Systems and methods for measuring wireless uplink signal quality of a P25 H-CPM uplink waveform are provided. In particular, such systems and methods can include calculating an SINR measurement and/or an FBER measurement for the P25 H-CPM uplink waveform to determine whether P25 user equipment has been successfully deployed.

A low power receiver having a feedforward equalization, FFE, based continuous time linear equalizer, CTLE. The FFE CTLE comprises: an input for receiving an input signal; a main first path operably coupled to the input and comprising a source-follower transistor arranged to apply a scaling factor to the received input signal; a second path operably coupled to the input and comprising a delay arranged to apply a delay to the received input signal and a common source transistor common source transistor arranged to apply a scaling factor to the received delayed input signal, wherein the source-follower transistor and the common source, CS, transistor are connected as a single SF-CS stage whose output is arranged to subtract the output of the common source transistor from an output of the source-follower transistor.

A low power receiver having a feedforward equalization, FFE, based continuous time linear equalizer, CTLE. The FFE CTLE comprises: an input for receiving an input signal; a main first path operably coupled to the input and comprising a source-follower transistor arranged to apply a scaling factor to the received input signal; a second path operably coupled to the input and comprising a delay arranged to apply a delay to the received input signal and a common source transistor common source transistor arranged to apply a scaling factor to the received delayed input signal, wherein the source-follower transistor and the common source, CS, transistor are connected as a single SF-CS stage whose output is arranged to subtract the output of the common source transistor from an output of the source-follower transistor.

To reflect advantages of continuous phase modulation (CPM), the invention provides a low complexity transmitter and receiver to transmit and receive CPM signals and addresses a significant reduction in the CPM demodulator complexity, and is especially well-suited for large values of L, e.g., L3. The invention utilizes a linear filter front end as an integral part of the CPM demodulation process to reduce the ISI inherent in CPM transmit signal, and minimizes the influence of L in the reception process. To that end, the invention renders the complexity of a CPM demodulator non-exponentially dependent on L, and L only has a weak impact on the number of coefficients of the linear front end filters. Moreover, the invention provides a simple way of forming CPM signals for a digital communication transmitter using parallel Time Invariant Phase Encoders, which simplifies the production of CPM waveforms on software or hardware.

To reflect advantages of continuous phase modulation (CPM), the invention provides a low complexity transmitter and receiver to transmit and receive CPM signals. CPM is a spectrum-efficient digital modulation scheme, which enables constant or quasi-constant envelope communication, leading to significant battery savings on top of bandwidth and energy savings. Despite the desirable properties of CPM, the complexity of an optimum CPM demodulator can be very high, due to the inherent memory nature of CPM. Specifically, the number of states in an optimum CPM demodulator is exponentially dependent on the length of the frequency pulse, L.

The present invention addresses a significant reduction in the CPM demodulator complexity, and is especially well-suited for large values of L, e.g., L3. The invention utilizes a linear filter front end as an integral part of the CPM demodulation process so as to reduce the ISI inherent in CPM transmit signal, and minimizes the influence of L in the reception process. To that end, the invention renders the complexity of a CPM demodulator non-exponentially dependent on L, and L only has a weak impact on the number of coefficients of the linear front end filters. Moreover, the invention provides a simple way of forming CPM signals for a digital communication transmitter using parallel Time Invariant Phase Encoders, which simplifies the production of CPM waveforms on software or hardware.

A continuous phase modulation method comprises the following steps: receiving a sequence of digital data symbols a(n) to be emitted; transforming the sequence of symbols a(n) to be emitted into a transformed sequence of symbols b(n), each symbol b(n) of which is equal to the sum of a symbol a(n) to be emitted and of a corrective factor equal to a transformation Tf applied to a plurality of differences (a(n)-a(n1)) between two consecutive symbols to be emitted, the transformation Tf applied being a combination c of at least two differences between two consecutive symbols of the sequence to be emitted, transformed by the application of a non-linear function f; filtering the sequence of transformed symbols b(n) with a shaping filter and modulating the filtered sequence with a phase modulator; said transformation Tf being defined so as to minimize interference between modulated symbols filtered by a receiving filter.

A blind equalizer apparatus includes a decision-directed (DD) least mean squares (LMS) blind equalizer. A blind equalizer apparatus includes: a DD LMS blind equalizer, wherein: the blind equalizer uses a finite impulse response filter with tap weights that are adaptively updated using a filter tap update algorithm, wherein blind equalization of one of an in-phase (I) channel and a quadrature (Q) channel is carried out by maximizing the Euclidean distance of binary modulated waveforms, wherein the blind equalizer averages a block to compute an independent phase estimate for a block, wherein the blind equalizer computes an error variable for a block from the phase estimate for the block, wherein the blind equalizer uses the phase estimate and alternating I/Q one dimensional/binary slicing to make a hard decision, and wherein the blind equalizer uses the hard decision to derive an error variable that is used to update the filter tap weights.