TECHNICAL FIELD

This description relates to systems and methods for transmitting wireless signals for electronic communications and, in particular, to increasing the data rate of, and reducing the computational complexity of, wireless communications.

BACKGROUND

In multiple access communications, multiple user devices transmit signals over a given communications channel to a receiver. These signals are superimposed, forming a combined signal that propagates over that channel. The receiver then performs a separation operation on the combined signal to recover one or more individual signals from the combined signal. For example, each user device may be a cell phone belonging to a different user and the receiver may be a cell tower. By separating signals transmitted by different user devices, the different user devices may share the same communications channel without interference.

A transmitter may transmit different symbols by varying a state of a carrier or subcarrier, such as by varying an amplitude, phase and/or frequency of the carrier. Each symbol may represent one or more bits. These symbols can each be mapped to a discrete value in the complex plane, thus producing Quadrature Amplitude Modulation, or by assigning each symbol to a discrete frequency, producing Frequency Shift Keying. The symbols are then sampled at the Nyquist rate, which is at least twice the symbol transmission rate. The resulting signal is converted to analog through a digital-to-analog converter, and then translated up to the carrier frequency for transmission. When different user devices send symbols at the same time over the communications channel, the sine waves represented by those symbols are superimposed to form a combined signal that is received at the receiver.

SUMMARY

A method for achieving high data rates includes generating a set of symbols based on an incoming data vector. The set of symbols includes K symbols, K being a positive integer. A first transformation matrix including an equiangular tight frame (ETF) transformation or a nearly equiangular tight frame (NETF) transformation is generated, having dimensions N×K, where N is a positive integer and has a value less than K. A second transformation matrix having dimensions K×K is generated based on the first transformation matrix. A third transformation matrix having dimensions K×K is generated by performing a series of unitary transformations on the second transformation matrix. A first data vector is transformed into a second data vector having a length N based on the third transformation matrix and the set of symbols. A signal representing the second data vector is sent to a transmitter for transmission of a signal representing the second data vector to a receiver.

The details of one or more implementations are set forth in the accompanying drawings and the description below. Other features will be apparent from the description and drawings, and from the claims.

