In a QAM (“quadrature amplitude modulation”) data transmission system, the in-phase (“I”) and quadrature (“Q”) components of a signal identify a symbol being carried by that signal. To transmit a desired symbol, the IQ components corresponding to that symbol must be modulated onto a carrier wave. In a direct modulation system, the IQ ratio is modulated by controlling the amplitudes of two sinusoids separated by ninety degrees in phase. When these two sinusoids are combined, the resulting signal defines a point (hereafter referred to as the “received point”) in the IQ plane.
A set of constellation points in the IQ plane defines the set of symbols that can be transmitted. To the extent that a received point fails to align perfectly with a constellation point corresponding to the desired symbol, an IQ imbalance error may have been introduced.
The extent to which such IQ imbalance errors can be tolerated depends on the distribution of constellation points. For example, in a QPSK system, there are only four constellation points, one in each quadrant of the IQ plane. As a result, so long as the IQ imbalance error leaves the received point in the correct quadrant, there is no symbol transmission error. However, in a modern 64-QAM system, sixty-four constellation points crowd the IQ plane. As a result, even a modest IQ imbalance error can easily place the received point near the wrong constellation point. This results in a symbol transmission error.
To increase data transmission speed, it is desirable to send several symbols at the same time. This can be achieved by concurrently transmitting each of several symbols onto carriers having different frequencies. To avoid interference between the carriers without consuming excessive bandwidth, the carrier frequencies are selected such that the peak of the spectrum of any one carrier coincides with nulls of the spectra of all other carriers. This technique, referred to as “orthogonal frequency division multiplexing” (“OFDM”) enables several carriers to share a small bandwidth without interfering with each other. In the context of OFDM, these individual carriers are often referred to as “sub-carriers”.
In a data transmission system, a variety of mishaps along the data transmission channel conspire to introduce IQ imbalance errors into the signal as it makes its way from the transmitter to the receiver. For example, as a result of aging, temperature effects, or imperfections in their design, the electronic components that carry out modulation at the transmitter or demodulation at the receiver may fail to generate two sinusoids that are perfectly matched in amplitude and perfectly orthogonal in phase.