In modern point to point microwave radio systems used to backhaul cellular voice and data traffic, quadrature amplitude modulation (QAM) is the norm. These systems require a highly linear power amplifier which is expensive and has relatively low power efficiency. Recently, continuous phase modulation (CPM) has been deployed in this market. The CPM transmitted waveform has a constant envelope and so a non-linear RF power amplifier can be used. This significantly reduces cost and improves power efficiency. Two important disadvantages of CPM are receiver complexity and inferior spectral efficiency compared to QAM. This thesis demonstrates a 50% spectral efficiency improvement over an existing CPM configuration without loss of detection efficiency. This is achieved by moving to coherent demodulation and extending the duration of the CPM phase pulse to 3 symbol periods. This new CPM configuration of h=1/4, M=4, L=3, is evaluated against ETSI requirements for a 28 MHz channel carrying 24 E1 circuits. Simulation of the receiver floating point model demonstrates all requirements are met. The detection efficiency requirement is exceeded by 4.7 dB. Carrier recovery, phase and timing synchronisation are assumed to be ideal. The 50% increased symbol rate, coherent reception and a longer smoother phase pulse, conspire to increase receiver complexity substantially. The Viterbi algorithm is used to perform maximum-likelihood detection resulting in a 128 state trellis. This application has a stringent cost requirement that limits the implementation target to a Field Programmable Gate Array (FPGA) costing less than US$30. To demonstrate this demanding cost target is met, the two most computationally expensive receiver functions, the branch metric unit and path metric processing unit, are implemented in VHDL and targeted to a Xilinx Spartan 3A-DSP 1800 FPGA. The implementation uses 67% of the available logic resources, thus meeting the cost requirement. The branch metric unit is implemented using a distributed arithmetic technique that performs the equivalent of 27.6 giga-multiplies/s, consuming only 23% of the available FPGA logic cells. This is very efficient compared to a conventional approach using all the FPGA’s embedded multipliers which combined can only achieve 21 giga-multiplies/s. The Viterbi path metric processing unit is implemented using a more conventional state-parallel architecture. To reduce state metric routing complexity, states are grouped into radix-4 units comprising dual add-compare-select (ACS) units. By utilising a spare cycle in the deep ACS pipeline, each ACS unit processes two output state metrics, thus halving the number of ACS units required. This implementation uses 44% of the available FPGA resources and meets timing at 204.5 MHz, exceeding the throughput requirement of 54 Mbit/s.