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This paper presents the synthesis and design of a wide-band radio communication system capable of providing trunk circuits 6000 miles in length with a capacity of 72 voice channels. A hypothetical reference circuit is used which corresponds to that recommended by the CCIR for radio relay systems. From the reference system, performance requirements for radio relay systems using line-of-sight and tropospheric propagation modes are developed. The requirements are reduced to numerical quantities which are directly related to the parameters required in the system design. The basic qualities of the system which are used for performance criteria are the signal-to-noise ratio of a voice channel and the minimum margin above system threshold. The noise in any link of the system comes from a number of sources and the noise accumulates as links are added in tandem; therefore to insure that minimum signal-to-noise ratios are obtained over circuits as long as 6000 miles, the total noise objectives must be carefully apportioned among links and among sources within the links. The statistical properties of certain of the noise sources are accounted for by statistical accumulation and a complete specification of the individual path performance requirements for both line-of-sight paths and tropospheric scatter paths is developed. The individual paths are also analyzed from the standpoint of reliability or digital error rate and the resulting criteria are used in setting the necessary system gain required to achieve the noise performance simultaneously with the reliability.