A base station including an IQ -modulator pre-distorter, wherein the IQ- modulator pre-distorter includes: an iteratively updated digital filter for filtering one of the branches of an IQ -signal to compensate for IQ -modulator generated amplitude errors; an iteratively updated digital filter, cross-connected from one of the branches to the other branch, for filtering one of the components of an IQ -signal to compensate for IQ -modulator generated inter-modulation between the branches; and iteratively updated offsets compensators to compensate for IQ- modulator generated offset errors, wherein the iteratively updated filters are configured to be updated in accordance with a Least Mean Squares algorithm, { g I q, i + 1 b = g I q, i b + μ g ⁢ I b ⋅ 1 N ∑ z k - d q ∈ M b N Re x k - d q ⋅ Re x k - Re y k g Q q, i + 1 b = g Q q, i b + μ g ⁢ Q b ⋅ 1 N ∑ z k - d q ∈ M b N Im x k - d q ⋅ Im x k - Im y k q = 0,..., M { c ⁢ I Q q, i + 1 b = c ⁢ I Q q, i b + μ c ⁢ I ⁢ Q b ⋅ 1 N ∑ z k - d q ∈ M b N Im x k - d q ⋅ Re x k - Re y k c Q ⁢ I q, i + 1 b = c Q ⁢ I q, i b + μ c ⁢ Q ⁢ I b ⋅ 1 N ∑ z k - d q ∈ M b N Re x k - d q ⋅ Im x k - Im y k q = 0,..., K { d ⁢ c ⁢ I i + 1 = d ⁢ c ⁢ I i + μ d ⁢ c ⋅ 1 N ∑ k = 1 N Re x k - Re y k d ⁢ c ⁢ Q i + 1 = d ⁢ c ⁢ Q i + μ d ⁢ c ⋅ 1 N ∑ k = 1 N Im x k - Im y k, wherein a) represents filter taps gIQ, gQq for filtering the I - and Q-components to compensate for amplitude errors generated by the IQ- modulator without regard to an inter-modulation error; wherein inter-modulation is handled by filter taps cIQ q, cQI q in b), and offset errors are handled by dcI, dcQ in c); wherein x k and y k represent an IQ -modulator pre-distorter input signal and a down-converted IQ -modulator output signal, respectively, and wherein q is an index representing a delay d(q), various μ's are loop constants, b identifies a filter tap bin, i is an iteration index, N is a number of input samples of a reference signal x in a sample batch that have an amplitude that falls within an interval M b around a center amplitude of filter tap bin b, and wherein M, K represent a number of filter taps +1; characterized in that the IQ-modulator pre-distorter is integrated with a power amplifier pre-distorter in a same control loop and in that the base station further comprises a trainer configured to update said iteratively updated filters and offset compensators according to the following Least Mean Squares algorithm equations: wherein the output signal z from the power amplifier pre-distorter, instead of input signal x, is used to determine whether a sample is included in interval M b and wherein said input signal x is still used in the actual summation. an iteratively updated digital filter for filtering one of the branches of an IQ -signal to compensate for IQ -modulator generated amplitude errors; an iteratively updated digital filter, cross-connected from one of the branches to the other branch, for filtering one of the components of an IQ -signal to compensate for IQ -modulator generated inter-modulation between the branches; and iteratively updated offsets compensators to compensate for IQ- modulator generated offset errors, wherein the iteratively updated filters are configured to be updated in accordance with a Least Mean Squares algorithm, { g I q, i + 1 b = g I q, i b + μ g ⁢ I b ⋅ 1 N ∑ z k - d q ∈ M b N Re x k - d q ⋅ Re x k - Re y k g Q q, i + 1 b = g Q q, i b + μ g ⁢ Q b ⋅ 1 N ∑ z k - d q ∈ M b N Im x k - d q ⋅ Im x k - Im y k q = 0,..., M { c ⁢ I Q q, i + 1 b = c ⁢ I Q q, i b + μ c ⁢ I ⁢ Q b ⋅ 1 N ∑ z k - d q ∈ M b N Im x k - d q ⋅ Re x k - Re y k c Q ⁢ I q, i + 1 b = c Q ⁢ I q, i b + μ c ⁢ Q ⁢ I b ⋅ 1 N ∑ z k - d q ∈ M b N Re x k - d q ⋅ Im x k - Im y k q = 0,..., K { d ⁢ c ⁢ I i + 1 = d ⁢ c ⁢ I i + μ d ⁢ c ⋅ 1 N ∑ k = 1 N Re x k - Re y k d ⁢ c ⁢ Q i + 1 = d ⁢ c ⁢ Q i + μ d ⁢ c ⋅ 1 N ∑ k = 1 N Im x k - Im y k,