motion Picture)
In 2368, Captain Jean-Luc Picard and Lieutenant Commander Data contacted the USS Enterprise-D from Romulan space on a Klingon Bird-of-Prey by using a Romulan carrier wave so their transmission would not be detected. (TNG: "Unification II")
In 2369, the United Federation of Planets suspected the Cardassian Union was producing metagenic weapons, which could kill the entire population of a planet. The weapon could be activated by a theta-band carrier wave, which would be indistinguishable from normal background noise. Captain Picard was selected for a mission to Celtris III, as he had expertise in theta-band carrier waves. (TNG: "Chain Of Command, Part I", "Chain Of Command, Part II")
In 2370, Geordi La Forge speculated that Lore had Data take his VISOR away because La Forge could see a carrier wave radiating from Data, which Captain Picard suggested was how Lore was controlling him. (TNG: "Descent, Part II")
Later that year, William T. Riker transmitted his command codes from Baran's mercenary ship to lower the Enterprise-D's shields so Baran's ship could attack the Enterprise. Embedded in his command codes were coordinates that were sent on the same carrier wave, which indicated to Data that the ship was heading for the Hyralan sector. (TNG: "Gambit, Part II")
Later on, La Forge discovered that the D'Arsay archive was using the Enterprise's sensor beam as a carrier wave to transmit information about their culture to the ship's computers and replicators. (TNG: "Masks")
Later that year, Data detected a subspace carrier wave heading for the Enterprise-D with the same signature as Bok's transporter. (TNG: "Bloodlines")
In 2371, on stardate 48543.2, Ulani Belor, a Cardassian scientist, and Chief Miles O'Brien transmitted a carrier wave through the Bajoran Wormhole while on board the USS Defiant in an attempt to cut through interference between the communication array attached to the Defiant and Deep Space 9. (DS9: "Destiny")
In 2372, Tanis tried to contact the Nacene Suspiria from the USS Voyager by using a subspace carrier wave and told Captain Kathryn Janeway that she would respond to it in 47 hours. (VOY: "Cold Fire")
Later that year, Lieutenant Tuvok authenticated a signal coming from a Federation beacon as being a Starfleet frequency, since it corresponded to a standard Federation carrier wave. (VOY: "Maneuvers")
While trying to contact a duplicate Voyager created by a subspace divergence field, Kathryn Janeway suggested to B'Elanna Torres that the two ships could re-calibrate their carrier wave to match phase variants so they could communicate with each other. (VOY: "Deadlock")
In 2373, Ensign Harry Kim attempted to beam Arridor and Kol aboard Voyager from their Ferengi shuttle by using a subspace carrier wave. (VOY: "False Profits")
Later that year, Trentin Fala attempted to contact Major Kira Nerys on Deep Space 9 by using a phase-divergent carrier wave, a carrier wave that changed phases, as well as running it through a scrambler, so no one would be able to trace her signal, since an unknown assailant was executing members of the Shakaar resistance cell, of which Kira and Trentin were members of. (DS9: "The Darkness and the Light")
In 2374, Lieutenant junior grades Tom Paris and B'Elanna Torres transmitted a phased carrier wave to the USS Voyager after they abandoned their shuttlecraft, the Cochrane and were left floating in space in their EV suits. They created the wave by linking the communicators of both suits. (VOY: "Day of Honor")
Later that year, Voyager tried sending a message to the USS Prometheus from the Delta Quadrant through the massive Hirogen communications network. However, the message was unable to reach the Prometheus, located at the edge of the Alpha Quadrant because Voyager's carrier wave degraded as it moved through the communications network. (VOY: "Message in a Bottle")
In 2375, Voyager contacted Tom Paris, The Doctor, and Tuvok on a class D planet inside a subspace sinkhole through a distress beacon. The message from Voyager was sent nine hours previously on a very slow carrier wave due to a temporal differential between Voyager and the sinkhole. (VOY: "Gravity")
Later that year, Tuvok transmitted a carrier wave to Seven of Nine's neural transceiver in order for the Think Tank's telepathic link to be severed and to allow the Hazari to attack the ship they were on. (VOY: "Think Tank")
In 2376, two scientists on Kelemane's planet surmised that in order to contact the "Sky Ship", which in reality was the USS Voyager, they might need to switch to a different carrier wave. (VOY: "Blink of an Eye")
Later that year, Captain Janeway attempted to contact a missing Harry Kim by trying to activate his combadge using a carrier wave. Janeway asked Lieutenant Commander Tuvok to have the carrier wave match a Borg interlink frequency so the transmission would not be detected by a Borg cube facing off Voyager. (VOY: "Collective")
Later, the Delta Flyer picked up a Starfleet frequency, but it was repeating a distress call sent by Kathryn Janeway to the USS Voyager hours before. Crewman Mortimer Harren thought it was a subspace echo. Janeway disputed this, as it had a .005 deviation in its carrier wave. She surmised that dark matter lifeforms were trying to communicate with the Delta Flyer by modifying Janeway's distress call to Voyager. (VOY: "Good Shepherd")
In 2377, Chakotay picked up a distress call with a carrier wave from a colony on an asteroid, but there was no message attached. When Voyager arrived to the coordinates of the colony, it appeared to have been destroyed by the Borg. (VOY: "Unimatrix Zero")
In 2378, Seven of Nine performed a Fourier analysis on a garbled piece of music playing through Voyager from The Doctor. While looking at the analysis in astrometrics, Ensign Harry Kim speculated that it might be a com signal. Seven disputed that, as it did not have a carrier wave. (VOY: "Renaissance Man")