It has been shown that the rank and the determinant of the distance matrices are the design criteria for spacetime trellis codes over quasi-static Rayleigh fading channels. Recently, a new design criterion that maximires only the trace has been proposed for systems with a large product of the numbers of transmit and receive antennas. This criterion is usefir[ and yields superior codes when the product of the numbers of receive and transmit antennas is at least 4. In this paper, new QPSK space-time trellis codes for 3 and 4 transmit antennas with up to 1024 states will he presented. Our 64-state codes for 3 and 4 transmit antennas present a larger trace andprovide a better errorperjbimance than previously published codes with the same number of states. Ifa smaller error probability is required, afirrther improvement can he achieved by increasing the number of states at the expense of additional complexi&.

Absiract -It has been shown that the design criteria for space-time trellis codes over quasi-static Rayleigh fading channels are the rank criterion and the determinant criterion. Recently, a new design criterion that maximizes only the trace of the distance matrices has been proposed for systems with a large product of the numbers of transmit and receive antennas. These codes are superior when the number of receive antennas is 4 or more. In this paper, the two design criteria are combined so that the codes are good or robust whatever the number of receive antennas is. New QPSK codes that optimize the tracddeterminant pair and achieve the full rank are presented. These codes outperform other previously known codes whether there are two receive antennas or more.

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Space-time trellis codes can significantly improve the error performance or the data rate of wireless communications systems with multiple transmit antennas. These codes are usually generated using a generator matrix with 2 columns and modulo 4 operations for QPSK modulation with two transmit antennas. They can also be implemented as Z 4 convolutional codes. Another way of representing them is to use a conventional binary convolutional code of rate 2/4. Such a representation is more flexible and allows an easy implementation of space-time encoders and decoders with different modulation schemes and numbers of transmit antennas. Only the rate of the convolutional code needs to be changed using the puncturing technique to accommodate these different schemes. Simulations results have shown that the new codes can achieve an error performance very close to that of the best usual space-time codes.

Space-time codes are usually generated using a generator matrix with 2 columns and mod 4 operations for QPSK modulation with two transmit antennas. A Z4 convolutional code has also been used to represent these space-time codes.Another way of representing them is to use a conventional binary convolutional code of rate 214. The space-time code obtained in this way is in general diferent from the usual space-time codes. Simulations results have shown that the new codes can achieve an error performance very close to that of the best usual space-time codes and even outperform them.Furthermore, such a representation is moreflexible and allows an easy implementation of space-time encoders and decoders for different numbers oftransmit antennas. Only the rate ofthe convolutional code needs to be changed using the puncturing technique to accommodate these diferent schemes.