The aim of this study is to design a receiver architecture which can jointly estimate the frequency selective (FS) channel impulse response (CIR), frequency independent (FI)/FS Receiver (Rx) Inphase Quadrature (IQ) imbalance, carrier frequency offset (CFO) and direct current offset using long training sequences. All of these problems are typical for low-cost radio-frequency front-ends. This study proposes a set of two scalable solutions to estimate CFO, whereas FS CIR and FI/FS Rx IQ imbalance are estimated in tandem through a closed-form expression. A low-complexity single stage equaliser is also proposed which can mitigate the effects of CFO and equalise the CIR along with FI/FS IQ imbalance in a single step. The proposed solutions are also extended to multiple-input-multiple-output-orthogonal frequency division multiplexing systems. The simulation results illustrate that solutions proposed in this study provide an excellent performance/complexity trade-off.