In a frequency division duplex system, a transmitter adaptive antenna array
can potentially improve the performance of a wireless downlink, but becaus
e the uplink and downlink channels have different wavelengths, and, therefo
re, different responses, direct downlink adaptation based on channel estima
tes of the uplink is generally not feasible, Instead, there has been some r
ecent interest in adaptations that require only the second-order statistics
of the uplink and downlink to be similar. These algorithms derive adaptive
weights from the covariance of the received signal to apply to a downlink
transmitter array. We make two contributions to this area. First, we introd
uce an array configuration employing M+1 elements with log-periodic sparing
that comprises two overlapping subarrays, each with M elements, that are s
caled versions of each other, with the scale factor equal to the ratio of t
he uplink wavelength to the downlink wavelength. This array has identical b
eampatterns at the two wavelengths, thus helping to fulfill the requirement
that the uplink and downlink second-order statistics be the same. Second,
we demonstrate that obtaining a good estimate of the uplink covariance matr
ix is not essential for the successful operation of the adaptive scheme. Ev
en when the mobile is at rest and the uplink information comprises only a s
ingle snapshot from the receiver array, an adaptive scheme can improve the
SNR.