Phase and amplitude modulation of single or multiple pulses and/or dual polarizations are used in a digital communications system which transmits multidimensional codes. Four dimensional code transmission is specifically disclosed, although the scheme may be extended to eight-dimensional and even 16-dimensional code transmission. The four-dimensional codes are constructed by mapping a digital word into two two-dimensional plane as two sets of x and y coordinates. Signals proportional to these x and y coordinates are used to modulate a transmitted pulse or pulses. When a single pulse is used to transmit the four-dimensional code, polarization modulation is used. A signal proportional to the square root of the sum of the squares of the coordinates assigned to both the horizontal and vertical polarizations is used to control the total RF amplitude of the pulse. A signal proportional to the ratio of the square roots of the sum of the squares to each set of coordinates is used to control the ratio of horizontal to vertical polarization. Finally, the phases of the two polarizations are controlled by signals proportional to the ratios of the coordinates in the respective sets of coordinates. When two pulses are used to transmit the four-dimensional code, quadrature amplitude modulation is used. Signals proportional to the coordinates of each set are used to quadrature amplitude modulate a respective one of the two pulses. Encoding and decoding between digital and the four-dimensional code is accomplished with read only memories.
A method and arrangement for decoding n-dimensional codes in which the alphabet of codewords is selected from the points of a lattice comprised of a union of cosets of the lattice D.sub.n, the latter being comprised of those n-dimensional integer-valued-coordinate points which have a predetermined parity.
An n-dimensional channel code is used in a data transmission system. The alphabet of codewords (data symbols) comprises a subset of points of a selected coset of a selected lattice. The alphabet includes at least one point of the coset whose norm (signal energy) is greater than at least one other point of the coset which is excluded from the alphabet.
A transmission/reception module suitable for use in electronically phase-controlled antennas for a synthetic aperture radar includes a circulator provided for each individual radiator element terminal to achieve vertical and horizontal polarization. A low-noise amplifier is connected to the circulator in the reception path. A high-power amplifier is connected to the circulator in the transmission path. The two separate polarization reception channels each include a low-noise amplifier. The two separate polarization transmission channels each include a high-power amplifier. The reception channels and transmission channels are respectively connected to a polarization change-over. Switching arms of the polarization change-over are then connected to either the reception contact or the transmission contact of the transmission/reception switch.
Carrier recovery arrangement in a receiving system for digital data which are transmitted by sixteen-state amplitude and phase modulation (16 QAM), the arrangement having, successively six parallel paths (V.sub.1 -V.sub.6) each including the series arrangement of a multiplying circuit (M.sub.i) and a low-pass filter (F.sub.i); a selection circuit for selecting one of the three pairs of filter output signals thus obtained; a phase control circuit having a Costas signal processing circuit receiving the selected pair of signals and producing a signal representative of the phase error of the received signal, a filter and a voltage-controlled oscillator; and a phase-shifting circuit receiving the output signal of the oscillator in order to couple this output signal to respective second inputs of the multiplying circuits (M.sub.1)-(M.sub.6), this signal coupling being effected with a phase shift zero for (M.sub.1), .theta. for (M.sub.3), 2.theta. for (M.sub.5), and with a phase shift .pi./2 for (M.sub.2), .theta.+.pi./2 for (M.sub.4), and 2.theta.+.pi./2 for (M.sub.6), where .theta. is equal to tan.sup.-1 (1/2).
A stream of data to be transmitted is arranged in n streams of 2-bit words. Successive pairs of bits in each of those streams are differentially encoded by generating for each different combination of their values a predetermined one of the differentially encoded bit pairs (i,q), (q,i), (i,q) and (q,i) associated with that combination, where (i,q) is the previously generated differentially encoded bit pair. Words each comprised of the first (second) bit of a respective bit pair in each of the resulting n differentially encoded streams are then provided as n-bit words in a first (second) input stream for a two-dimensional channel coder. In the receiver, the channel decoder provides first and second streams of n-bit words. The bits of the latter are then arranged such that each word in the first (second) stream of channel-decoded words becomes the first (second) bit of a differentially encoded bit pair in a respective one of n differentially encoded bit pair streams. The pairs of bits in each of the n differentially encoded streams are then differentially decoded to recover the original data.
