Proposed modifications of an offset quadri-phase-shift keying (offset- QPSK) transmitter and receiver would reduce the amount of signal processing that must be done in the receiver to resolve the QPSK fourfold phase ambiguity. Resolution of the phase ambiguity is necessary in order to synchronize, with the received carrier signal, the signal generated by a local oscillator in a carrier-tracking loop in the receiver. Without resolution of the fourfold phase ambiguity, the loop could lock to any of four possible phase points, only one of which has the proper phase relationship with the carrier.

Figure 1. This Carrier-Tracking Loop of an offset-QPSK receiver differs from a maximum a posteriori (MAP) carrier-tracking loop of a non-offset-QPSK receiver by incorporating a unit that imposes a delay of one symbol period (T).
The proposal applies, more specifically, to an offset-QPSK receiver that contains a carrier-tracking loop like that shown in Figure 1. This carrier tracking loop does not resolve or reduce the phase ambiguity. A carrier tracking loop of a different design optimized for the reception of offset QPSK could reduce the phase ambiguity from fourfold to twofold, but would be more complex. Alternatively, one could resolve the fourfold phase ambiguity by use of differential coding in the transmitter, at a cost of reduced power efficiency. The proposed modifications would make it possible to reduce the fourfold phase ambiguity to twofold, with no loss in power efficiency and only relatively simple additional signal processing steps in the transmitter and receiver. The twofold phase ambiguity would then be resolved by use of a unique synchronization word, as is commonly done in binary phase-shift keying (BPSK).

Figure 2. Inversions of Bits in cycles of four bits (d0 d1 d2 dsub>3) would cause all the output bits to be either inverted or noninverted together, depending on the phase difference (¦) between the received carrier and the local-oscillator signal in the carrier-tracking loop. The loop could lock at any of four points (¦ = 0, À/2, À, or 3À/2 radians).
Although the mathematical and signal- processing principles underlying the modifications are too complex to explain in detail here, the modifications themselves would be relatively simple and are best described with the help of simple block diagrams (see Figure 2). In the transmitter, one would add a unit that would periodically invert bits going into the QPSK modulator; in the receiver, one would add a unit that would effect different but corresponding inversions of bits coming out of the QPSK demodulator. The net effect of all the inversions would be that depending on which lock point the carrier- tracking loop had selected, all the output bits would be either inverted or non-inverted together; hence, the ambiguity would be reduced from fourfold to twofold, as desired.

This work was done by Jeff Berner and Peter Kinman of Caltech for NASA's Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at under the Electronics/Computers category.


NASA Tech Briefs Magazine

This article first appeared in the May, 2004 issue of NASA Tech Briefs Magazine.

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