Software-defined radio (SDR) is an advanced wireless transmission paradigm that supports all the consumer wireless protocols such as 2G, 3G, Long-Term Evolution, Wi-Fi (2.4 and 5 GHz), Bluetooth, and Zigbee, by software rather than hardware. A typical frequency band of operation is in the range of 0.5–6 GHz. The challenge to bring an SDR system on portable devices is the availability of ultra-wide-band compact amplifiers with a high gain over a wide frequency band. A novel hybrid silicon bipolar junction transistor (BJT) and an enhancement-mode pseudomorphic-high-electron-mobility-transistor (E- pHEMT) matrix amplifier with two rows and four columns (2 × 4) of transistors are designed, realised, and tested demonstrating a 0.65–5.8 GHz frequency band to satisfy the SDR specifications. The novel optimum filter-matching technique is applied to optimise the performance and overcome the limit of the hybrid approach. The proposed matrix amplifier exhibits an average gain of 37.5 dB and an average output power of 18 dBm across the 0.65–5.8 GHz band with only 3 V supply voltage. The gain is the highest in the state of the art for the frequency range. A bandwidth of 5.15 GHz, 20.3 dBm above the 1-dB compression point at 1.35 GHz, 10–16% power added efficiency, and 1.2 W DC power consumptions are obtained.