Convolutionally encodedM-ary quadrature amplitude modulation (M-QAM) systems operated over multidimensional channels, for example dual-polarized radio systems, are considered in this paper. We have derived upper bounds on the average bit-error probability for 4QAM (QPSK) with conventional convolutional coding by means of a truncated union bound technique and averaging over the cross-polarization interference by means of the method of moments. By modifying this technique, we have found approximate upper bounds on the average biterror probability for bandwidth efficient trellis-coded QAM systems. This is an extension of our previous work  that was based on one dominating error event probability as a performance measure. Our evaluations seem to indicate that bandwidth efficient trellis-codedMQAM schemes offer much larger coding gains in an interference environment, e.g., a cross-coupled interference channel, than in a Gaussian noise channel. In general, our findings point out that optimum codes for a Gaussian channel are not optimum when applied in an interference environment. We note that a rate 1/2 convolutional code for example, with a code memory greater than two, if applied to two of the bits in each signal point representation, can be utilized with a simple decoder to greatly improve the performance of a QAM signal in interference. Also, we have introduced a new concept referred to as dualchannel polarization hopping in this paper which can improve the system performance significantly for systems with nonsymmetrical interference.