Low bandwidth PHY with frequency offset constraints

An apparatus for estimating a carrier frequency offset (CFO) between a transmitting device and a receiving device, the apparatus comprising:

• a network interface configured to receive a data unit transmitted by the transmitting device, wherein the data unit includes a periodic sequence;
• and wherein the network interface includes:
• a phase estimation unit configured to
• generate an initial phase shift value of a phase shift between adjacent periods of the periodic sequence,
• perform a plurality of cross-correlations using at least one period of the periodic sequence to generate a plurality of cross-correlation results, wherein each cross-correlation is performed using one of a plurality of possible actual phase shift values, and
• select, based the plurality of cross-correlation results, an actual phase shift value from the plurality of possible actual phase shift values;
• and
• a CFO estimation unit configured to generate an estimate of the CFO based at least in part on one of i) the initial phase shift value or ii) the actual phase shift value.