Timing recovery and frame synchronization in communications systems

Apparatus for determining a sampling delay for sampling a received communications signal, comprising:

• a plurality of finite impulse response filters responsive to received signal samples for producing a plurality of indirect variables of a linear complex vector which approximates the received signal samples according to a maximum likelihood criterion;
• and
• a calculation unit responsive to the plurality of indirect variables for calculating an estimated sampling delay.

A method of determining sampling delay in complex signal samples of a received communications signal, comprising the steps of:

• estimating, using a maximum likelihood criterion, indirect variables of a linear complex vector which approximates the received signal samples, each component of the linear complex vector comprising a linear combination of a predetermined pair of functions dependent upon a sampling delay;
• and
• determining the sampling delay from the estimated indirect variables for timing recovery of the received communications signal, the determining step comprising multiplying the estimated indirect variables by real elements of predetermined stored matrices.

A method of determining sampling delay in complex signal samples of a received communications signal, comprising the steps of:

• estimating, using a maximum likelihood criterion, indirect variables of a linear complex vector which approximates the received signal samples, each component of the linear complex vector comprising a linear combination of a predetermined pair of functions dependent upon a sampling delay;
• and
• determining the sampling delay from the estimated indirect variables for timing recovery of the received communications signal, the determining step comprising performing a single non-linear transformation of the estimated indirect variables.

A method of determining sampling delay in complex signal samples of a received communications signal, comprising the steps of:

• estimating, using a maximum likelihood criterion, indirect variables of a linear complex vector which approximates the received signal samples, each component of the linear complex vector comprising a linear combination of a predetermined pair of functions dependent upon a sampling delay;
• and
• determining the sampling delay from the estimated indirect variables for timing recovery of the received communications signal, the determining step comprising calculating the sampling delay in accordance with a predetermined function of the real part of a product of the complex conjugate of a first estimated indirect variable with a second estimated indirect variable, divided by the square of the amplitude of the first estimated indirect variable.